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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
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20210913T090000
DTEND;TZID=America/New_York:20220513T170000
DTSTAMP:20260511T000502
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:20260511T000502
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:20211122T130000
DTEND;TZID=America/New_York:20211122T140000
DTSTAMP:20260511T000502
CREATED:20240214T091807Z
LAST-MODIFIED:20240301T075427Z
UID:10002616-1637586000-1637589600@cmsa.fas.harvard.edu
SUMMARY:Taming the Landscape
DESCRIPTION:Abstract: In this talk I will introduce a generalized notion of finiteness that provides a structural principle for the set of effective theories that can be consistently coupled to quantum gravity. More concretely\, I will propose a ‘tameness conjecture’ that states that all scalar field spaces and coupling functions that appear in such an effective theory must be definable in an o-minimal structure. The fascinating field of tame geometry has seen much recent progress and I will argue that the results can be used to support the above swampland conjecture. The strongest evidence arises from a new finiteness theorem for the flux landscape which is shown using the tameness of the period map.
URL:https://cmsa.fas.harvard.edu/event/11-22-2021-swampland-seminar/
LOCATION:MA
CATEGORIES:Swampland Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211123T093000
DTEND;TZID=America/New_York:20211123T103000
DTSTAMP:20260511T000502
CREATED:20240213T064610Z
LAST-MODIFIED:20240213T064610Z
UID:10002127-1637659800-1637663400@cmsa.fas.harvard.edu
SUMMARY:Wall crossing for moduli of stable log varieties
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/wall-crossing-for-moduli-of-stable-log-varieties/
LOCATION:MA
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211123T093000
DTEND;TZID=America/New_York:20211123T103000
DTSTAMP:20260511T000502
CREATED:20240213T065330Z
LAST-MODIFIED:20240226T111143Z
UID:10002138-1637659800-1637663400@cmsa.fas.harvard.edu
SUMMARY:Prague dimension of random graphs
DESCRIPTION:Abstract: The Prague dimension of graphs was introduced by Nesetril\, Pultr and Rodl in the 1970s: as a combinatorial measure of complexity\, it is closely related to clique edges coverings and partitions. Proving a conjecture of Furedi and Kantor\, we show that the Prague dimension of the binomial random graph is typically of order n/(log n) for constant edge-probabilities. The main new proof ingredient is a Pippenger-Spencer type edge-coloring result for random hypergraphs with large uniformities\, i.e.\, edges of size O(log n).
URL:https://cmsa.fas.harvard.edu/event/11-23-21-combinatorics-physics-and-probability-seminar/
LOCATION:MA
CATEGORIES:Combinatorics Physics and Probability
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Combinatorics-Physics-and-Probability-Seminar-11.23.21-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211124T103000
DTEND;TZID=America/New_York:20211124T120000
DTSTAMP:20260511T000502
CREATED:20240213T065517Z
LAST-MODIFIED:20240213T065517Z
UID:10002141-1637749800-1637755200@cmsa.fas.harvard.edu
SUMMARY:11/24/21 Quantum Matter in Mathematics and Physics
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/11-24-21-quantum-matter-in-mathematics-and-physics/
LOCATION:MA
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211124T103000
DTEND;TZID=America/New_York:20211124T120000
DTSTAMP:20260511T000502
CREATED:20240214T100439Z
LAST-MODIFIED:20240301T084626Z
UID:10002655-1637749800-1637755200@cmsa.fas.harvard.edu
SUMMARY:Multipartitioning topological phases and quantum entanglement
DESCRIPTION:Speaker: Shinsei Ryu (Princeton University) \nTitle: Multipartitioning topological phases and quantum entanglement \nAbstract: We discuss multipartitions of the gapped ground states of (2+1)-dimensional topological liquids into three (or more) spatial regions that are adjacent to each other and meet at points. By considering the reduced density matrix obtained by tracing over a subset of the regions\, we compute various correlation measures\, such as entanglement negativity\, reflected entropy\, and associated spectra. We utilize the bulk-boundary correspondence to achieve such multipartitions and construct the reduced density matrix near the entangling boundaries. We find the fingerprints of topological liquid in these quantities\, such as (universal pieces in) the scaling of the entanglement negativity\, and a non-trivial distribution of the spectrum of the partially transposed density matrix.
URL:https://cmsa.fas.harvard.edu/event/11-24-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-11.24.21-1583x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211124T160000
DTEND;TZID=America/New_York:20211124T170000
DTSTAMP:20260511T000502
CREATED:20240213T065022Z
LAST-MODIFIED:20240226T111010Z
UID:10002133-1637769600-1637773200@cmsa.fas.harvard.edu
SUMMARY:Quantum cohomology as a deformation of symplectic cohomology
DESCRIPTION:Abstract: Let X be a compact symplectic manifold\, and D a normal crossings symplectic divisor in X. We give a criterion under which the quantum cohomology of X is the cohomology of a natural deformation of the symplectic cochain complex of X \ D. The criterion can be thought of in terms of the Kodaira dimension of X (which should be non-positive)\, and the log Kodaira dimension of X \ D (which should be non-negative). We will discuss applications to mirror symmetry. This is joint work with Strom Borman and Umut Varolgunes.
