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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/
LOCATION:MA
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
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210913T090000
DTEND;TZID=America/New_York:20220513T170000
DTSTAMP:20260510T025302
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:20210915T093000
DTEND;TZID=America/New_York:20220525T103000
DTSTAMP:20260510T025302
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:20211021T153000
DTEND;TZID=America/New_York:20211021T170000
DTSTAMP:20260510T025302
CREATED:20240214T102900Z
LAST-MODIFIED:20240301T091902Z
UID:10002672-1634830200-1634835600@cmsa.fas.harvard.edu
SUMMARY:Electric-magnetic duality and the Geometric Langlands duality
DESCRIPTION:Title: Electric-magnetic duality and the Geometric Langlands duality \nAbstract: I will give a pedagogical review of the connection between electric-magnetic duality and the Geometric Langlands duality.
URL:https://cmsa.fas.harvard.edu/event/10-21-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211021T184400
DTEND;TZID=America/New_York:20211021T204400
DTSTAMP:20260510T025302
CREATED:20240214T082555Z
LAST-MODIFIED:20240301T104328Z
UID:10002587-1634841840-1634849040@cmsa.fas.harvard.edu
SUMMARY:10/21/2021 Interdisciplinary Science Seminar
DESCRIPTION:Title: Mathematical resolution of the Liouville conformal field theory. \nAbstract: The Liouville conformal field theory is a well-known beautiful quantum field theory in physics describing random surfaces. Only recently a mathematical approach based on a well-defined path integral to this theory has been proposed using probability by David\, Kupiainen\, Rhodes\, Vargas. \nMany works since the ’80s in theoretical physics (starting with Belavin-Polyakov-Zamolodchikov) tell us that conformal field theories in dimension 2 are in general « Integrable »\, the correlations functions are solutions of PDEs and can in principle be computed explicitely by using algebraic tools (vertex operator algebras\, representations of Virasoro algebras\, the theory of conformal blocks). However\, for Liouville Theory this was not done at the mathematical level by algebraic methods. \nI’ll explain how to combine probabilistic\, analytic and geometric tools to give explicit (although complicated) expressions for all the correlation functions on all Riemann surfaces in terms of certain holomorphic functions of the moduli parameters called conformal blocks\, and of the structure constant (3-point function on the sphere). This gives a concrete mathematical proof of the so-called conformal bootstrap and of Segal’s gluing axioms for this CFT. The idea is to break the path integral on a closed surface into path integrals on pairs of pants and reduce all correlation functions to the 3-point correlation function on the Riemann sphere $S^2$. This amounts in particular to prove a spectral resolution of a certain operator acting on $L^2(H^{-s}(S^1))$ where $H^{-s}(S^1)$ is the Sobolev space of order -s<0 equipped with a Gaussian measure\, which is viewed as the space of fields\, and to construct a certain representation of the Virasoro algebra into unbounded operators acting on this Hilbert space. \nThis is joint work with A. Kupiainen\, R. Rhodes and V. Vargas.
URL:https://cmsa.fas.harvard.edu/event/10-21-2021-interdisciplinary-science-seminar/
LOCATION:MA
CATEGORIES:Interdisciplinary Science Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211022T093000
DTEND;TZID=America/New_York:20211022T103000
DTSTAMP:20260510T025302
CREATED:20240213T105511Z
LAST-MODIFIED:20240304T101145Z
UID:10002466-1634895000-1634898600@cmsa.fas.harvard.edu
SUMMARY:The Large D Limit of Einstein’s Equations
DESCRIPTION:Abstract: Taking the large dimension limit of Einstein’s equations is a useful strategy for solving and understanding the dynamics that these equations encode. I will introduce the underlying ideas and the progress that has resulted in recent years from this line of research. Most of the discussion will be classical in nature and will concern situations where there is a black hole horizon. A main highlight of this approach is the formulation of effective membrane theories of black hole dynamics. These have made possible to efficiently study\, with relatively simple techniques\, some of the thorniest problems in black hole physics\, such as the non-linear evolution of the instabilities of black strings and black branes\, and the collisions and mergers of higher-dimensional black holes. Open directions and opportunities will also be discussed. To get a flavor of what this is about\, you may read the first few pages of the review (with C.P. Herzog) e-Print: 2003.11394.
