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SUMMARY:Strongly Correlated Quantum Materials and High-Temperature Superconductors Series
DESCRIPTION:In the 2020-2021 academic year\, the CMSA will be hosting a lecture series on Strongly Correlated Materials and High Tc Superconductor. All talks will take place from 10:30-12:00pm ET virtually on Zoom. \nCuprate high-temperature superconductors are a classic quantum material system to demonstrate the beauty of “Emergence and Entanglement” in the quantum phases of matter. Merely by adding more holes into an antiferromagnetic insulator\, several fascinating phases emerge\, including a d-wave superconductor\, a pseudo-gap metal\, and strange metal. After intensive studies from experimental\, theoretical\, and numerical communities for more than three decades\, remarkable progress has been made\, but basic questions remain: \n\nWhat is the origin of the superconductivity? What are the relative contributions of electron-phonon coupling\, spin fluctuations\, or resonating-valence-bonds?\nHow do we explain the pseudo-gap and the Fermi arc in the underdoped region above the critical temperature? Are they from some symmetry breaking order parameters\, or do we need an unconventional picture involving fractionalization?\nIs the strange metal at optimal doping associated with a quantum critical point? And if so\, what is the driving force of this phase transition?\n\nThe cuprate quantum materials have been a major source for many new concepts in modern condensed matter physics\, such as quantum spin liquids\, topological order\, and non-Fermi liquids. In the coming years\, it is clear that the study of the cuprates will continually motivate new concepts and development of new techniques. In this seminar series\, we hope to accelerate this process by bringing together deeper conversations between experimental\, theoretical\, and numerical experts with different backgrounds and perspectives. \nThe Strongly Correlated Quantum Materials and High-Temperature Superconductors series is a part of the Quantum Matter in Mathematics and Physics seminar. \nSeminar organizers: Juven Wang (Harvard CMSA) and Yahui Zhang (Harvard). \nScientific program advisors: Professor Subir Sachdev (Harvard)\, Professor Patrick Lee (MIT). \nIn order to learn how to attend this series\, please fill out this form. \nFor more information\, please contact Juven Wang (jw@cmsa.fas.harvard.edu) and Yahui Zhang (yahui_zhang@g.harvard.edu) \nSpring 2022\nApril 20\, 2022 | 11:30 – 1:00 pm ET \nHarold Y. Hwang (Stanford University & SLAC National Accelerator Laboratory) \nTitle: Superconductivity in infinite-layer nickelates \nAbstract: Since its discovery\, unconventional superconductivity in cuprates has motivated the search for materials with analogous electronic or atomic structure. We have used soft chemistry approaches to synthesize superconducting infinite layer nickelates from their perovskite precursor phase. We will present the synthesis and transport properties of the nickelates\, observation of a doping-dependent superconducting dome\, and our current understanding of their electronic and magnetic structure. \n\nFebruary 3\, 2022 | 11:30 – 1:00 pm ET \nLu Li (U Michigan) \nTitle: Quantum Oscillations of Electrical Resistivity in an Insulator \nAbstract: In metals\, orbital motions of conduction electrons are quantized in magnetic fields\, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators\, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12\, despite much larger than that of usual metals\, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems. \n2020 – 2021\nSeptember 2\, 2020 | 10:30am ET\n\n\n\n\n\n\n\nSubir Sachdev (Harvard) \nTitle: Metal-to-metal quantum phase transitions not described by symmetry-breaking orders \nAbstract: Numerous experiments have explored the phases of the cuprates with increasing doping density p from the antiferromagnetic insulator. There is now strong evidence that the small p region is a novel phase of matter\, often called the pseudogap metal\, separated from conventional Fermi liquid at larger p by a quantum phase transition. Symmetry-breaking orders play a spectator role\, at best\, at this quantum phase transition. I will describe trial wavefunctions across this metal-metal transition employing hidden layers of ancilla qubits (proposed by Ya-Hui Zhang). Quantum fluctuations are described by a gauge theory  of ghost fermions that carry neither spin nor charge. I will also\ndescribe a separate approach to this transition in a t-J model with random exchange interactions in the limit of large dimensions. This approach leads to a partly solvable SYK-like critical theory of holons and spinons\, and a linear in temperature resistivity from time reparameterization fluctuations. Near criticality\, both approaches have in common emergent fractionalized excitations\, and a significantly larger entropy than naively expected. \nVideo\n\n\n\n\nSeptember 23\, 2020 | 10:30am ET\n\n\n\n\n\n\n\nSubir Sachdev (Harvard) \nTitle: Metal-to-metal quantum phase transitions not described by symmetry-breaking orders II \nAbstract: In this second talk\, I will focus on (nearly) solvable models of metal-metal transition in random systems. The t-J model with random and all-to-all hopping and exchange can be mapped onto a quantum impurity model coupled self-consistently to an environment (the mapping also applies to a t-J model in a large dimension lattice\,  with random nearest-neighbor exchange). Such models will be argued to exhibit metal-metal quantum phase transitions in the universality class of the SYK model\, accompanied by a linear-in-T resistivity from time reparameterization  fluctuations. I will also present the results of exact diagonalization of random t-J clusters\, obtained recently with Henry Shackleton\, Alexander Wietek\, and Antoine Georges. \nVideo\n\n\n\n\nSeptember 24\, 2020 | 12:00pm ET\n\n\n\n\n\n\n\nInna Vishik (University of California\, Davis)\n\nTitle: Universality vs materials-dependence in cuprates: ARPES studies of the model cuprate Hg1201Abstract: The cuprate superconductors exhibit the highest ambient-pressure superconducting transition temperatures (T c )\, and after more than three decades of extraordinary research activity\, continue to pose formidable scientific challenges. A major experimental obstacle has been to distinguish universal phenomena from materials- or technique-dependent ones. Angle-resolved photoemission spectroscopy (ARPES) measures momentum-dependent single-particle electronic excitations and has been invaluable in the endeavor to determine the anisotropic momentum-space properties of the cuprates. HgBa 2 CuO 4+d (Hg1201) is a single-layer cuprate with a particularly high optimal T c and a simple crystal structure; yet there exists little information from ARPES about the electronic properties of this model system. I will present recent ARPES studies of doping-\, temperature-\, and momentum-dependent systematics of near-nodal dispersion anomalies in Hg1201. The data reveal a hierarchy of three distinct energy scales which establish several universal phenomena\, both in terms of connecting multiple experimental techniques for a single material\, and in terms of connecting comparable spectral features in multiple structurally similar cuprates.Video\n\n\n\n\nOctober 15\, 2020 | 10:30am ET\n\n\n\n\n\n\n\nLouis Taillefer (Université de Sherbrooke) \nTitle: New signatures of the pseudogap phase of cuprate superconductors \nAbstract: The pseudogap phase of cuprate superconductors is arguably the most enigmatic phase of quantum matter. We aim to shed new light on this phase by investigating the non- superconducting ground state of several cuprate materials at low temperature across a wide doping range\, suppressing superconductivity with a magnetic field. Hall effect measurements across the pseudogap critical doping p* reveal a sharp drop in carrier density n from n = 1 + p above p* to n = p below p\, signaling a major transformation of the Fermi surface. Angle-dependent magneto-resistance (ADMR) directly reveals a change in Fermi surface topology across p. From specific heat measurements\, we observe the classic thermodynamic signatures of quantum criticality: the electronic specific heat C el shows a sharp peak at p\, where it varies in temperature as C el ~ – T logT. At p and just above\, the electrical resistivity is linear in T at low T\, with an inelastic scattering rate that obeys the Planckian limit. Finally\, the pseudogap phase is found to have a large negative thermal Hall conductivity\, which extends to zero doping. We show that the pseudogap phase makes phonons become chiral. Understanding the mechanisms responsible for these various new signatures will help elucidate the nature of the pseudogap phase. \nVideo\n\n\n\n\nOctober 28\, 2020 | 10:30am ET\n\n\n\n\n\n\n\nPatrick Lee (MIT) \nTitle: The not-so-normal normal state of underdoped Cuprate \nAbstract: The underdoped Cuprate exhibits a rich variety of unusual properties that have been exposed after years of experimental investigations. They include a pseudo-gap near the anti-nodal points and “Fermi arcs” of gapless excitations\, together with a variety of order such as charge order\, nematicity and possibly loop currents and time reversal and inversion breaking. I shall argue that by making a single assumption of strong pair fluctuations at finite momentum (Pair density wave)\, a unified description of this phenomenology is possible. As an example\, I will focus on a description of the ground state that emerges when superconductivity is suppressed by a magnetic field which supports small electron pockets. [Dai\, Senthil\, Lee\, Phys Rev B101\, 064502 (2020)] There is some support for the pair density wave hypothesis from STM data that found charge order at double the usual wave-vector in the vicinity of vortices\, as well as evidence for a fragile form of superconductivity persisting to fields much above Hc2. I shall suggest a more direct experimental probe of the proposed fluctuating pair density wave. \nVideo\n\n\n\n\nNovember 6\, 2020 |12:30pm ET\n\n\n\n\n\n\n\nZhi-Xun Shen (Stanford University) \nTitle: Essential Ingredients for Superconductivity in Cupper Oxide Superconductors \nAbstract: High‐temperature superconductivity in cupper oxides\, with critical temperature well above what wasanticipated by the BCS theory\, remains a major unsolved physics problem. The problem is fascinating because it is simultaneously simple ‐ being a single band and 1⁄2 spin system\, yet extremely rich ‐ boasting d‐wave superconductivity\, pseudogap\, spin and charge orders\, and strange metal phenomenology. For this reason\, cuprates emerge as the most important model system for correlated electrons – stimulating conversations on the physics of Hubbard model\, quantum critical point\, Planckian metal and beyond.\nCentral to this debate is whether the Hubbard model\, which is the natural starting point for the undoped\nmagnetic insulator\, contains the essential ingredients for key physics in cuprates. In this talk\, I will discuss our photoemission evidence for a multifaceted answer to this question [1‐3]. First\, we show results that naturally points to the importance of Coulomb and magnetic interactions\, including d‐wave superconducting gap structure [4]\, exchange energy (J) control of bandwidth in single‐hole dynamics [5]. Second\, we evidence effects beyond the Hubbard model\, including band dispersion anomalies at known phonon frequencies [6\, 7]\, polaronic spectral lineshape and the emergence of quasiparticle with doping [8]. Third\, we show properties likely of hybrid electronic and phononic origin\, including the pseudogap [9‐11]\, and the almost vertical phase boundary near the critical 19% doping [12]. Fourth\, we show examples of small q phononic coupling that cooperates with d‐wave superconductivity [13‐15]. Finally\, we discuss recent experimental advance in synthesizing and investigating doped one‐dimensional (1D) cuprates [16]. As theoretical calculations of the 1D Hubbard model are reliable\, a robust comparison can be carried out. The experiment reveals a near‐neighbor attractive interaction that is an order of magnitude larger than the attraction generated by spin‐superexchange in the Hubbard model. Addition of such an attractive term\, likely of phononic origin\, into the Hubbard model with canonical parameters provides a quantitative explanation for all important experimental observable: spinon and holon dispersions\, and holon‐ holon attraction. Given the structural similarity of the materials\, It is likely that an extended two‐dimensional\n(2D) Hubbard model with such an attractive term\, will connect the dots of the above four classes of\nexperimental observables and provide a holistic understanding of cuprates\, including the elusive d‐wave superconductivity in 2D Hubbard model. \n[1] A. Damascelli\, Z. Hussain\, and Z.‐X. Shen\, Review of Modern Physics\, 75\, 473 (2003)\n[2] M. Hashimoto et al.\, Nature Physics 10\, 483 (2014)\n[3] JA Sobota\, Y He\, ZX Shen ‐ arXiv preprint arXiv:2008.02378\, 2020; submitted to Rev. of Mod. Phys.\n[4] Z.‐X. Shen et al.\, Phys. Rev. Lett. 70\, 1553 (1993)\n[5] B.O. Wells et al.\, Phys. Rev. Lett. 74\, 964 (1995)\n[6] A. Lanzara et al.\, Nature 412\, 510 (2001)\n[7] T. Cuk et al.\, Phys. Rev. Lett.\, 93\, 117003 (2004)\n[8] K.M. Shen et al.\, Phys. Rev. Lett.\, 93\, 267002 (2004)\n[9] D.M. King et al.\, J. of Phys. & Chem of Solids 56\, 1865 (1995)\n[10] D.S. Marshall et al.\, Phy. Rev. Lett. 76\, 484 (1996)\n[11] A.G. Loeser et al.\, Science 273\, 325 (1996)\n[12] S. Chen et al.\, Science\, 366\, 6469 (2019)\n[13] T.P. Devereaux\, T. Cuk\, Z.X. Shen\, N. Nagaosa\, Phys. Rev. Lett.\, 93\, 117004 (2004)\n[14] S. Johnston et al.\, Phys. Rev. Lett. 108\, 166404 (2012)\n[15] Yu He et al.\, Science\, 362\, 62 (Oct. 2018)\n[16] Z. Chen\, Y. Wang et al.\, preprint\, 2020 \nVideo\n\n\n\n\nNovember 12\, 2020 |10:30am ET\n\n\n\n\n\n\n\nChandra Varma (Visting Professor\, University of California\, Berkeley.\nEmeritus Distinguished Professor\, University of California\, Riverside.)Title: Loop-Current Order and Quantum-Criticality in CupratesThis talk is organized as follows:\n1. Physical Principles leading to Loop-current order and quantum criticality as the central feature in the physics of Cuprates.\n2. Summary of the essentially exact solution of the dissipative xy model for Loop-current fluctuations.\n3. Quantitative comparison of theory for the quantum-criticality with a variety of experiments.\n4. Topological decoration of loop-current order to understand ”Fermi-arcs” and small Fermi-surface magneto-oscillations.Time permitting\,\n(i) Quantitative theory and experiment for fluctuations leading to d-wave superconductivity.\n(ii) Extensions to understand AFM quantum-criticality in heavy-fermions and Fe-based superconductors.\n(iii) Problems.Video\n\n\n\n\nNovember 18\, 2020 |10:30am ET\n\n\n\n\n\n\n\nAntoine Georges (Collège de France\, Paris and Flatiron Institute\, New York) \nTitle: Superconductivity\, Stripes\, Antiferromagnetism and the Pseudogap: What Do We Know Today about the 2D Hubbard model? \nAbstract: Simplified as it is\, the Hubbard model embodies much of the complexity of the `strong correlation problem’ and has established itself as a paradigmatic model in the field. In this talk\, I will argue that several key aspects of its physics in two dimensions can now be established beyond doubt\, thanks to the development of controlled and accurate computational methods. These methods implement different and complementary points of view on the quantum many-body problem. Along with pushing forward each method\, the community has recently embarked into a major effort to combine and critically compare these approaches\, and in several instances a consistent picture of the physics has emerged as a result. I will review in this perspective our current understanding of the emergence of a pseudogap in both the weak and strong coupling regimes. I will present recent progress in understanding how the pseudogap phase may evolve into a stripe-dominated regime at low temperature\, and briefly address the delicate question of the competition between stripes and superconductivity. I will also emphasize outstanding questions which are still open\, such as the possibility of a Fermi surface reconstruction without symmetry breaking. Whenever possible\, connections to the physics of cuprate superconductors will be made. If time permits\, I may also address the question of Planckian transport and bad metallic transport at high temperature. \nVideo\n\n\n\n\nNovember 19\, 2020 |10:30am ET\n\n\n\n\n\n\n\nEduardo Fradkin (University of Illinois at Urbana-Champaign) \nTitle: Pair Density Waves and Intertwined Orders in High Tc Superconductors\n\nAbstract: I will argue that the orders that are present in high temperature superconductors naturally arise with the same strength and are better regarded as intertwined rather than competing. I illustrate this concept in the context of the orders that are present in the pair-density-wave state and the phase diagrams that result from this analysis. \nVideo\n\n\n\n\nNovember 25\, 2020 |10:30am ET\n\n\n\n\n\n\n\nQimiao Si (Rice University) \nTitle: Bad Metals and Electronic Orders – Nematicity from Iron Pnictides to Graphene Moiré Systems \nAbstract: Strongly correlated electron systems often show bad-metal behavior\, as operationally specified in terms of a resistivity at room temperature that reaches or exceeds the Mott-Ioffe-Regel limit. They display a rich landscape of electronic orders\, which provide clues to the underlying microscopic physics. Iron-based superconductors present a striking case study\, and have been the subject of extensive efforts during the past decade or so. They are well established to be bad metals\, and their phase diagrams prominently feature various types of electronic orders that are essentially always accompanied by nematicity. In this talk\, I will summarize these characteristic features and discuss our own efforts towards understanding the normal state through the lens of the electronic orders and their fluctuations. Implications for superconductivity will be briefly discussed. In the second part of the talk\, I will consider the nematic correlations that have been observed in the graphene-based moiré narrow-band systems. I will present a theoretical study which demonstrates nematicity in a “fragile insulator”\, predicts its persistence in the bad metal regime and provides an overall perspective on the phase diagram of these correlated systems.\n\n\n\n\nDecember 2\, 2020 |10:30am ET\n\n\n\n\n\n\n\nAndrey Chubukov (University of Minnesota) \nTitle: Interplay between superconductivity and non-Fermi liquid at a quantum critical point in a metal \n\nAbstract:  I discuss the interplay between non-Fermi liquid behaviour and pairing near a quantum-critical point (QCP) in a metal. These tendencies are intertwined in the sense that both originate from the same interaction mediated by gapless fluctuations of a critical order parameter. The two tendencies compete because fermionic incoherence destroys the Cooper logarithm\, while the pairing eliminates scattering at low energies and restores fermionic coherence. I discuss this physics for a class of models with an effective dynamical interaction V (Ω) ~1/|Ω|^γ (the γ-model). This model describes\, in particular\, the pairing at a 2D Ising-nematic critical point in (γ=1/3)\, a 2D antiferromagnetic critical point (γ=1/2) and the pairing by an Einstein phonon with vanishing dressed Debye frequency (γ=2). I argue the pairing wins\, unless the pairing component of the interaction is artificially reduced\, but because of fermionic incoherence in the normal state\, the system develops a pseudogap\, preformed pairs behaviour in the temperature range between the onset of the pairing at Tp and the onset of phase coherence at the actual superconducting Tc. The ratio Tc/Tp decreases with γ and vanishes at γ =2. I present two complementary arguments of why this happens. One is the softening of longitudinal gap fluctuations\, which become gapless at γ =2. Another is the emergence of a 1D array of dynamical vortices\, whose number diverges at γ =2. I argue that once the number of vortices becomes infinite\, quasiparticle energies effectively get quantized and do not get re-arranged in the presence of a small phase variation. I show that a new non-superconducting ground state emerges at γ >2.\n\n\n\n\nDecember 9\, 2020 |10:30am ET\n\n\n\n\n\n\n\nDavid Hsieh (Caltech) \nTitle:  Signatures of anomalous symmetry breaking in the cuprates   \nAbstract: The temperature versus doping phase diagram of the cuprate high-Tc superconductors features an enigmatic pseudogap region whose microscopic origin remains a subject of intensive study. Experimentally resolving its symmetry properties is imperative for narrowing down the list of possible explanations. In this talk I will give an overview of how optical second harmonic generation (SHG) can be used as a sensitive probe of symmetry breaking\, and recap the ways it has been used to solve outstanding problems in condensed matter physics. I will then describe how we have been applying SHG polarimetry and spectroscopy to interrogate the cuprate pseudogap. In particular\, I will discuss our data on YBa2Cu3Oy [1]\, which show an order parameter-like increase in SHG intensity below the pseudogap temperature T* across a broad range of doping levels. I will then focus on our more recent results on a model parent cuprate Sr2CuO2Cl2 [2]\, where evidence of anomalous broken symmetries surprisingly also exists. Possible connections between these observations will be speculated upon.\n[1] L. Zhao\, C. A. Belvin\, R. Liang\, D. A. Bonn\, W. N. Hardy\, N. P. Armitage and D. Hsieh\, “A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy\,” Nature Phys. 13\, 250 (2017). \n[2] A. de la Torre\, K. L. Seyler\, L. Zhao\, S. Di Matteo\, M. S. Scheurer\, Y. Li\, B. Yu\, M. Greven\, S. Sachdev\, M. R. Norman and D. Hsieh. “Anomalous mirror symmetry breaking in a model insulating cuprate Sr2CuO2Cl2\,” Preprint at https://arxiv.org/abs/2008.06516\n\n\n\n\nDecember 16\, 2020 |10:30am ET\n\n\n\n\n\n\n\nZheng-Yu Weng (Tsinghua University) \nTitle: Organizing Principle of Mottness and Complex Phenomenon in High Temperature Superconductors\n\nAbstract: The complex phenomenon in the high-Tc cuprate calls for a microscopic understanding based on general principles. In this Lecture\, an exact organizing principle for a typical doped Mott insulator will be presented\, in which the fermion sign structure is drastically reduced to a mutual statistics. Its nature as a long-range spin-charge entanglement of many-body quantum mechanics will be exemplified by exact numerical calculations. The phase diagram of the cuprate may be unified in a “bottom-up” fashion by a “parent” ground state ansatz with hidden orders constructed based on the organizing principle. Here the pairing mechanism will go beyond the “RVB” picture and the superconducting state is of non-BCS nature with modified London equation and novel elementary excitations. In particular\, the Bogoliubov/Landau quasiparticle excitation are emerging with a two-gap structure in the superconducting state and the Fermi arc in a pseudogap regime. A mathematic framework of fractionalization and duality transformation guided by the organizing principle will be introduced to describe the above emergent phenomenon.\n\n\n\n\nDecember 17\, 2020 |10:30am ET\n\n\n\n\n\n\n\nSteven Kivelson (Stanford University) \nTitle: What do we know about the essential physics of high temperature superconductivity after one third of a century? \nAbstract: Despite the fact that papers submitted to glossy journals universally start by bemoaning the absence of theoretical understanding\, I will argue that the answer to the title question is “quite a lot.” To focus the discussion\, I will take the late P.W. Anderson’s “Last Words on the Cuprates” (arXiv:1612.03919) as a point of departure\, although from a perspective that differs from his in many key points.\n\n\n\n\nJanuary 20\, 2021 |10:30am ET\n\n\n\n\n\n\n\nThomas Peter Devereaux (Stanford University) \nTitle:  Numerical investigations of models of the cuprates\n\nAbstract: Richard Feynman once said “Anyone who wants to analyze the properties of matter in a real problem might want to start by writing down the fundamental equations and then try to solve them mathematically. Although there are people who try to use such an approach\, these people are the failures in this field. . . ” \nI will summarize efforts to solve microscopic models of the cuprates using quantum Monte Carlo and density matrix renormalization group computational methods\, with emphasis on how far one can get before failing to describe the real materials. I will start with an overview of the quantum chemistry of the cuprates that guides our choices of models\, and then I will discuss “phases” of these models\, both realized and not. I will lastly discuss the transport properties of the models in the “not-so-normal” regions of the phase diagram.