URL:https://cmsa.fas.harvard.edu/event/10-22-2021-general-relativity-seminar/
LOCATION:MA
CATEGORIES:General Relativity Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211022T093000
DTEND;TZID=America/New_York:20211022T103000
DTSTAMP:20260510T025302
CREATED:20240214T073722Z
LAST-MODIFIED:20240301T111559Z
UID:10002564-1634895000-1634898600@cmsa.fas.harvard.edu
SUMMARY:Wall-crossing from Higgs bundles to vortices
DESCRIPTION:Speaker: Du Pei \nTitle: Wall-crossing from Higgs bundles to vortices \nAbstract: Quantum field theories can often be used to uncover hidden algebraic structures in geometry and hidden geometric structures in algebra. In this talk\, I will demonstrate how such “wall-crossing” can relate the moduli space of Higgs bundles with the moduli space of vortices.
URL:https://cmsa.fas.harvard.edu/event/10-22-2021-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211025T130000
DTEND;TZID=America/New_York:20211025T140000
DTSTAMP:20260510T025302
CREATED:20240214T093259Z
LAST-MODIFIED:20240301T082800Z
UID:10002633-1635166800-1635170400@cmsa.fas.harvard.edu
SUMMARY:Exploring the Holographic Swampland
DESCRIPTION:Abstract: 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.
URL:https://cmsa.fas.harvard.edu/event/10-25-2021-swampland-seminar/
LOCATION:MA
CATEGORIES:Swampland Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211026T090000
DTEND;TZID=America/New_York:20211026T100000
DTSTAMP:20260510T025302
CREATED:20240213T113529Z
LAST-MODIFIED:20240304T101126Z
UID:10002507-1635238800-1635242400@cmsa.fas.harvard.edu
SUMMARY:The n-queens problem
DESCRIPTION:Abstract: The n-queens problem asks how many ways there are to place n queens on an n x n chessboard so that no two queens can attack one another\, and the toroidal n-queens problem asks the same question where the board is considered on the surface of a torus. Let Q(n) denote the number of n-queens configurations on the classical board and T(n) the number of toroidal n-queens configurations. The toroidal problem was first studied in 1918 by Pólya who showed that T(n)>0 if and only if n is not divisible by 2 or 3. Much more recently Luria showed that T(n) is at most ((1+o(1))ne^{-3})^n and conjectured equality when n is not divisible by 2 or 3. We prove this conjecture\, prior to which no non-trivial lower bounds were known to hold for all (sufficiently large) n not divisible by 2 or 3. We also show that Q(n) is at least ((1+o(1))ne^{-3})^n for all natural numbers n which was independently proved by Luria and Simkin and\, combined with our toroidal result\, completely settles a conjecture of Rivin\, Vardi and Zimmerman regarding both Q(n) and T(n). \nIn this talk we’ll discuss our methods used to prove these results. A crucial element of this is translating the problem to one of counting matchings in a 4-partite 4-uniform hypergraph. Our strategy combines a random greedy algorithm to count `almost’ configurations with a complex absorbing strategy that uses ideas from the methods of randomised algebraic construction and iterative absorption. \nThis is joint work with Peter Keevash.
URL:https://cmsa.fas.harvard.edu/event/10-26-2021-combinatorics-physics-and-probability-seminar/
LOCATION:MA
CATEGORIES:Combinatorics Physics and Probability
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211026T130000
DTEND;TZID=America/New_York:20211026T140000
DTSTAMP:20260510T025302
CREATED:20240214T062643Z
LAST-MODIFIED:20240304T063155Z
UID:10002549-1635253200-1635256800@cmsa.fas.harvard.edu
SUMMARY:On singular Hilbert schemes of points
DESCRIPTION:Abstract: It is well known that the Hilbert schemes of points on smooth surfaces are smooth. In higher dimensions the Hilbert schemes of points are in general singular. In this talk we will present some examples and conjectures on the local structures of the Hilbert scheme of points on $\mathbb{P}^3$. As an application we study a conjecture of Wang-Zhou on the Euler characteristics of the tautological sheaves on Hilbert schemes of points.