\n\n\n\n\nFebruary 3\, 2021 |10:30am ET\n\n\n\n\n\n\n\nPhilip Phillips (University of Illinois Urbana-Champaign) \nTitle: Beyond BCS: An Exact Model for Superconductivity and Mottness\n\nAbstract: High-temperature superconductivity in the cuprates remains an unsolved problem because the cuprates start off their lives as Mott insulators in which no organizing principle such a Fermi surface can be invoked to treat the electron interactions. Consequently\, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity. Part of the problem is that the basic model for a Mott insulator\, namely the Hubbard model is unsolvable in any dimension we really care about. To address this problem\, I will start by focusing on the overlooked Z_2 emergent symmetry of a Fermi surface first noted by Anderson and Haldane. Mott insulators break this emergent symmetry. The simplest model of this type is due to Hatsugai/Kohmoto. I will argue that this model can be thought of a fixed point for Mottness. I will then show exactly[1] that this model when appended with a weak pairing interaction exhibits not only the analogue of Cooper’s instability but also a superconducting ground state\, thereby demonstrating that a model for a doped Mott insulator can exhibit superconductivity. The properties of the superconducting state differ drastically from that of the standard BCS theory. The elementary excitations of this superconductor are not linear combinations of particle and hole states but rather are superpositions of doublons and holons\, composite excitations signaling that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state. Additional unexpected features of this model are that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies and a suppression of the superfluid density as seen in the cuprates.\n[1] PWP\, L. Yeo\, E. Huang\, Nature Physics\, 16\, 1175-1180 (2020).\n\n\n\n\nFebruary 10\, 2021 |10:30am ET\n\n\n\n\n\n\n\nSenthil Todadri (MIT) \nTitle: Strange metals as ersatz Fermi liquids: emergent symmetries\, general constraints\, and experimental tests \nAbstract: The strange metal regime is one of the most prominent features of the cuprate phase diagram but yet has remained amongst the most mysterious. Seemingly similar metallic behavior is seen in a few other metals. In this talk\, I will discuss\, in great generality\, some properties of `strange metals’ in an ideal clean system. I will discuss general constraints[1] on the emergent low energy symmetries of any such strange metal. These constraints may be viewed as a generalization of the Luttinger theorem of ordinary Fermi liquids. Many\, if not all\, non-Fermi liquids will have the same realization of emergent symmetry as a Fermi liquid (even though they could have very different dynamics). Such phases – dubbed ersatz Fermi liquids – share some (but not all) universal properties with Fermi liquids. I will discuss the implications for understanding the strange metal physics observed in experiments . Combined with a few experimental observations\, I will show that these general model-independent considerations lead to concrete predictions[2] about a class of strange metals. The most striking of these is a divergent susceptibility of an observable that has the same symmetries as the loop current order parameter.\n[1]. Dominic Else\, Ryan Thorngren\, T. Senthil\, https://arxiv.org/abs/2007.07896\n[2]. Dominic Else\, T. Senthil\, https://arxiv.org/abs/2010.10523\n\n\n\n\nApril 1\, 2021 |9:00am ET\n\n\n\n\n\n\n\nNaoto Nagaosa (University of Tokyo) \nTitle: Applied physics of high-Tc theories \nAbstract: Since the discovery of high temperature superconductors in cuprates in 1986\, many theoretical ideas have been proposed which have enriched condensed matter theory. Especially\, the resonating valence bond (RVB) state for (doped) spin liquids is one of the most fruitful idea. In this talk\, I would like to describe the development of RVB idea to broader class of materials\, especially more conventional magnets. It is related to the noncollinear spin structures with spin chirality and associated quantal Berry phase applied to many phenomena and spintronics applications. It includes the (quantum) anomalous Hall effect\, spin Hall effect\, topological insulator\, multiferroics\, various topological spin textures\, e.g.\, skyrmions\, and nonlinear optics. I will show that even though the phenomena are extensive\, the basic idea is rather simple and common in all of these topics.\n\n\n\n\nApril 22\, 2021 |10:30am ET\n\n\n\n\n\n\n\nDung-Hai Lee (UC Berkeley) \nTitle: “Non-abelian bosonization in two and three spatial dimensions and some applications” \nAbstract: In this talk\, we generalize Witten’s non-abelian bosonization in $(1+1)$-D to two and three spatial dimensions. Our theory applies to fermions with relativistic dispersion. The bosonized theories are non-linear sigma models with level-1 Wess-Zumino-Witten terms. As applications\, we apply the bosonization results to the $SU(2)$ gauge theory of the $\pi$ flux mean-field theory of half-filled Hubbard model\, critical spin liquids of “bipartite-Mott insulators” in 1\,2\,3 spatial dimensions\, and twisted bilayer graphene.\n\n\n\n\nMay 12\, 2021 |10:30am ET\n\n\n\n\n\n\n\nAndré-Marie Tremblay (Université de Sherbrooke) \nTitle: A unified theoretical perspective on the cuprate phase diagram \nAbstract: Many features of the cuprate phase diagram are a challenge for the usual tools of solid state physics. I will show how a perspective that takes into account both the localized and delocalized aspects of conduction electrons can explain\, at least qualitatively\, many of these features. More specifically\, I will show that the work of several groups using cluster extensions of dynamical mean-field theory sheds light on the pseudogap\, on the quantum-critical point and on d-wave superconductivity. I will argue that the charge transfer gap and oxygen hole content are the best indicators of strong superconductivity and that many observations are a signature of the influence of Mott physics away from half-filling. I will also briefly comment on what information theoretic measures tell us about this problem.\n\n\n\n\nAugust 11\, 2021 |10:30am ET\n\n\n\n\n\n\n\nPiers Coleman (Rutgers) \nTitle: Order Fractionalization* \nAbstract: I will discuss the interplay of spin fractionalization with broken\nsymmetry. When a spin fractionalizes into a fermion\, the resulting particle\ncan hybridize or pair with the mobile electrons to develop a new kind of\nfractional order parameter. The concept of “order fractionalization” enables\nus to extend the concept of off-diagonal order to encompass the formation of\nsuch order parameters with fractional quantum numbers\, such as spinorial\norder[1].\nA beautiful illustration of this phenomenon is provided by a model\nwhich incorporates the Yao-Lee-Kitaev model into a Kondo lattice[2]. This\nmodel explicitly exhibits order fractionalization and is expected to undergo a\ndiscrete Ising phase transition at finite temperature into an\norder-fractionalized phase with gapless Majorana excitations.\nThe broader implications of these considerations for Quantum\nMaterials and Quantum Field Theory will be discussed.\nWork done in collaboration with Yashar Komijani\, Anna Toth and Alexei\nTsvelik.\n[1] Order Fractionalization\, Yashar Komijani\, Anna Toth\, Premala Chandra\, Piers Coleman\, (2018).\n[2] Order Fractionalization in a Kitaev Kondo model\, Alexei Tsvelik and Piers Coleman\, (2021).\n\n\n\n\nSeptember 15\, 2021 |10:30am ET\n\n\n\n\n\n\n\nLiang Fu (MIT) \nTitle: Three-particle mechanism for pairing and superconductivity \nAbstract: I will present a new mechanism and an exact theory of electron pairing due to repulsive interaction in doped insulators. When the kinetic energy is small\, the dynamics of adjacent electrons on the lattice is strongly correlated. By developing a controlled kinetic energy expansion\, I will show that two doped charges can attract and form a bound state\, despite and because of the underlying repulsion. This attraction by repulsion is enabled by the virtual excitation of a third electron in the filled band. This three-particle pairing mechanism leads to a variety of novel phenomena at finite doping\, including spin-triplet superconductivity\, pair density wave\, BCS-BEC crossover and Feshbach resonance involving “trimers”. Possible realizations in moire materials\, ZrNCl and WTe2 will be discussed. \n[1] V. Crepel and L. Fu\, Science Advances 7\, eabh2233 (2021)\n[2] V. Crepel and L. Fu\, arXiv:2103.12060\n[3] K. Slagle and L. Fu\,  Phys. Rev. B 102\, 235423 (2020)\n\n\n\n\nSeptember 29\, 2021 |11:30am ET (special time)\n\n\n\n\n\n\n\nNai Phuan Ong (Princeton University)\n\nTitle:.Abstract: The layered honeycomb magnet alpha-RuCl3 orders below 7 K in a zigzag phase in zero field. An in-plane magnetic field H||a suppresses the zigzag order at 7 Tesla\, leaving a spin-disordered phase widely believed to be a quantum spin liquid (QSL) that extends to ~12 T. We have observed oscillations in the longitudinal thermal conductivity Kxx vs. H from 0.4 to 4 K. The oscillations are periodic in 1/H (with a break-in-slope at 7 T). The amplitude function is maximal in the QSL phase (7 –11.5 T). I will describe a benchmark for crystalline disorder\, the reproducibility and intrinsic nature of the oscillations\, and discuss implications for the QSL state. I will also show detailed data on the thermal Hall conductivity Kxy measured from 0.4 K to 10 K and comment on recent half-quantization results.*Czajka et al.\, Nature Physics 17\, 915 (2021).Collaborators: Czajka\, Gao\, Hirschberger\, Lampen Kelley\, Banerjee\, Yan\, Mandrus and Nagler.\n\n\n\n\nDate TBA |10:30am ET\n\n\n\n\n\n\n\nSuchitra Sebastian (University of Cambridge) \nTitle: TBA\n\n\n\n\nDate TBA |10:30am ET\n\n\n\n\n\n\n\nJenny Hoffman (Harvard University) \nTitle: TBA
URL:https://cmsa.fas.harvard.edu/event/strongly-correlated-quantum-materials-and-high-temperature-superconductors-series/
CATEGORIES:Event,Strongly Correlated Quantum Materials and High-Temperature Superconductors
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/unnamed-3-600x338-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210721T103000
DTEND;TZID=America/New_York:20210721T120000
DTSTAMP:20260503T103211
CREATED:20240213T085105Z
LAST-MODIFIED:20240213T085105Z
UID:10002262-1626863400-1626868800@cmsa.fas.harvard.edu
SUMMARY:7/21/2021 Quantum Matter Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/7-21-2021-quantum-matter-seminar/
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210722T080000
DTEND;TZID=America/New_York:20210722T093000
DTSTAMP:20260503T103211
CREATED:20240213T085228Z
LAST-MODIFIED:20240213T085228Z
UID:10002266-1626940800-1626946200@cmsa.fas.harvard.edu
SUMMARY:7/22/2021 Quantum Matter Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/7-22-2021-quantum-matter-seminar/
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210722T090000
DTEND;TZID=America/New_York:20210722T100000
DTSTAMP:20260503T103211
CREATED:20240213T085509Z
LAST-MODIFIED:20240227T090807Z
UID:10002271-1626944400-1626948000@cmsa.fas.harvard.edu
SUMMARY:Moduli spaces of stable pairs on algebraic surfaces
DESCRIPTION:Interdisciplinary Science Seminar \nSpeaker: Yinbang Lin (Tongji University) \nTitle: Moduli spaces of stable pairs on algebraic surfaces \nAbstract: As a variant of Grothendieck’s Quot schemes\, we introduce the moduli space of limit stable pairs. We show an example over a smooth projective algebraic surface where there is a virtual fundamental class. We are able to describe this class explicitly. We will also show an application towards moduli of sheaves.
URL:https://cmsa.fas.harvard.edu/event/7-22-2021-interdisciplinary-science-seminar/
LOCATION:Virtual
CATEGORIES:Interdisciplinary Science Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210729T103000
DTEND;TZID=America/New_York:20210729T120000
DTSTAMP:20260503T103211
CREATED:20240213T085639Z
LAST-MODIFIED:20240213T085639Z
UID:10002273-1627554600-1627560000@cmsa.fas.harvard.edu
SUMMARY:The nu=5/2 enigma: Recent insights from theory and experiment
DESCRIPTION:peaker: Ady Stern & David Mross (Weizmann) \nSpeaker: Ady Stern & David Mross (Weizmann \nTitle: The nu=5/2 enigma: Recent insights from theory and experiment \nAbstract: Non-Abelian phases of matter have long inspired quantum physicists across various disciplines. The strongest experimental evidence of such a phase arises in quantum Hall systems at the filling factor 5/2 but conflicts with decades of numerical works. We will briefly introduce the 5/2 plateau and explain some of the key obstacles to identifying its topological order. We will then describe recent experimental and theoretical progress\, including a proposal for resolving the 5/2 enigma based on electrical conductance measurements.