URL:https://cmsa.fas.harvard.edu/event/on-singular-hilbert-schemes-of-points/
LOCATION:MA
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211027T093000
DTEND;TZID=America/New_York:20211027T103000
DTSTAMP:20260510T025302
CREATED:20240214T043101Z
LAST-MODIFIED:20240502T151724Z
UID:10002529-1635327000-1635330600@cmsa.fas.harvard.edu
SUMMARY:Anisotropy\, biased pairing theory and applications
DESCRIPTION:Speaker: Karim 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.
URL:https://cmsa.fas.harvard.edu/event/anisotropy-biased-pairing-theory-and-applications/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.27.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211027T140000
DTEND;TZID=America/New_York:20211027T150000
DTSTAMP:20260510T025302
CREATED:20240214T093929Z
LAST-MODIFIED:20240517T193105Z
UID:10002641-1635343200-1635346800@cmsa.fas.harvard.edu
SUMMARY:Why explain mathematics to computers?
DESCRIPTION:Speaker: Patrick Massot\, Laboratoire de Mathématiques d’Orsay and CNRS \nTitle: Why explain mathematics to computers? \nAbstract: A growing number of mathematicians are having fun explaining mathematics to computers using proof assistant softwares. This process is called formalization. In this talk I’ll describe what formalization looks like\, what kind of things it teaches us\, and how it could even turn out to be useful (in our usual sense of “useful”). This will not be a talk about foundations of mathematics\, and I won’t assume any prior knowledge about formalization.
URL:https://cmsa.fas.harvard.edu/event/10-27-2021-new-technologies-in-mathematics-seminar/
LOCATION:MA
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-10.27.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211028T093000
DTEND;TZID=America/New_York:20211028T103000
DTSTAMP:20260510T025302
CREATED:20240213T112817Z
LAST-MODIFIED:20240304T102039Z
UID:10002500-1635413400-1635417000@cmsa.fas.harvard.edu
SUMMARY:The classical interior of charged black holes with AdS asymptotics
DESCRIPTION:Abstract: The gravitational dual to the grand canonical ensemble of a large N holographic theory is a charged black hole. These spacetimes can have Cauchy horizons that render the classical gravitational dynamics of the black hole interior incomplete. We show that a (spatially uniform) deformation of the CFT by a neutral scalar operator generically leads to a black hole with no inner horizon. There is instead a spacelike Kasner singularity in the interior. For relevant deformations\, Cauchy horizons never form. We then consider charged scalars\, which are known to condense at low temperatures\, thus providing a holographic realization of superconductivity. We look inside the horizon of these holographic superconductors and find intricate dynamical behavior.  The spacetime ends at a spacelike Kasner singularity\, and there is no Cauchy horizon. Before reaching the singularity\, there are several intermediate regimes which we study both analytically and numerically. These include strong Josephson oscillations in the condensate and possible `Kasner inversions’ in which after many e-folds of expansion\, the Einstein-Rosen bridge contracts towards the singularity.  Due to the Josephson oscillations\, the number of Kasner inversions depends very sensitively on temperature\, and diverges at a discrete set of temperatures that accumulate at the critical temperature. Near this discrete set of temperatures\, the final Kasner exponent exhibits fractal-like behavior.
URL:https://cmsa.fas.harvard.edu/event/10-28-2021-general-relativity-seminar/
LOCATION:MA
CATEGORIES:General Relativity Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211028T130000
DTEND;TZID=America/New_York:20211028T143000
DTSTAMP:20260510T025302
CREATED:20240213T112644Z
LAST-MODIFIED:20240304T084647Z
UID:10002498-1635426000-1635431400@cmsa.fas.harvard.edu
SUMMARY:Drivers of Morphological Complexity
DESCRIPTION:Abstract: During development\, organisms interact with their natural habitats while undergoing morphological changes\, yet we know little about how the interplay between developing systems and their environments impacts animal morphogenesis. Cnidaria\, a basal animal lineage that includes sea anemones\, corals\, hydras\, and jellyfish\, offers unique insight into the development and evolution of morphological complexity.  In my talk\, I will introduce our research on “ethology of morphogenesis\,” a novel concept that links the behavior of organisms to the development of their size and shape at both cellular and biophysical levels\, opening new perspectives about the design principle of soft-bodied animals. In addition\, I will discuss a fascinating feature of cnidarian biology. For humans\, our genetic code determines that we will grow two arms and two legs. The same fate is true for all mammals. Similarly\, the number of fins of a fish or legs and wings of an insect is embedded in their genetic code. I will describe how sea anemones defy this rule. \nReferences\nAnniek Stokkermans\, Aditi Chakrabarti\, Ling Wang\, Prachiti Moghe\, Kaushikaram Subramanian\, Petrus Steenbergen\, Gregor Mönke\, Takashi Hiiragi\, Robert Prevedel\, L. Mahadevan\, and Aissam Ikmi. Ethology of morphogenesis reveals the design principles of cnidarian size and shape development. bioRxiv 2021.08.19.456976 \nIkmi A\, Steenbergen P\, Anzo M\, McMullen M\, Stokkermans M\, Ellington L\, and Gibson M (2020). Feeding-dependent tentacle development in the sea anemone Nematostella vectensis. Nature communications\, Sept 02; 11:4399 \nHe S\, Del Viso F\, Chen C\, Ikmi A\, Kroesen A\, Gibson MC (2018). An axial Hox code controls tissue segmentation and body patterning in Nematostella vectensis. Science\, Vol. 361\, Issue 6409\, pp. 1377-1380.\nIkmi A\, McKinney SA\, Delventhal KM\, Gibson MC (2014). TALEN and CRISPR/Cas9 mediated genome editing in the early-branching metazoan Nematostella vectensis. Nature communications. Nov 24; 5:5486.
URL:https://cmsa.fas.harvard.edu/event/drivers-of-morphological-complexity/
LOCATION:MA
CATEGORIES:Active Matter Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211028T184500
DTEND;TZID=America/New_York:20211028T204500
DTSTAMP:20260510T025302
CREATED:20240301T104157Z
LAST-MODIFIED:20240305T104709Z
UID:10002894-1635446700-1635453900@cmsa.fas.harvard.edu
SUMMARY:ARCH: Know What Your Machine Doesn’t Know
DESCRIPTION:Speaker: Jie Yang\, Delft University of Technology \nTitle: ARCH: Know What Your Machine Doesn’t Know \nAbstract: Despite their impressive performance\, machine learning systems remain prohibitively unreliable in safety-\, trust-\, and ethically sensitive domains. Recent discussions in different sub-fields of AI have reached the consensus of knowledge need in machine learning; few discussions have touched upon the diagnosis of what knowledge is needed. In this talk\, I will present our ongoing work on ARCH\, a knowledge-driven\, human-centered\, and reasoning-based tool\, for diagnosing the unknowns of a machine learning system. ARCH leverages human intelligence to create domain knowledge required for a given task and to describe the internal behavior of a machine learning system; it infers the missing or incorrect knowledge of the system with the built-in probabilistic\, abductive reasoning engine. ARCH is a generic tool that can be applied to machine learning in different contexts. In the talk\, I will present several applications in which ARCH is currently being developed and tested\, including health\, finance\, and smart buildings.
URL:https://cmsa.fas.harvard.edu/event/10-28-2021-interdisciplinary-science-seminar/
LOCATION:MA
CATEGORIES:Interdisciplinary Science Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211029T093000
DTEND;TZID=America/New_York:20211029T103000
DTSTAMP:20260510T025302
CREATED:20240214T073521Z
LAST-MODIFIED:20240301T111455Z
UID:10002563-1635499800-1635503400@cmsa.fas.harvard.edu
SUMMARY:The complex Monge-Ampere equation in K\”ahler geometry
DESCRIPTION:Speaker: Freid Tong \nTitle: The complex Monge-Ampere equation in Kahler geometry \nAbstract: The complex Monge-Ampere equations occupies an central role in K\”ahler geometry\, beginning with Yau’s famous solutions of the Calabi conjecture. Later developments has led to many interesting geometric applications and opening of new fields. In this talk\, I will introduce the complex Monge-Ampere equation and discuss the interplay between their analysis and geometry\, with a particular focus on the a priori C^0 estimates and their various applications. In the end\, I will also try to discuss some recent work with B. Guo and D.H. Phong on a new approach for proving sharp C^0 estimates for complex Monge-Ampere equations\, this new approach avoids the machinery of pluripotential theory that was previously necessary and has the advantage of generalizing to a large class of fully nonlinear equations.