URL:https://cmsa.fas.harvard.edu/event/the-nu5-2-enigma-recent-insights-from-theory-and-experiment/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;VALUE=DATE:20210824
DTEND;VALUE=DATE:20210825
DTSTAMP:20260503T103211
CREATED:20230705T081718Z
LAST-MODIFIED:20250328T145235Z
UID:10000070-1629763200-1629849599@cmsa.fas.harvard.edu
SUMMARY:Big Data Conference 2021
DESCRIPTION:On August 24\, 2021\, the CMSA hosted our seventh annual Conference on Big Data. The Conference features many speakers from the Harvard community as well as scholars from across the globe\, with talks focusing on computer science\, statistics\, math and physics\, and economics. \nThe 2021 Big Data Conference took place virtually on Zoom. \nOrganizers:  \n\nShing-Tung Yau\, William Caspar Graustein Professor of Mathematics\, Harvard University\nScott Duke Kominers\, MBA Class of 1960 Associate Professor\, Harvard Business\nHorng-Tzer Yau\, Professor of Mathematics\, Harvard University\nSergiy Verstyuk\, CMSA\, Harvard University\n\nSpeakers: \n\nAndrew Blumberg\, University of Texas at Austin\nMoran Koren\, Harvard CMSA\nHima Lakkaraju\, Harvard University\nKatrina Ligett\, The Hebrew University of Jerusalem\n\n\n\n\n\nTime (ET; Boston time)\nSpeaker\nTitle/Abstract\n\n\n9:00AM\nConference Organizers\nIntroduction and Welcome\n\n\n9:10AM – 9:55AM\nAndrew Blumberg\, University of Texas at Austin\nTitle: Robustness and stability for multidimensional persistent homology \nAbstract: A basic principle in topological data analysis is to study the shape of data by looking at multiscale homological invariants. The idea is to filter the data using a scale parameter that reflects feature size. However\, for many data sets\, it is very natural to consider multiple filtrations\, for example coming from feature scale and density. A key question that arises is how such invariants behave with respect to noise and outliers. This talk will describe a framework for understanding those questions and explore open problems in the area.\n\n\n10:00AM – 10:45AM\nKatrina Ligett\, The Hebrew University of Jerusalem\nTitle: Privacy as Stability\, for Generalization \nAbstract: Many data analysis pipelines are adaptive: the choice of which analysis to run next depends on the outcome of previous analyses. Common examples include variable selection for regression problems and hyper-parameter optimization in large-scale machine learning problems: in both cases\, common practice involves repeatedly evaluating a series of models on the same dataset. Unfortunately\, this kind of adaptive re-use of data invalidates many traditional methods of avoiding overfitting and false discovery\, and has been blamed in part for the recent flood of non-reproducible findings in the empirical sciences. An exciting line of work beginning with Dwork et al. in 2015 establishes the first formal model and first algorithmic results providing a general approach to mitigating the harms of adaptivity\, via a connection to the notion of differential privacy. In this talk\, we’ll explore the notion of differential privacy and gain some understanding of how and why it provides protection against adaptivity-driven overfitting. Many interesting questions in this space remain open. \nJoint work with: Christopher Jung (UPenn)\, Seth Neel (Harvard)\, Aaron Roth (UPenn)\, Saeed Sharifi-Malvajerdi (UPenn)\, and Moshe Shenfeld (HUJI). This talk will draw on work that appeared at NeurIPS 2019 and ITCS 2020\n\n\n10:50AM – 11:35AM\nHima Lakkaraju\, Harvard University\nTitle: Towards Reliable and Robust Model Explanations \nAbstract: As machine learning black boxes are increasingly being deployed in domains such as healthcare and criminal justice\, there is growing emphasis on building tools and techniques for explaining these black boxes in an interpretable manner. Such explanations are being leveraged by domain experts to diagnose systematic errors and underlying biases of black boxes. In this talk\, I will present some of our recent research that sheds light on the vulnerabilities of popular post hoc explanation techniques such as LIME and SHAP\, and also introduce novel methods to address some of these vulnerabilities. More specifically\, I will first demonstrate that these methods are brittle\, unstable\, and are vulnerable to a variety of adversarial attacks. Then\, I will discuss two solutions to address some of the vulnerabilities of these methods – (i) a framework based on adversarial training that is designed to make post hoc explanations more stable and robust to shifts in the underlying data; (ii) a Bayesian framework that captures the uncertainty associated with post hoc explanations and in turn allows us to generate explanations with user specified levels of confidences. I will conclude the talk by discussing results from real world datasets to both demonstrate the vulnerabilities in post hoc explanation techniques as well as the efficacy of our aforementioned solutions.\n\n\n11:40AM – 12:25PM\nMoran Koren\, Harvard CMSA\nTitle: A Gatekeeper’s Conundrum \nAbstract: Many selection processes contain a “gatekeeper”. The gatekeeper’s goal is to examine an applicant’s suitability to a proposed position before both parties endure substantial costs. Intuitively\, the introduction of a gatekeeper should reduce selection costs as unlikely applicants are sifted out. However\, we show that this is not always the case as the gatekeeper’s introduction inadvertently reduces the applicant’s expected costs and thus interferes with her self-selection. We study the conditions under which the gatekeeper’s presence improves the system’s efficiency and those conditions under which the gatekeeper’s presence induces inefficiency. Additionally\, we show that the gatekeeper can sometimes improve selection correctness by behaving strategically (i.e.\, ignore her private information with some probability).\n\n\n12:25PM\nConference Organizers\nClosing Remarks
URL:https://cmsa.fas.harvard.edu/event/big-data-conference-2021/
LOCATION:Virtual
CATEGORIES:Big Data Conference,Conference,Event
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/BD_21-Poster.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210901T183100
DTEND;TZID=America/New_York:20210901T193100
DTSTAMP:20260503T103211
CREATED:20240214T093606Z
LAST-MODIFIED:20240301T100331Z
UID:10002639-1630521060-1630524660@cmsa.fas.harvard.edu
SUMMARY:Naturalness and muon anomalous magnetic moment
DESCRIPTION:Title: Naturalness and muon anomalous magnetic moment \nAbstract: We study a model for explaining the apparent deviation of the muon anomalous magnetic moment\, (g-2)\, from the Standard Model expectation. There are no new scalars and hence no new hierarchy puzzles beyond those associated with the Standard model Higgs; the only new particles that are relevant for (g-2) are vector-like singlet and doublet leptons. Interestingly\, this simple model provides a calculable example violating the Wilsonian notion of naturalness: despite the absence of any symmetries prohibiting its generation\, the coefficient of the naively leading dimension-six operator for (g−2) vanishes at one-loop. While effective field theorists interpret this either as a surprising UV cancellation of power divergences\, or as a delicate cancellation between matching UV and calculable IR corrections to (g−2) from parametrically separated scales\, there is a simple explanation in the full theory: the loop integrand is a total derivative of a function vanishing in both the deep UV and IR. The leading contribution to (g−2) arises from dimension-eight operators\, and thus the required masses of new fermions are lower than naively expected\, with a sizable portion of parameter space already covered by direct searches at the LHC. All of the the viable parameter can be probed by the LHC and planned future colliders.
URL:https://cmsa.fas.harvard.edu/event/9-1-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210902T130000
DTEND;TZID=America/New_York:20210902T143000
DTSTAMP:20260503T103211
CREATED:20240213T112100Z
LAST-MODIFIED:20240304T084111Z
UID:10002491-1630587600-1630593000@cmsa.fas.harvard.edu
SUMMARY:Eppur si muovono: rotations in active matter
DESCRIPTION:Abstract: Living matter relies on the self organization of its components into higher order structures\, on the molecular as well as on the cellular\, organ or even organism scale. Collective motion due to active transport processes has been shown to be a promising route for attributing fascinating order formation processes on these different length scales. Here I will present recent results on structure formation on actively transported actin filaments on lipid membranes and vesicles\, as well as the cell migration induced structure formation in the developmental phase of mammary gland organoids. For both systems spherical structures with persistent collective rotations are observed.
URL:https://cmsa.fas.harvard.edu/event/eppur-si-muovono-rotations-in-active-matter/
CATEGORIES:Active Matter Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210902T183400
DTEND;TZID=America/New_York:20210902T193400
DTSTAMP:20260503T103211
CREATED:20240214T093431Z
LAST-MODIFIED:20240301T095944Z
UID:10002634-1630607640-1630611240@cmsa.fas.harvard.edu
SUMMARY:Exotic quantum matter: From lattice gauge theory to hyperbolic lattices
DESCRIPTION:Title: Exotic quantum matter: From lattice gauge theory to hyperbolic lattices \nAbstract: This talk\, in two parts\, will discuss two (unrelated) instances of exotic quantum matter. In the first part\, I will discuss quantum critical points describing possible transitions out of the Dirac spin liquid\, towards either symmetry-breaking phases or topologically ordered spin liquids. I will also comment on the role of instanton zero modes for symmetry breaking in parton gauge theories. In the second part\, I will propose an extension of Bloch band theory to hyperbolic lattices\, such as those recently realized in circuit QED experiments\, based on ideas from algebraic geometry and Riemann surface theory.