URL:https://cmsa.fas.harvard.edu/event/10-29-2021-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211029T120000
DTEND;TZID=America/New_York:20211029T130000
DTSTAMP:20260510T025302
CREATED:20240214T102641Z
LAST-MODIFIED:20240301T091452Z
UID:10002670-1635508800-1635512400@cmsa.fas.harvard.edu
SUMMARY:Anomaly resolution via decomposition
DESCRIPTION:Speaker: Eric Sharpe (Virginia Tech) \nTitle: Anomaly resolution via decomposition \nAbstract: In this talk we will discuss a method of anomaly resolution due to Wang-Wen-Witten in the special case of (1+1) dimensional theories. Briefly\, for our purposes\, Wang-Wen-Witten argued that an ill-defined anomalous orbifold [X/G] could be resolved by extending G to a larger group and adding suitable phases.  We analyze this process from the perspective of decomposition\, a property of (1+1)-dimensional theories with “one-form symmetries” first described in 2006.  Examples of such theories include orbifolds with trivially-acting subgroups\, of which the extensions of [X/G] are examples.  After a review of decomposition\, we will see that decomposition implies that in (1+1) dimensions\, the Wang-Wen-Witten procedure results in orbifolds that are equivalent to disjoint unions of orbifolds of X by explicitly nonanomalous subgroups of G.
URL:https://cmsa.fas.harvard.edu/event/10-29-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211029T120000
DTEND;TZID=America/New_York:20211029T130000
DTSTAMP:20260510T025302
CREATED:20240301T091725Z
LAST-MODIFIED:20240301T091725Z
UID:10002890-1635508800-1635512400@cmsa.fas.harvard.edu
SUMMARY:Integrability and chaos of 1+1d chiral edge states
DESCRIPTION:Speaker: Biao Lian (Princeton) \nTitle: Integrability and chaos of 1+1d chiral edge states \nAbstract: I will talk about the integrability and chaos of 1+1d interacting chiral edge states\, which may arise on the edge of 2+1d topological phases. We show that integrable chiral Luttinger liquid is not always a good low energy description of the edge states\, and marginal interactions can significantly affect their spectrum and integrability. We first study N identical chiral Majorana fermion modes with random 4-fermion interactions\, where we show that the system undergoes a transition from integrable to quantum chaotic as N increases. The large N limit defines a chiral SYK model where the Lyapunov exponent in the out-of-time-ordered correlation can be solved analytically. I will also present a chiral SY model consisting of N interacting SU(M)_1 WZW models\, which host anyons and exhibits similar quantum chaos for Abelian anyons. Lastly\, I will talk about the analytical and numerical study of the 4/3 FQH edge theory\, which shows unusual behavior in its integrability.
URL:https://cmsa.fas.harvard.edu/event/10-29-2021-quantum-matter-in-mathematics-and-physics-2/
LOCATION:MA
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211101T130000
DTEND;TZID=America/New_York:20211101T140000
DTSTAMP:20260510T025302
CREATED:20240214T092956Z
LAST-MODIFIED:20240301T081324Z
UID:10002631-1635771600-1635775200@cmsa.fas.harvard.edu
SUMMARY:Bubble instability of mIIA on AdS_4 x S^6
DESCRIPTION:Speaker: Pieter 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.
URL:https://cmsa.fas.harvard.edu/event/11-1-2021-swampland-seminar/
LOCATION:MA
CATEGORIES:Swampland Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211102T093000
DTEND;TZID=America/New_York:20211102T103000
DTSTAMP:20260510T025302
CREATED:20240213T062436Z
LAST-MODIFIED:20240213T062436Z
UID:10002107-1635845400-1635849000@cmsa.fas.harvard.edu
SUMMARY:Counting invariant curves on a Calabi-Yau threefold with an involution
DESCRIPTION:Abstract: Gopakumar-Vafa invariants are integers n_beta(g) which give a virtual count of genus g curves in the class beta on a Calabi-Yau threefold. In this talk\, I will give a general overview of two of the sheaf-theoretic approaches to defining these invariants: via stable pairs a la Pandharipande-Thomas (PT) and via perverse sheaves a la Maulik-Toda (MT). I will then outline a parallel theory of Gopakumar-Vafa invariants for a Calabi-Yau threefold X with an involution. They are integers n_beta(g\,h) which give a virtual count of curves of genus g in the class beta which are invariant under the involution and whose quotient by the involution has genus h. I will give two definitions of n_beta(g\,h) which are conjectured to be equivalent\, one in terms of a version of PT theory\, and one in terms of a version of MT theory. These invariants can be computed and the conjecture proved in the case where X=SxC where S is an Abelian or K3 surface with a symplectic involution. In these cases\, the invariants are given by formulas expressed with Jacobi modular forms. In the case where S is an Abelian surface\, the specialization of n_beta(g\,h) to h=0 recovers the count of hyperelliptic curves on Abelian surfaces first computed by B-Oberdieck-Pandharipande-Yin. This is joint work with Stephen Pietromonaco.
URL:https://cmsa.fas.harvard.edu/event/counting-invariant-curves-on-a-calabi-yau-threefold-with-an-involution/
LOCATION:MA
CATEGORIES:Joint Harvard-CUHK-YMSC Differential Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Jim-Bryan_poster_3Nov2021.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211102T130000
DTEND;TZID=America/New_York:20211102T140000
DTSTAMP:20260510T025302
CREATED:20240214T052811Z
LAST-MODIFIED:20240304T062921Z
UID:10002538-1635858000-1635861600@cmsa.fas.harvard.edu
SUMMARY:Gauss-Manin connection in disguise: Quasi Jacobi forms of index zero
DESCRIPTION:Abstract: We consider the moduli space of abelian varieties with two marked points and a frame of the relative de Rham cohomology with boundary at these points compatible with its mixed Hodge structure. Such a moduli space gives a natural algebro-geometric framework for higher genus quasi Jacobi forms of index zero and their differential equations which are given as vector fields. In the case of elliptic curves we compute explicitly the Gauss-Manin connection and such vector fields. This is a joint work with J. Cao and R. Villaflor. (arXiv:2109.00587)
URL:https://cmsa.fas.harvard.edu/event/gauss-manin-connection-in-disguise-quasi-jacobi-forms-of-index-zero/
LOCATION:MA
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211103T093000
DTEND;TZID=America/New_York:20211103T103000
DTSTAMP:20260510T025302
CREATED:20240212T104227Z
LAST-MODIFIED:20240502T152621Z
UID:10002003-1635931800-1635935400@cmsa.fas.harvard.edu
SUMMARY:Hitchin map as spectrum of equivariant cohomology
DESCRIPTION:Speaker: Tamás 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.
URL:https://cmsa.fas.harvard.edu/event/hitchin-map-as-spectrum-of-equivariant-cohomology/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-11.03.21-791x1024-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211103T140000
DTEND;TZID=America/New_York:20211103T153000
DTSTAMP:20260510T025302
CREATED:20240214T102259Z
LAST-MODIFIED:20240301T091205Z
UID:10002667-1635948000-1635953400@cmsa.fas.harvard.edu
SUMMARY:Non-Invertible Duality Defects in 3+1 Dimensions
DESCRIPTION:Speaker: Clay Cordova (U Chicago) \nTitle: Non-Invertible Duality Defects in 3+1 Dimensions \nAbstract:  For any quantum system invariant under gauging a higher-form global symmetry\, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to higher spacetime dimensions. We focus on the case of a one-form symmetry in 3+1 dimensions and determine the fusion rule. From modular invariance and a direct analysis of one-form symmetry-protected topological phases\, we show that the existence of certain kinds of duality defects is intrinsically incompatible with a trivially gapped phase. By further assuming time-reversal symmetry\, we find that the presence of certain duality defects implies that the low-energy phase has to be gapless unless the one-form symmetry is spontaneously broken. We give an explicit realization of this duality defect in the free Maxwell theory where the duality defect is realized by a Chern-Simons coupling between the gauge fields from the two sides.