URL:https://cmsa.fas.harvard.edu/event/9-2-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210903T103000
DTEND;TZID=America/New_York:20210903T120000
DTSTAMP:20260503T103211
CREATED:20240125T164403Z
LAST-MODIFIED:20240125T164403Z
UID:10001337-1630665000-1630670400@cmsa.fas.harvard.edu
SUMMARY:Swampland Seminar Series
DESCRIPTION:During the 2021-22 academic year\, the CMSA will be co-hosting a seminar on Swampland\, with the Harvard Physics Department\, organized by Miguel Montero\, Cumrun Vafa\, Irene Valenzuela. This seminar is a part of the Swampland Program. This seminar will take place on Mondays at 10:00 am – 11:30 am (Boston time). To learn how to attend\, please subscribe here. \nTalks will be posted on the Swampland Seminars YouTube channel. The schedule below will be updated as talks are confirmed. \nSpring 2022\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n1/31/2022\nRafael Álvarez-García (DESY Hamburg)\nTitle: Membrane Limits in Quantum Gravity\n\n\n2/7/2022\nDu Pei (Harvard CMSA)\nTitle: Holomorphic CFTs and topological modular forms \nAbstract: The theory of topological modular forms leads to many interesting constraints and predictions for two-dimensional quantum field theories\, and some of them might have interesting implications for the swampland program. In this talk\, I will show that a conjecture by Segal\, Stolz and Teichner requires the constant term of the partition function of a bosonic holomorphic CFTs to be divisible by specific integers determined by the central charge. We verify this constraint in large classes of physical examples\, and rule out the existence of an infinite set of “extremal CFTs”\, including those with central charges c = 48\, 72\, 96 and 120.\n\n\n2/28/2022\n Tom Rudelius (UC\, Berkeley)\nTitle: Generalized Global Symmetries and the Weak Gravity Conjecture\n\n\n3/7/2022\nFernando Marchesano (UAM-CSIC\, Madrid)  and Max Wiesner (Harvard CMSA)\nTitle: 4d strings at strong coupling\n\n\n3/21/2022\nPatrick Draper (Univ. of Illinois) and Alvaro Herraez (IPhT Saclay).\nOpen Mic Discussion\nTopic: Entropy bounds (species bound\, Bekenstein bound\, CKN bound\, and the like)\n\n\n3/28/2022\nFernando Quevedo (Cambridge)\nTitle: On renormalisation group induced moduli stabilisation and brane-antibrane inflation \nAbstract: A proposal to use the renormalisation group to address moduli stabilisation in IIB string perturbation theory will be described. We revisit brane-antibrane inflation combining this proposal with non-linearly realised supersymmetry.\n\n\n4/5/2022\nSimon Caron-Huot (McGill University) and Julio Parra (Caltech)\nTitle: Causality constraints on corrections to Einstein gravity \nAbstract: We study constraints from causality and unitarity on 2→2 graviton scattering in four-dimensional weakly-coupled effective field theories. Together\, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations\, we derive two-sided bounds on gravitational Wilson coefficients in terms of the mass M of new higher-spin states. Our bounds imply that gravitational interactions must shut off uniformly in the limit G→0\, and prove the scaling with M expected from dimensional analysis (up to an infrared logarithm). We speculate that causality\, together with the non-observation of gravitationally-coupled higher-spin states at colliders\, severely restricts modifications to Einstein gravity that could be probed by experiments in the near future.\n\n\n4/11/2022\nTimm Wrase and Eduardo Gonzalo (Lehigh)\nTitle: Type IIB flux compactifications with $h^{1\,1}=0$ \nAbstract: We revisit type IIB flux compactification that are mirror dual to type IIA on rigid Calabi-Yau manifolds. We find a variety of interesting new solutions\, like fully stabilized Minkowski vacua and infinite families of AdS$_4$ solutions with arbitrarily large numbers of spacetime filling D3 branes. We discuss how these solutions fit into the web of swampland conjectures.\n\n\n4/18/2022\nJosé Calderón (IFT Madrid)\nOpen mic Swampland Discussion \nTopic: Cobordism\n\n\n5/9/2022\nGeorges Obie (Harvard)\nTitle: Inflation and light Dark Matter constraints from the Swampland \nAbstract: I will explore the interplay between Swampland conjectures and models of inflation and light Dark Matter. To that end\, I will briefly review the weak gravity conjecture (WGC) and the related Festina Lente (FL) bound. These have implications for light darkly and milli-charged particles and can disfavor a large portion of parameter space. The FL bound also implies strong restrictions on the field content of our universe during inflation and presents an opportunity for inflationary model building. At the same time\, it rules out some popular models like chromo-natural inflation and gauge-flation. Finally\, I will review another Swampland conjecture related to Stückelberg photon masses and discuss its implications for astro-particle physics.\n\n\n\n\nFall 2021\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n9/13/2021\nJohn Stout (Harvard)\nTitle: Decoding Divergent Distances \nAbstract: Motivated by a relationship between the Zamolodchikov and NLSM metrics to the so-called quantum information metric\, I will discuss recent work (2106.11313) on understanding infinite distance limits within the context of information theory. I will describe how infinite distance points represent theories that are hyper-distinguishable\, in the sense that they can be distinguished from “nearby” theories with certainty in relatively few measurements. I will then discuss necessary and sufficient ingredients for the appearance of these infinite distance points\, illustrate these in simple examples\, and describe how this perspective can help the swampland program.\n\n\n9/20/2021\nManki Kim (MIT)\nTitle: Small Cosmological Constants in String Theory \nAbstract: We construct supersymmetric AdS4 vacua of type IIB string theory in compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. We first find explicit orientifolds and quantized fluxes for which the superpotential takes the form proposed by Kachru\, Kallosh\, Linde\, and Trivedi. Given very mild assumptions on the numerical values of the Pfaffians\, these compactifications admit vacua in which all moduli are stabilized at weak string coupling. By computing high-degree Gopakumar-Vafa invariants we give strong evidence that the α 0 expansion is likewise well-controlled. We find extremely small cosmological constants\, with magnitude < 10^{-123} in Planck units. The compactifications are large\, but not exponentially so\, and hence these vacua manifest hierarchical scale-separation\, with the AdS length exceeding the Kaluza-Klein length by a factor of a googol.\n\n\n9/27/2021\nEran Palti (Ben Gurion)\nTitle: Convexity of Charged Operators in CFTs and the Weak Gravity Conjecture \nAbstract: In this talk I will introduce a particular formulation of the Weak Gravity Conjecture in AdS space in terms of the self-binding energy of a particle. The holographic CFT dual of this formulation corresponds to a certain convex-like structure for operators charged under continuous global symmetries. Motivated by this\, we propose a conjecture that this convexity is a general property of all CFTs\, not just those with weakly-curved gravitational duals. It is possible to test this in simple CFTs\, the conjecture passes all the tests performed so far.\n\n\n10/18/2021\nThomas Van Riet (KU Leuven)\nTitle: The Festina Lente Bound \nAbstract: I will explain what the Festina Lente bound means and where it comes from. Then I discuss its possible implications for  phenomenology\, both top-down and bottom-up.\n\n\n10/25/2021\nJoe Conlon (Oxford)\nTitle: Exploring the Holographic Swampland \nAbstract: I describe our work looking at `traditional’ scenarios of moduli stabilisation from a holographic perspective. This reveals some interesting structure that is not apparent from the top-down perspective. For vacua in the extreme regions of moduli space\, such as LVS in type IIB or the DGKT flux vacua in type IIA\, the dual moduli conformal dimensions reduce to fixed values – in a certain sense\, the low-conformal dimension part of the CFT is unique and independent of the large number of flux choices. For the DGKT flux vacua these conformal dimensions are also integer\, for reasons we do not understand.\n\n\n11/01/2021\nPieter Bomans (Princeton)\nTitle: Bubble instability of mIIA on AdS_4 x S^6 \nAbstract: Recently\, a set of non-supersymmetric AdS_4 vacua of massive type IIA string theory has been constructed. These vacua are perturbatively stable with respect to the full KK spectrum of type mIIA supergravity and furthermore\, they are stable against a variety of non-perturbative decay channels. Hence\, at this point\, they represent a serious challenge to the AdS swampland conjecture. In my talk\, I will review in detail the construction of these vacua as well as introduce a new decay channel\, ultimately sealing their fate as being unstable.\n\n\n11/15/2021\nNima Arkani-Hamed (IAS)\, and Gary Shiu (UW-Madison)\n This week’s seminar will be an open mic discussion which will be led by Nima Arkani-Hamed (IAS)\, and by Gary Shiu (UW-Madison)\, and the topic will be “Swampland constraints\, Unitarity and Causality”. They will start with a brief introduction sharing their thoughts about the topic and moderate a discussion afterwards.\n\n\n11/22/2021\nThomas Grimm (Utrecht University)\nTitle: Taming the Landscape \nAbstract: In this talk I will introduce a generalized notion of finiteness that provides a structural principle for the set of effective theories that can be consistently coupled to quantum gravity. More concretely\, I will propose a ‘tameness conjecture’ that states that all scalar field spaces and coupling functions that appear in such an effective theory must be definable in an o-minimal structure. The fascinating field of tame geometry has seen much recent progress and I will argue that the results can be used to support the above swampland conjecture. The strongest evidence arises from a new finiteness theorem for the flux landscape which is shown using the tameness of the period map.\n\n\n11/29/2021\nTimm Wrase (Lehigh University)\nTitle: Scale separated AdS vacua? \nAbstract: In this talk I will review massive type IIA flux compactifications that seem to give rise to infinite families of supersymmetric 4d AdS vacua. These vacua provide an interesting testing ground for the swampland program. After reviewing potential shortcomings of this setup\, I will discuss recent progress on overcoming them and getting a better understanding of these solutions.\n\n\n12/6/2021\nLars Aalsma (University of Wisconsin-Madison)\nTitle: Extremal Black Hole Corrections from Iyer-Wald \nAbstract: Extremal black holes play a key role in our understanding of various swampland conjectures and in particular the WGC. The mild form of the WGC states that higher-derivative corrections should decrease the mass of extremal black holes at fixed charge. Whether or not this conjecture is satisfied depends on the sign of the combination of Wilson coefficients that control corrections to extremality. Typically\, corrections to extremality need to be computed on a case-by-case basis\, but in this talk I will present a universal derivation of extremal black hole corrections using the Iyer-Wald formalism. This leads to a formula that expresses general corrections to the extremality bound in terms of the stress tensor of the perturbations under consideration\, clarifying the relation between the WGC and energy conditions. This shows that a necessary condition for the mild form of the WGC to be satisfied is a violation of the Dominant Energy Condition. This talk is based on 2111.04201.
URL:https://cmsa.fas.harvard.edu/event/swampland-seminar-series/
CATEGORIES:Swampland Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210907T093000
DTEND;TZID=America/New_York:20210907T103000
DTSTAMP:20260503T103211
CREATED:20240213T112149Z
LAST-MODIFIED:20240304T105626Z
UID:10002492-1631007000-1631010600@cmsa.fas.harvard.edu
SUMMARY:Derived categories of nodal quintic del Pezzo threefolds
DESCRIPTION:Abstract: Conifold transitions are important algebraic geometric constructions that have been of special interests in mirror symmetry\, transforming Calabi-Yau 3-folds between A- and B-models. In this talk\, I will discuss the change of the quintic del Pezzo 3-fold (Fano 3-fold of index 2 and degree 5) under the conifold transition at the level of the bounded derived category of coherent sheaves. The nodal quintic del Pezzo 3-fold X has at most 3 nodes. I will construct a semiorthogonal decomposition for D^b(X) and in the case of 1-nodal X\, detail the change of derived categories from its smoothing to its small resolution.
URL:https://cmsa.fas.harvard.edu/event/derived-categories-of-nodal-quintic-del-pezzo-threefolds/
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210908T183700
DTEND;TZID=America/New_York:20210908T193700
DTSTAMP:20260503T103211
CREATED:20240214T093235Z
LAST-MODIFIED:20240301T095658Z
UID:10002632-1631126220-1631129820@cmsa.fas.harvard.edu
SUMMARY:Cornering the universal shape of fluctuations and entanglement
DESCRIPTION:Title: Cornering the universal shape of fluctuations and entanglement \nAbstract: Understanding the fluctuations of observables is one of the main goals in physics. We investigate such fluctuations when a subregion of the full system can be observed\, focusing on geometries with corners. We report that the dependence on the opening angle is super-universal: up to a numerical prefactor\, this function does not depend on anything\, provided the system under study is uniform\, isotropic\, and correlations do not decay too slowly. The prefactor contains important physical information: we show in particular that it gives access to the long-wavelength limit of the structure factor. We illustrate our findings with several examples: classical fluids\, fractional quantum Hall (FQH) states\, scale invariant quantum critical theories\, and metals. Finally\, we discuss connections with the entanglement entropy\, including new results for Laughlin FQH states. \nRef: arXiv:2102.06223
URL:https://cmsa.fas.harvard.edu/event/9-8-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210909T140000
DTEND;TZID=America/New_York:20210909T150000
DTSTAMP:20260503T103211
CREATED:20240214T092250Z
LAST-MODIFIED:20240517T200424Z
UID:10002621-1631196000-1631199600@cmsa.fas.harvard.edu
SUMMARY:The complexity of matrix multiplication approached via algebraic geometry and representation theory
DESCRIPTION:Speaker: JM Landsberg\, Texas A&M \nTitle: The complexity of matrix multiplication approached via algebraic geometry and representation theory \nAbstract: In 1968 V. Strassen discovered the way we usually multiply matrices is not the most efficient possible\, and after considerable work by many authors\, it is generally conjectured by computer scientists that as the size of matrices becomes large\, it becomes almost as easy to multiply them as it is to add them. I will give a brief history of the problem\, explain how this conjecture is naturally understood in the framework of classical algebraic geometry and representation theory\, and conclude by describing recent advances using more sophisticated tools from algebraic geometry. For most of the talk\, no knowledge of algebraic geometry or representation theory will be needed.
URL:https://cmsa.fas.harvard.edu/event/9-22-2021-new-technologies-in-mathematics-seminar/
CATEGORIES:New Technologies in Mathematics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210909T183800
DTEND;TZID=America/New_York:20210909T193800
DTSTAMP:20260503T103211
CREATED:20240214T092815Z
LAST-MODIFIED:20240301T095523Z
UID:10002628-1631212680-1631216280@cmsa.fas.harvard.edu
SUMMARY:Quantum gravity from quantum matter
DESCRIPTION:Title: Quantum gravity from quantum matter \nAbstract: We present a model of quantum gravity in which dimension\, topology and geometry of spacetime are collective dynamical variables that describe the pattern of entanglement of underlying quantum matter. As spacetimes with arbitrary dimensions can emerge\, the gauge symmetry is generalized to a group that includes diffeomorphisms in general dimensions. The gauge symmetry obeys a first-class constraint operator algebra\, and is reduced to a generalized hypersurface deformation algebra in states that exhibit classical spacetimes. In the semi-classical limit\, we find a saddle-point solution that describes a series of (3+1)-dimensional de Sitter-like spacetimes with the Lorentzian signature bridged by Euclidean spaces in between.
URL:https://cmsa.fas.harvard.edu/event/9-9-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210910T093000
DTEND;TZID=America/New_York:20210910T103000
DTSTAMP:20260503T103211
CREATED:20240213T105719Z
LAST-MODIFIED:20240304T105748Z
UID:10002468-1631266200-1631269800@cmsa.fas.harvard.edu
SUMMARY:9/10/2021 General Relativity Seminar
DESCRIPTION:Title: Asymptotic localization\, massive fields\, and gravitational singularities \nAbstract: I will review three recent developments on Einstein’s field equations under low decay or low regularity conditions. First\, the Seed-to-Solution Method for Einstein’s constraint equations\, introduced in collaboration with T.-C. Nguyen generates asymptotically Euclidean manifolds with the weakest or strongest possible decay (infinite ADM mass\, Schwarzschild decay\, etc.). The ‘asymptotic localization problem’ is also proposed an alternative to the ‘optimal localization problem’ by Carlotto and Schoen. We solve this new problem at the harmonic level of decay. Second\, the Euclidian-Hyperboloidal Foliation Method\, introduced in collaboration with Yue Ma\, applies to nonlinear wave systems which need not be asymptotically invariant under Minkowski’s scaling field and to solutions with low decay in space. We established the global nonlinear stability of self-gravitating massive matter field in the regime near Minkowski spacetime. Third\, in collaboration with Bruno Le Floch and Gabriele Veneziano\, I studied spacetimes in the vicinity of singularity hypersurfaces and constructed bouncing cosmological spacetimes of big bang-big crunch type. The notion of singularity scattering map provides a flexible tool for formulating junction conditions and\, by analyzing Einstein’s constraint equations\, we established a surprising classification of all gravitational bouncing laws. Blog: philippelefloch.org
URL:https://cmsa.fas.harvard.edu/event/9-10-2021-general-relativity-seminar/
CATEGORIES:General Relativity Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210910T093000
DTEND;TZID=America/New_York:20210910T103000
DTSTAMP:20260503T103211
CREATED:20240213T114336Z
LAST-MODIFIED:20240304T100309Z
UID:10002512-1631266200-1631269800@cmsa.fas.harvard.edu
SUMMARY:Threshold phenomena in random graphs and hypergraphs
DESCRIPTION:Member Seminar \nSpeaker: Michael Simkin \nTitle: Threshold phenomena in random graphs and hypergraphs \nAbstract: In 1959 Paul Erdos and Alfred Renyi introduced a model of random graphs that is the cornerstone of modern probabilistic combinatorics. Now known as the “Erdos-Renyi” model of random graphs it has far-reaching applications in combinatorics\, computer science\, and other fields. \nThe model is defined as follows: Given a natural number $n$ and a parameter $p \in [0\,1]$\, let $G(n;p)$ be the distribution on graphs with $n$ vertices in which each of the $\binom{n}{2}$ possible edges is present with probability $p$\, independent of all others. Despite their apparent simplicity\, the study of Erdos-Renyi random graphs has revealed many deep and non-trivial phenomena. \nA central feature is the appearance of threshold phenomena: For all monotone properties (e.g.\, connectivity and Hamiltonicity) there is a critical probability $p_c$ such that if $p >> p_c$ then $G(n;p)$ possesses the property with high probability (i.e.\, with probability tending to 1 as $n \to \infty$) whereas if $p << p_c$ then with high probability $G(n;p)$ does not possess the property. In this talk we will focus on basic properties such as connectivity and containing a perfect matching. We will see an intriguing connection between these global properties and the local property of having no isolated vertices. We will then generalize the Erdos-Renyi model to higher dimensions where many open problems remain.
URL:https://cmsa.fas.harvard.edu/event/9-10-2021-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210910T184400
DTEND;TZID=America/New_York:20210910T194400
DTSTAMP:20260503T103211
CREATED:20240214T092532Z
LAST-MODIFIED:20240301T095315Z
UID:10002624-1631299440-1631303040@cmsa.fas.harvard.edu
SUMMARY:More Exact Results in Gauge Theories: Confinement and Chiral Symmetry Breaking
DESCRIPTION:Title: More Exact Results in Gauge Theories: Confinement and Chiral Symmetry Breaking \nAbstract: In this follow-up to Hitoshi Murayama’s talk “Some Exact Results in QCD-like and Chiral Gauge Theories”\, I present a detailed analysis of the phases of $SO(N_c)$ gauge theory.\nStarting with supersymmetric $SO(N_c)$ with $N_F$ flavors\, we extrapolate to the non-supersymmetric limit using anomaly-mediated supersymmetry breaking (AMSB). Interestingly\, the abelian Coulomb and free magnetic phases do not survive supersymmetry breaking and collapse to a confining phase. This provided one of the first demonstrations of true confinement with chiral symmetry breaking in a non-SUSY theory.
URL:https://cmsa.fas.harvard.edu/event/9-10-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210911T093000
DTEND;TZID=America/New_York:20210911T103000
DTSTAMP:20260503T103211
CREATED:20240222T111949Z
LAST-MODIFIED:20240222T112111Z
UID:10002807-1631352600-1631356200@cmsa.fas.harvard.edu
SUMMARY:Gradient flows on totally nonnegative flag varieties
DESCRIPTION:Abstract: One can view a partial flag variety in C^n as an adjoint orbit inside the Lie algebra of n x n skew-Hermitian matrices. We use the orbit context to study the totally nonnegative part of a partial flag variety from an algebraic\, geometric\, and dynamical perspective. We classify gradient flows on adjoint orbits in various metrics which are compatible with total positivity. As applications\, we show how the classical Toda flow fits into this framework\, and prove that a new family of amplituhedra are homeomorphic to closed balls. This is joint work with Anthony Bloch.
URL:https://cmsa.fas.harvard.edu/event/11-9-21-combinatorics-physics-and-probability-seminar/
CATEGORIES:Combinatorics Physics and Probability
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210913T090000
DTEND;TZID=America/New_York:20220513T170000
DTSTAMP:20260503T103211
CREATED:20230904T083009Z
LAST-MODIFIED:20240213T113945Z
UID:10000053-1631523600-1652461200@cmsa.fas.harvard.edu
SUMMARY:Swampland Program
DESCRIPTION:During the 2021–2022 academic year\, the CMSA will host a program on the so-called “Swampland.” \nThe Swampland program aims to determine which low-energy effective field theories are consistent with nonperturbative quantum gravity considerations. Not everything is possible in String Theory\, and finding out what is and what is not strongly constrains the low energy physics. These constraints are naturally interesting for particle physics and cosmology\,  which has led to a great deal of activity in the field in the last years. \nThe Swampland is intrinsically interdisciplinary\, with ramifications in string compactifications\, holography\, black hole physics\, cosmology\, particle physics\, and even mathematics. \nThis program will include an extensive group of visitors and a slate of seminars. Additionally\, the CMSA will host a school oriented toward graduate students. \nMore information will be posted here. \nSeminars\nSwampland Seminar Series & Group Meetings \nProgram Visitors\n\nPieter Bomans\, Princeton\, 10/30/21 – 11/02/21\nIrene Valenzuela\, Instituto de Física Teórica\, 02/14/22 – 02/21/22\nMariana Grana\, CEA/Saclay\, 03/21/22 – 03/25/22\nHector Parra De Freitas\, IPHT Saclay\, 03/21/22 – 04/01/22\nTimo Weigand\, 03/21/22 – 03/28/22\nGary Shiu\, University of Wisconsin-Madison\, 04/03/22 – 04/10/22\nThomas van Riet\, Leuven University\, 04/03/22 – 04/09/22\nLars Aalsma\, University of Wisconsin-Madison\, 04/11/22 – 04/15/22\nSergio Cecotti\, 05/08/22 – 05/21/22\nTom Rudelius\, 05/09/22 – 05/13/22
URL:https://cmsa.fas.harvard.edu/event/swampland-program/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Programs
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210913T100000
DTEND;TZID=America/New_York:20210913T113000
DTSTAMP:20260503T103211
CREATED:20240213T111138Z
LAST-MODIFIED:20240304T102959Z
UID:10002481-1631527200-1631532600@cmsa.fas.harvard.edu
SUMMARY:Decoding Divergent Distances
DESCRIPTION:Speaker: John Stout\, Harvard University \nTitle: Decoding Divergent Distances \nAbstract: Motivated by a relationship between the Zamolodchikov and NLSM metrics to the so-called quantum information metric\, I will discuss recent work (2106.11313) on understanding infinite distance limits within the context of information theory. I will describe how infinite distance points represent theories that are hyper-distinguishable\, in the sense that they can be distinguished from “nearby” theories with certainty in relatively few measurements. I will then discuss necessary and sufficient ingredients for the appearance of these infinite distance points\, illustrate these in simple examples\, and describe how this perspective can help the swampland program.
URL:https://cmsa.fas.harvard.edu/event/9-13-2021-swampland-seminar/
CATEGORIES:Swampland Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210914T110200
DTEND;TZID=America/New_York:20210914T120200
DTSTAMP:20260503T103211
CREATED:20240214T055014Z
LAST-MODIFIED:20240304T064603Z
UID:10002544-1631617320-1631620920@cmsa.fas.harvard.edu
SUMMARY:Simplices in the Calabi–Yau web
DESCRIPTION:Abstract: Calabi–Yau manifolds of a given dimension are connected by an intricate web of birational maps. This web has deep consequences for the derived categories of coherent sheaves on such manifolds\, and for the associated string theories. In particular\, for 4-folds and beyond\, I will highlight certain simplices appearing in the web\, and identify corresponding derived category structures.
URL:https://cmsa.fas.harvard.edu/event/simplices-in-the-calabi-yau-web/
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210915T093000
DTEND;TZID=America/New_York:20210915T103000
DTSTAMP:20260503T103211
CREATED:20240214T044745Z
LAST-MODIFIED:20240501T205627Z
UID:10002533-1631698200-1631701800@cmsa.fas.harvard.edu
SUMMARY:Hyperbolic Geometry and Quantum Invariants
DESCRIPTION:Speaker: Tian Yang (Texas A&M University) \nTitle: Hyperbolic Geometry and Quantum Invariants \nAbstract: There are two very different approaches to 3-dimensional topology\, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk\, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.