URL:https://cmsa.fas.harvard.edu/event/11-3-3021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211103T171200
DTEND;TZID=America/New_York:20211103T181200
DTSTAMP:20260510T025302
CREATED:20240214T094241Z
LAST-MODIFIED:20240813T155909Z
UID:10002643-1635959520-1635963120@cmsa.fas.harvard.edu
SUMMARY:When Computer Algebra Meets Satisfiability: A New Approach to Combinatorial Mathematics
DESCRIPTION:Speakers: Curtis Bright\, School of Computer Science\, University of Windsor and Vijay Ganesh\, Dept. of Electrical and Computer Engineering\, University of Waterloo \nTitle: When Computer Algebra Meets Satisfiability: A New Approach to Combinatorial Mathematics \nAbstract: Solvers for the Boolean satisfiability (SAT) problem have been increasingly used to resolve problems in mathematics due to their excellent search algorithms.  This talk will describe a new method for mathematical search that couples SAT solvers with computer algebra systems (CAS)\, thereby combining the expressiveness of CASs with the search power of SAT solvers.  This paradigm has led to a number of results on long-standing mathematical questions such as the first computer-verifiable resolution of Lam’s problem and the discovery of a new infinite class of Williamson matrices.
URL:https://cmsa.fas.harvard.edu/event/11-3-21-cmsa-new-technologies-in-mathematics/
LOCATION:MA
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-11.03.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211104T103000
DTEND;TZID=America/New_York:20211104T120000
DTSTAMP:20260510T025302
CREATED:20240214T101922Z
LAST-MODIFIED:20240301T091041Z
UID:10002665-1636021800-1636027200@cmsa.fas.harvard.edu
SUMMARY:Fusion Category Symmetries in Quantum Field Theory
DESCRIPTION:Speaker: Yifan Wang (NYU) \nTitle: Fusion Category Symmetries in Quantum Field Theory \nAbstract: Topological defects provide a modern perspective on symmetries in quantum field theory. They generalize the familiar inverti \n \nble symmetries described by groups to non-invertible symmetries described by fusion categories. Such generalized symmetries are ubiquitous in quantum field theory and provide new constraints on renormalization group flows and the IR phase diagram. In this talk I’ll review some recent progress in identifying and understanding fusion category symmetries in 1+1d conformal field theories. Time permitting\, I’ll also comment on higher dimensional generalizations.
URL:https://cmsa.fas.harvard.edu/event/11-4-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:MA
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211104T130000
DTEND;TZID=America/New_York:20211104T140000
DTSTAMP:20260510T025302
CREATED:20240214T073728Z
LAST-MODIFIED:20240304T054749Z
UID:10002565-1636030800-1636034400@cmsa.fas.harvard.edu
SUMMARY:The stability of charged black holes
DESCRIPTION:Abstract: Black holes solutions in General Relativity are parametrized by their mass\, spin and charge. In this talk\, I will motivate why the charge of black holes adds interesting dynamics to solutions of the Einstein equation thanks to the interaction between gravitational and electromagnetic radiation. Such radiations are solutions of a system of coupled wave equations with a symmetric structure which allows to define a combined energy-momentum tensor for the system. Finally\, I will show how this physical-space approach is resolutive in the most general case of Kerr-Newman black hole\, where the interaction between the radiations prevents the separability in modes.
URL:https://cmsa.fas.harvard.edu/event/11-4-2021-general-relativity-seminar/
LOCATION:MA
CATEGORIES:General Relativity Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211104T184600
DTEND;TZID=America/New_York:20211104T204600
DTSTAMP:20260510T025302
CREATED:20240214T080650Z
LAST-MODIFIED:20240301T103919Z
UID:10002580-1636051560-1636058760@cmsa.fas.harvard.edu
SUMMARY:11/4/21 CMSA Interdisciplinary Science Seminar
DESCRIPTION:Title: Exploring Invertibility in Image Processing and Restoration \nAbstract: Today’s smartphones have enabled numerous stunning visual effects from denoising to beautification\, and we can share high-quality JPEG images easily on the internet\, but it is still valuable for photographers and researchers to keep the original raw camera data for further post-processing (e.g.\, retouching) and analysis. However\, the huge size of raw data hinders its popularity in practice\, so can we almost perfectly restore the raw data from a compressed RGB image and thus avoid storing any raw data? This question leads us to design an invertible image signal processing pipeline. Then we further explore invertibility in other image processing and restoration tasks\, including image compression\, reversible image conversion (e.g.\, image-to-video conversion)\, and embedding novel views in a single JPEG image. We demonstrate that customized invertible neural networks are highly effective in these inherently non-invertible tasks.
URL:https://cmsa.fas.harvard.edu/event/11-4-21-cmsa-interdisciplinary-science-seminar/
LOCATION:MA
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-Interdisciplinary-Science-Seminar-11.04.21-1583x2048-1-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211105T093000
DTEND;TZID=America/New_York:20211105T113000
DTSTAMP:20260510T025302
CREATED:20240214T073106Z
LAST-MODIFIED:20240301T111130Z
UID:10002562-1636104600-1636111800@cmsa.fas.harvard.edu
SUMMARY:The Greene-Plesser Construction Revisited
DESCRIPTION:Member Seminar  \nSpeaker: Chuck Doran \nTitle: The Greene-Plesser Construction Revisited \nAbstract: The first known construction of mirror pairs of Calabi-Yau manifolds was the Greene-Plesser “quotient and resolve” procedure which applies to pencils of hypersurfaces in projective space. We’ll review this approach\, uncover the hints it gives for some more general mirror constructions\, and describe a brand-new variant that applies to pencils of hypersurfaces in Grassmannians. This last is joint work with Tom Coates and Elana Kalashnikov (arXiv:2110.0727).
URL:https://cmsa.fas.harvard.edu/event/11-5-2021-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211109T103000
DTEND;TZID=America/New_York:20211109T113000
DTSTAMP:20260510T025302
CREATED:20240213T062822Z
LAST-MODIFIED:20240304T062818Z
UID:10002112-1636453800-1636457400@cmsa.fas.harvard.edu
SUMMARY:Cosection localization for virtual fundamental classes of d-manifolds and Donaldson-Thomas invariants of Calabi-Yau fourfolds
DESCRIPTION:Abstract: Localization by cosection\, first introduced by Kiem-Li in 2010\, is one of the fundamental techniques used to study invariants in complex enumerative geometry. Donaldson-Thomas (DT) invariants counting sheaves on Calabi-Yau fourfolds were first defined by Borisov-Joyce in 2015 by combining derived algebraic and differential geometry.\nIn this talk\, we develop the theory of cosection localization for derived manifolds in the context of derived differential geometry of Joyce. As a consequence\, we also obtain cosection localization results for (-2)-shifted symplectic derived schemes. This provides a cosection localization formalism for the Borisov-Joyce DT invariant. As an immediate application\, the stable pair invariants of hyperkähler fourfolds\, constructed by Maulik-Cao-Toda\, vanish\, as expected.
URL:https://cmsa.fas.harvard.edu/event/cosection-localization-for-virtual-fundamental-classes-of-d-manifolds-and-donaldson-thomas-invariants-of-calabi-yau-fourfolds/
LOCATION:MA
CATEGORIES:Algebraic Geometry in String Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Algebraic-Geometry-in-String-Theory-Seminar-11.09.21-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211109T103000
DTEND;TZID=America/New_York:20211109T223000
DTSTAMP:20260510T025302
CREATED:20240304T062554Z
LAST-MODIFIED:20240304T062554Z
UID:10002897-1636453800-1636497000@cmsa.fas.harvard.edu
SUMMARY:Cosection localization for virtual fundamental classes of d-manifolds and Donaldson-Thomas invariants of Calabi-Yau fourfolds
DESCRIPTION:Speaker: Michail Savvas\, UT Austin \nTitle: Cosection localization for virtual fundamental classes of d-manifolds and Donaldson-Thomas invariants of Calabi-Yau fourfolds \nAbstract: Localization by cosection\, first introduced by Kiem-Li in 2010\, is one of the fundamental techniques used to study invariants in complex enumerative geometry. Donaldson-Thomas (DT) invariants counting sheaves on Calabi-Yau fourfolds were first defined by Borisov-Joyce in 2015 by combining derived algebraic and differential geometry.\nIn this talk\, we develop the theory of cosection localization for derived manifolds in the context of derived differential geometry of Joyce. As a consequence\, we also obtain cosection localization results for (-2)-shifted symplectic derived schemes. This provides a cosection localization formalism for the Borisov-Joyce DT invariant. As an immediate application\, the stable pair invariants of hyperkähler fourfolds\, constructed by Maulik-Cao-Toda\, vanish\, as expected. \n\n\n\nevent\n\n\nOrganizer: Seminars
URL:https://cmsa.fas.harvard.edu/event/11-9-21-cmsa-algebraic-geometry-in-string-theory-seminar/
LOCATION:MA
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
END:VCALENDAR