URL:https://cmsa.fas.harvard.edu/event/hyperbolic-geometry-and-quantum-invariants/
LOCATION:Virtual
CATEGORIES:Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210915T093000
DTEND;TZID=America/New_York:20220525T103000
DTSTAMP:20260503T103211
CREATED:20240213T112446Z
LAST-MODIFIED:20240502T160729Z
UID:10002496-1631698200-1653474600@cmsa.fas.harvard.edu
SUMMARY:CMSA Colloquium 9/15/2021 - 5/25/2022
DESCRIPTION:During the 2021–22 academic year\, the CMSA will be hosting a Colloquium\, organized by Du Pei\, Changji Xu\, and Michael Simkin. It will take place on Wednesdays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars\, as well as the weekly CMSA Colloquium series. The schedule below will be updated as talks are confirmed. \nSpring 2022\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n1/26/2022\nSamir Mathur (Ohio State University)\nTitle: The black hole information paradox \nAbstract: In 1975\, Stephen Hawking showed that black holes radiate away in a manner that violates quantum theory. Starting in 1997\, it was observed that black holes in string theory did not have the form expected from general relativity: in place of “empty space will all the mass at the center\,” one finds a “fuzzball” where the mass is distributed throughout the interior of the horizon. This resolves the paradox\, but opposition to this resolution came from groups who sought to extrapolate some ideas in holography. In 2009 it was shown\, using some theorems from quantum information theory\, that these extrapolations were incorrect\, and the fuzzball structure was essential for resolving the puzzle. Opposition continued along different lines\, with a postulate that information would leak out through wormholes. Recently\, it was shown that this wormhole idea had some basic flaws\, leaving the fuzzball paradigm as the natural resolution of Hawking’s puzzle. \nVideo\n\n\n2/2/2022\nAdam Smith (Boston University)\nTitle: Learning and inference from sensitive data \nAbstract: Consider an agency holding a large database of sensitive personal information—say\,  medical records\, census survey answers\, web searches\, or genetic data. The agency would like to discover and publicly release global characteristics of the data while protecting the privacy of individuals’ records. \nI will discuss recent (and not-so-recent) results on this problem with a focus on the release of statistical models. I will first explain some of the fundamental limitations on the release of machine learning models—specifically\, why such models must sometimes memorize training data points nearly completely. On the more positive side\, I will present differential privacy\, a rigorous definition of privacy in statistical databases that is now widely studied\, and increasingly used to analyze and design deployed systems. I will explain some of the challenges of sound statistical inference based on differentially private statistics\, and lay out directions for future investigation.\n\n\n2/8/2022\nWenbin Yan (Tsinghua University)\n(special time: 9:30 pm ET)\nTitle: Tetrahedron instantons and M-theory indices \nAbstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk\, we will review instanton moduli spaces\, explain the construction\, moduli space and partition functions of tetrahedron instantons. We will also point out possible relations with M-theory index which could be a generalization of Gupakuma-Vafa theory. \nVideo\n\n\n2/16/2022\nTakuro Mochizuki (Kyoto University)\nTitle: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles \nAbstract: In 1960’s\, Narasimhan and Seshadri discovered the equivalence\nbetween irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980’s\, Donaldson\, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles\nand stable bundles on smooth projective varieties. This is a surprising bridge connecting differential geometry and algebraic geometry. Since then\, many interesting generalizations have been studied. \nIn this talk\, we would like to review a stream in the study of such correspondences for Higgs bundles\, integrable connections\, $D$-modules and periodic monopoles.\n\n\n2/23/2022\nBartek Czech (Tsinghua University)\nTitle: Holographic Cone of Average Entropies and Universality of Black Holes \nAbstract:  In the AdS/CFT correspondence\, the holographic entropy cone\, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual\, is currently known only up to n=5 regions. I explain that average\nentropies of p-partite subsystems can be checked for consistency with a semiclassical bulk dual far more easily\, for an arbitrary number of regions n. This analysis defines the “Holographic Cone of Average\nEntropies” (HCAE). I conjecture the exact form of HCAE\, and find that it has the following properties: (1) HCAE is the simplest it could be\, namely it is a simplicial cone. (2) Its extremal rays represent stages of thermalization (black hole formation). (3) In a time-reversed picture\, the extremal rays of HCAE represent stages of unitary black hole evaporation\, as stipulated by the island solution of the black hole information paradox. (4) HCAE is bound by a novel\, infinite family of holographic entropy inequalities. (5) HCAE is the simplest it could be also in its dependence on the number of regions n\, namely its bounding inequalities are n-independent. (6) In a precise sense I describe\, the bounding inequalities of HCAE unify (almost) all previously discovered holographic inequalities and strongly constrain future inequalities yet to be discovered. I also sketch an interpretation of HCAE in terms of error correction and the holographic Renormalization Group. The big lesson that HCAE seems to be teaching us is about the universality of black hole physics.\n\n\n3/2/2022\nRichard Kenyon (Yale University)\n\n\n\n3/9/2022\nRichard Tsai (UT Austin)\n\n\n\n3/23/2022\nJoel Cohen (University of Maryland)\n\n\n\n3/30/2022\nRob Leigh (UIUC)\n\n\n\n4/6/2022\nJohannes Kleiner (LMU München)\n\n\n\n4/13/2022\nYuri Manin (Max-Planck-Institut für Mathematik)\n\n\n\n4/20/2022\nTBA\n\n\n\n4/27/2022\nTBA\n\n\n\n5/4/2022\nMelody Chan (Brown University)\n\n\n\n5/11/2022\nTBA\n\n\n\n5/18/2022\nTBA\n\n\n\n5/25/2022\nHeeyeon Kim (Rutgers University)\n\n\n\n\n\nFall 2021\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n9/15/2021\nTian Yang\, Texas A&M\nTitle: Hyperbolic Geometry and Quantum Invariants \nAbstract: There are two very different approaches to 3-dimensional topology\, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk\, I will explain these conjectures and present some recent joint works with Ka Ho Wong related to or benefited from this relationship.\n\n\n9/29/2021\nDavid Jordan\, University of Edinburgh\nTitle: Langlands duality for 3 manifolds \nAbstract: Langlands duality began as a deep and still mysterious conjecture in number theory\, before branching into a similarly deep and mysterious conjecture of Beilinson and Drinfeld concerning the algebraic geometry of Riemann surfaces. In this guise it was given a physical explanation in the framework of 4-dimensional super symmetric quantum field theory by Kapustin and Witten.  However to this day the Hilbert space attached to 3-manifolds\, and hence the precise form of Langlands duality for them\, remains a mystery. \nIn this talk I will propose that so-called “skein modules” of 3-manifolds give natural candidates for these Hilbert spaces at generic twisting parameter Psi \, and I will explain a Langlands duality in this setting\, which we have conjectured with Ben-Zvi\, Gunningham and Safronov. \nIntriguingly\, the precise formulation of such a conjecture in the classical limit Psi=0 is still an open question\, beyond the scope of the talk.\n\n\n10/06/2021\nPiotr Sulkowski\, U Warsaw\nTitle: Strings\, knots and quivers \nAbstract: I will discuss a recently discovered relation between quivers and knots\, as well as – more generally – toric Calabi-Yau manifolds. In the context of knots this relation is referred to as the knots-quivers correspondence\, and it states that various invariants of a given knot are captured by characteristics of a certain quiver\, which can be associated to this knot. Among others\, this correspondence enables to prove integrality of LMOV invariants of a knot by relating them to motivic Donaldson-Thomas invariants of the corresponding quiver\, it provides a new insight on knot categorification\, etc. This correspondence arises from string theory interpretation and engineering of knots in brane systems in the conifold geometry; replacing the conifold by other toric Calabi-Yau manifolds leads to analogous relations between such manifolds and quivers.\n\n\n10/13/2021\nAlexei Oblomkov\, University of Massachusetts\nTitle: Knot homology and sheaves on the Hilbert scheme of points on the plane. \nAbstract: The knot homology (defined by Khovavov\, Rozansky) provide us with a refinement of the knot polynomial knot invariant defined by Jones. However\, the knot homology are much harder to compute compared to the polynomial invariant of Jones. In my talk I present recent developments that allow us to use tools of algebraic geometry to compute the homology of torus knots and prove long-standing conjecture on the Poincare duality the knot homology. In more details\, using physics ideas of Kapustin-Rozansky-Saulina\, in the joint work with Rozansky\, we provide a mathematical construction that associates to a braid on n strands a complex of sheaves on the Hilbert scheme of n points on the plane.  The knot homology of the closure of the braid is a space of sections of this sheaf. The sheaf is also invariant with respect to the natural symmetry of the plane\, the symmetry is the geometric counter-part of the mentioned Poincare duality.\n\n\n10/20/2021\nPeng Shan\, Tsinghua U\nTitle: Categorification and applications \nAbstract: I will give a survey of the program of categorification for quantum groups\, some of its recent development and applications to representation theory.\n\n\n10/27/2021\nKarim Adiprasito\, Hebrew University and University of Copenhagen\nTitle: Anisotropy\, biased pairing theory and applications \nAbstract: Not so long ago\, the relations between algebraic geometry and combinatorics were strictly governed by the former party\, with results like log-concavity of the coefficients of the characteristic polynomial of matroids shackled by intuitions and techniques from projective algebraic geometry\, specifically Hodge Theory. And so\, while we proved analogues for these results\, combinatorics felt subjugated to inspirations from outside of it.\nIn recent years\, a new powerful technique has emerged: Instead of following the geometric statements of Hodge theory about signature\, we use intuitions from the Hall marriage theorem\, translated to algebra: once there\, they are statements about self-pairings\, the non-degeneracy of pairings on subspaces to understand the global geometry of the pairing. This was used to establish Lefschetz type theorems far beyond the scope of algebraic geometry\, which in turn established solutions to long-standing conjectures in combinatorics. \nI will survey this theory\, called biased pairing theory\, and new developments within it\, as well as new applications to combinatorial problems. Reporting on joint work with Stavros Papadaki\, Vasiliki Petrotou and Johanna Steinmeyer.\n\n\n11/03/2021\nTamas Hausel\, IST Austria\nTitle: Hitchin map as spectrum of equivariant cohomology \nAbstract: We will explain how to model the Hitchin integrable system on a certain Lagrangian upward flow as the spectrum of equivariant cohomology of a Grassmannian.\n\n\n11/10/2021\nPeter Keevash\, Oxford\nTitle: Hypergraph decompositions and their applications \nAbstract: Many combinatorial objects can be thought of as a hypergraph decomposition\, i.e. a partition of (the edge set of) one hypergraph into (the edge sets of) copies of some other hypergraphs. For example\, a Steiner Triple System is equivalent to a decomposition of a complete graph into triangles. In general\, Steiner Systems are equivalent to decompositions of complete uniform hypergraphs into other complete uniform hypergraphs (of some specified sizes). The Existence Conjecture for Combinatorial Designs\, which I proved in 2014\, states that\, bar finitely many exceptions\, such decompositions exist whenever the necessary ‘divisibility conditions’ hold. I also obtained a generalisation to the quasirandom setting\, which implies an approximate formula for the number of designs; in particular\, this resolved Wilson’s Conjecture on the number of Steiner Triple Systems. A more general result that I proved in 2018 on decomposing lattice-valued vectors indexed by labelled complexes provides many further existence and counting results for a wide range of combinatorial objects\, such as resolvable designs (the generalised form of Kirkman’s Schoolgirl Problem)\, whist tournaments or generalised Sudoku squares. In this talk\, I plan to review this background and then describe some more recent and ongoing applications of these results and developments of the ideas behind them.\n\n\n11/17/2021\nAndrea Brini\, U Sheffield\nTitle: Curve counting on surfaces and topological strings \nAbstract: Enumerative geometry is a venerable subfield of Mathematics\, with roots dating back to Greek Antiquity and a present inextricably linked with developments in other domains. Since the early 90s\, in particular\, the interaction with String Theory has sent shockwaves through the subject\, giving both unexpected new perspectives and a remarkably powerful\, physics-motivated toolkit to tackle several traditionally hard questions in the field.\nI will survey some recent developments in this vein for the case of enumerative invariants associated to a pair (X\, D)\, with X a complex algebraic surface and D a singular anticanonical divisor in it. I will describe a surprising web of correspondences linking together several a priori distant classes of enumerative invariants associated to (X\, D)\, including the log Gromov-Witten invariants of the pair\, the Gromov-Witten invariants of an associated higher dimensional Calabi-Yau variety\, the open Gromov-Witten invariants of certain special Lagrangians in toric Calabi–Yau threefolds\, the Donaldson–Thomas theory of a class of symmetric quivers\, and certain open and closed Gopakumar-Vafa-type invariants. I will also discuss how these correspondences can be effectively used to provide a complete closed-form solution to the calculation of all these invariants.\n\n\n12/01/2021\nRichard Wentworth\, University of Maryland\nTitle: The Hitchin connection for parabolic G-bundles \nAbstract: For a simple and simply connected complex group G\, I will discuss some elements of the proof of the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of smooth projective curves with marked points. Under the isomorphism with the bundle of conformal blocks\, this connection is equivalent to the one constructed by conformal field theory. This is joint work with Indranil Biswas and Swarnava Mukhopadhyay.\n\n\n12/08/2021\nMaria Chudnovsky\, Princeton\nTitle: Induced subgraphs and tree decompositions \nAbstract: Tree decompositions are a powerful tool in both structural\ngraph theory and graph algorithms. Many hard problems become tractable if the input graph is known to have a tree decomposition of bounded “width”. Exhibiting a particular kind of a tree decomposition is also a useful way to describe the structure of a graph. \nTree decompositions have traditionally been used in the context of forbidden graph minors; bringing them into the realm of forbidden induced subgraphs has until recently remained out of reach. Over the last couple of years we have made significant progress in this direction\, exploring both the classical notion of bounded tree-width\, and concepts of more structural flavor. This talk will survey some of these ideas and results.\n\n\n12/15/21\nConstantin Teleman (UC Berkeley)\nTitle: The Kapustin-Rozanski-Saulina “2-category” of a holomorphic integrable system \nAbstract: I will present a construction of the object in the title which\, applied to the classical Toda system\, controls the theory of categorical representations of compact Lie groups\, along with applications (some conjectural\, some rigorous) to gauged Gromov-Witten theory. Time permitting\, we will review applications to Coulomb branches and the categorified Weyl character formula.
URL:https://cmsa.fas.harvard.edu/event/cmsa-colloquium_2021-22/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210915T150000
DTEND;TZID=America/New_York:20210915T160000
DTSTAMP:20260503T103211
CREATED:20240214T091846Z
LAST-MODIFIED:20240517T200145Z
UID:10002618-1631718000-1631721600@cmsa.fas.harvard.edu
SUMMARY:Why abstraction is the key to intelligence\, and what we’re still missing
DESCRIPTION:Speaker: Francois Chollet\, Google \nTitle: Why abstraction is the key to intelligence\, and what we’re still missing \nAbstract: This talk provides a personal perspective on the way forward towards more human-like and more intelligent artificial systems. Traditionally\, symbolic and probabilistic methods have dominated the domains of concept formation\, abstraction\, and automated reasoning. More recently\, deep learning-based approaches have led to significant breakthroughs\, including successes in games and combinatorial search tasks. However\, the resulting systems are still limited in scope and capabilities — they remain brittle\, data-hungry\, and their generalization capabilities are limited. We will address a set of questions: why is conceptual abstraction essential for intelligence? What is the nature of abstraction\, and its relationship to generalization? What kind of abstraction can deep learning models generate\, and where do they fail? What are the methods that are currently successful in generating strong conceptual abstraction? Finally\, we will consider how to leverage a hybrid approach to reinforce the strength of different approaches while compensating for their respective weaknesses.
URL:https://cmsa.fas.harvard.edu/event/9-15-2021-new-technologies-in-mathematics-seminar/
CATEGORIES:New Technologies in Mathematics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210915T184600
DTEND;TZID=America/New_York:20210915T194600
DTSTAMP:20260503T103211
CREATED:20240214T092313Z
LAST-MODIFIED:20240301T094948Z
UID:10002623-1631731560-1631735160@cmsa.fas.harvard.edu
SUMMARY:Three-particle mechanism for pairing and superconductivity
DESCRIPTION:Title: Three-particle mechanism for pairing and superconductivity \nAbstract: I will present a new mechanism and an exact theory of electron pairing due to repulsive interaction in doped insulators. When the kinetic energy is small\, the dynamics of adjacent electrons on the lattice is strongly correlated. By developing a controlled kinetic energy expansion\, I will show that two doped charges can attract and form a bound state\, despite and because of the underlying repulsion. This attraction by repulsion is enabled by the virtual excitation of a third electron in the filled band. This three-particle pairing mechanism leads to a variety of novel phenomena at finite doping\, including spin-triplet superconductivity\, pair density wave\, BCS-BEC crossover and Feshbach resonance involving “trimers”. Possible realizations in moire materials\, ZrNCl and WTe2 will be discussed. \n[1] V. Crepel and L. Fu\, Science Advances 7\, eabh2233 (2021)\n[2] V. Crepel and L. Fu\, arXiv:2103.12060\n[3] K. Slagle and L. Fu\,  Phys. Rev. B 102\, 235423 (2020)
URL:https://cmsa.fas.harvard.edu/event/9-15-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210916T184700
DTEND;TZID=America/New_York:20210916T194700
DTSTAMP:20260503T103211
CREATED:20240214T092053Z
LAST-MODIFIED:20240301T094752Z
UID:10002619-1631818020-1631821620@cmsa.fas.harvard.edu
SUMMARY:The Hilbert Space of large N Chern-Simons matter theories
DESCRIPTION:Title: The Hilbert Space of large N Chern-Simons matter theories \nAbstract: We demonstrate that all known formulae for the thermal partition function for large N Chern Simons matter theory admit a simple Hilbert Space interpretation. In each case this quantity equals the partition function of an associated ungauged large $N$ matter theory with a particular local Lagrangian with one additional element: the Fock Space of this associated theory is projected down to the subspace of its WZW singlets. This projection\, in particular\,  implies the previously encountered `Bosonic Exclusion Principle’\, namely that no single particle state can be occupied by more than $k_B$ particles ($k_B$ is the Chern Simons level). Unlike its Gauss Law counterpart\, the WZW constraint does not trivialize in the large volume limit. However thermodynamics does simplify in this limit;  the final partition function reduces to a product of partition functions associated with each single particle state. These individual single particle state partition functions are a one parameter generalizations of their free boson and free fermion counterparts\, and reduce to the later at extreme values of the ‘t Hooft coupling. At generic values of the rank and the level the occupation statistics of each energy level is given by a $q$ deformation of the usual free formulae of Bose and Fermi statistics.
URL:https://cmsa.fas.harvard.edu/event/9-16-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210917T093000
DTEND;TZID=America/New_York:20210917T103000
DTSTAMP:20260503T103211
CREATED:20240213T105100Z
LAST-MODIFIED:20240304T105845Z
UID:10002462-1631871000-1631874600@cmsa.fas.harvard.edu
SUMMARY:9/17/2021 General Relativity Seminar
DESCRIPTION:Title: Stable Big Bang formation for the Einstein equations \nAbstract: I will discuss recent work concerning stability of cosmological singularities described by the generalized Kasner solutions. There are heuristics in the mathematical physics literature\, going back more than 50 years\, suggesting that the Big Bang formation should be stable under perturbations of the Kasner initial data\, as long as the Kasner exponents are “sub-critical”. We prove that the Kasner singularity is dynamically stable for all sub-critical Kasner exponents\, thereby justifying the heuristics in the full regime where stable monotonic-type curvature blowup is expected. We treat the 3+1-dimensional Einstein-scalar field system and the D+1-dimensional Einstein-vacuum equations for D≥10. This is joint work with Speck and Fournodavlos.
URL:https://cmsa.fas.harvard.edu/event/9-17-2021-general-relativity-seminar/
CATEGORIES:General Relativity Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210917T093000
DTEND;TZID=America/New_York:20210917T103000
DTSTAMP:20260503T103211
CREATED:20240214T080149Z
LAST-MODIFIED:20240301T112535Z
UID:10002577-1631871000-1631874600@cmsa.fas.harvard.edu
SUMMARY:Geometry\, Entanglement and Quasi Local Data
DESCRIPTION:Member Seminar \nSpeaker: Itamar Shamir \nTitle: Geometry\, Entanglement and Quasi Local Data \nAbstract: I will review some general ideas about gravity as motivation for an approach based on quasi local quantities.
URL:https://cmsa.fas.harvard.edu/event/9-17-2021-member-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210917T185400
DTEND;TZID=America/New_York:20210917T195400
DTSTAMP:20260503T103211
CREATED:20240214T091836Z
LAST-MODIFIED:20240301T094616Z
UID:10002617-1631904840-1631908440@cmsa.fas.harvard.edu
SUMMARY:Strong Coupling Theory of Magic-Angle Graphene: A Pedagogical Introduction
DESCRIPTION:Title: Strong Coupling Theory of Magic-Angle Graphene: A Pedagogical Introduction \nAbstract: In this talk\, I will review a recently developed strong coupling theory of magic-angle twisted bilayer graphene. An advantage of this approach is that a single formulation can capture both the insulating and superconducting states\, and with a few simplifying assumptions\, can be treated analytically. I begin by reviewing the electronic structure of magic angle graphene’s flat bands\, in a limit that exposes their peculiar band topology and geometry. I will show how similarities between the flat bands and the lowest Landau level can provide valuable insights into the effect of interactions and form the basis for an analytic treatment of the problem. At integer fillings\, this approach points to flavor ordered insulators\, which can be captured by a sigma-model in its ordered phase. Remarkably\, topological textures of the sigma model carry electric charge which enables the same theory to describe the doped phases away from integer filling. I will show how this approach can lead to superconductivity on disordering the sigma model\, and estimate the Tc for the superconductor. I will highlight the important role played by an effective super-exchange coupling both in pairing and in setting the effective mass of Cooper pairs. At the end\, I will show how this theory provides criteria to predict which multilayer graphene stacks are expected to superconduct including the recently discovered alternating twist trilayer platform.
URL:https://cmsa.fas.harvard.edu/event/9-17-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210920T100000
DTEND;TZID=America/New_York:20210920T110000
DTSTAMP:20260503T103211
CREATED:20240213T111241Z
LAST-MODIFIED:20240304T105156Z
UID:10002482-1632132000-1632135600@cmsa.fas.harvard.edu
SUMMARY:Small Cosmological Constants in String Theory
DESCRIPTION:Abstract: We construct supersymmetric AdS4 vacua of type IIB string theory in compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. We first find explicit orientifolds and quantized fluxes for which the superpotential takes the form proposed by Kachru\, Kallosh\, Linde\, and Trivedi. Given very mild assumptions on the numerical values of the Pfaffians\, these compactifications admit vacua in which all moduli are stabilized at weak string coupling. By computing high-degree Gopakumar-Vafa invariants we give strong evidence that the α 0 expansion is likewise well-controlled. We find extremely small cosmological constants\, with magnitude < 10^{-123} in Planck units. The compactifications are large\, but not exponentially so\, and hence these vacua manifest hierarchical scale-separation\, with the AdS length exceeding the Kaluza-Klein length by a factor of a googol.
URL:https://cmsa.fas.harvard.edu/event/9-20-2021-swampland-seminar/
CATEGORIES:Swampland Seminar
END:VEVENT
END:VCALENDAR