URL:https://cmsa.fas.harvard.edu/event/11-24-21-joint-harvard-cuhk-ymsc-differential-geometry-seminar/
LOCATION:MA
CATEGORIES:Joint Harvard-CUHK-YMSC Differential Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/20211124_Nick-Sheridan_RESCHEDULED_poster.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211129T130000
DTEND;TZID=America/New_York:20211129T140000
DTSTAMP:20260511T000502
CREATED:20240214T112454Z
LAST-MODIFIED:20240301T075047Z
UID:10002697-1638190800-1638194400@cmsa.fas.harvard.edu
SUMMARY:Scale separated AdS vacua?
DESCRIPTION:Abstract: In this talk I will review massive type IIA flux compactifications that seem to give rise to infinite families of supersymmetric 4d AdS vacua. These vacua provide an interesting testing ground for the swampland program. After reviewing potential shortcomings of this setup\, I will discuss recent progress on overcoming them and getting a better understanding of these solutions.
URL:https://cmsa.fas.harvard.edu/event/11-29-2021-swampland-seminar/
LOCATION:MA
CATEGORIES:Swampland Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211130T093000
DTEND;TZID=America/New_York:20211130T103000
DTSTAMP:20260511T000502
CREATED:20230818T050118Z
LAST-MODIFIED:20240122T053703Z
UID:10001285-1638264600-1638268200@cmsa.fas.harvard.edu
SUMMARY:K_2 and Quantum Curves
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/k_2-and-quantum-curves/
LOCATION:Virtual
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211130T093000
DTEND;TZID=America/New_York:20211130T103000
DTSTAMP:20260511T000502
CREATED:20240213T065738Z
LAST-MODIFIED:20240213T065738Z
UID:10002146-1638264600-1638268200@cmsa.fas.harvard.edu
SUMMARY:Resistance curvature – a new discrete curvature on graphs
DESCRIPTION:Abstract: The last few decades have seen a surge of interest in building towards a theory of discrete curvature that attempts to translate the key properties of curvature in differential geometry to the setting of discrete objects and spaces. In the case of graphs there have been several successful proposals\, for instance by Lin-Lu-Yau\, Forman and Ollivier\, that replicate important curvature theorems and have inspired applications in a variety of practical settings.\nIn this talk\, I will introduce a new notion of discrete curvature on graphs\, which we call the resistance curvature\, and discuss some of its basic properties. The resistance curvature is defined based on the concept of effective resistance which is a metric between the vertices of a graph and has many other properties such as a close relation to random spanning trees. The rich theory of these effective resistances allows to study the resistance curvature in great detail; I will for instance show that “Lin-Lu-Yau >= resistance >= Forman curvature” in a specific sense\, show strong evidence that the resistance curvature converges to zero in expectation for Euclidean random graphs\, and give a connectivity theorem for positively curved graphs. The resistance curvature also has a naturally associated discrete Ricci flow which is a gradient flow and has a closed-form solution in the case of vertex-transitive and path graphs.\nFinally\, if time permits I will draw a connection with the geometry of hyperacute simplices\, following the work of Miroslav Fiedler.\nThis work was done in collaboration with Renaud Lambiotte.
URL:https://cmsa.fas.harvard.edu/event/resistance-curvature-a-new-discrete-curvature-on-graphs/
LOCATION:MA
CATEGORIES:Combinatorics Physics and Probability
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Combinatorics-Physics-and-Probability-Seminar-11.30.2021-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211201T093000
DTEND;TZID=America/New_York:20211201T103000
DTSTAMP:20260511T000502
CREATED:20240212T104729Z
LAST-MODIFIED:20240502T154527Z
UID:10002012-1638351000-1638354600@cmsa.fas.harvard.edu
SUMMARY:The Hitchin connection for parabolic G-bundles
DESCRIPTION:Speaker: Richard 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.
URL:https://cmsa.fas.harvard.edu/event/the-hitchin-connection-for-parabolic-g-bundles/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-12.01.21-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211201T100000
DTEND;TZID=America/New_York:20211201T113000
DTSTAMP:20260511T000502
CREATED:20240213T070149Z
LAST-MODIFIED:20240213T070149Z
UID:10002153-1638352800-1638358200@cmsa.fas.harvard.edu
SUMMARY:12/1/21 Quantum Matter in Mathematics and Physics
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/12-1-21-quantum-matter-in-mathematics-and-physics/
LOCATION:MA
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211201T140000
DTEND;TZID=America/New_York:20211201T143000
DTSTAMP:20260511T000502
CREATED:20230808T175251Z
LAST-MODIFIED:20240515T203641Z
UID:10001200-1638367200-1638369000@cmsa.fas.harvard.edu
SUMMARY:The Principles of Deep Learning Theory
DESCRIPTION:Speaker: Dan Roberts\, MIT & Salesforce \nTitle: The Principles of Deep Learning Theory \nAbstract: Deep learning is an exciting approach to modern artificial intelligence based on artificial neural networks. The goal of this talk is to provide a blueprint — using tools from physics — for theoretically analyzing deep neural networks of practical relevance. This task will encompass both understanding the statistics of initialized deep networks and determining the training dynamics of such an ensemble when learning from data. \nIn terms of their “microscopic” definition\, deep neural networks are a flexible set of functions built out of many basic computational blocks called neurons\, with many neurons in parallel organized into sequential layers. Borrowing from the effective theory framework\, we will develop a perturbative 1/n expansion around the limit of an infinite number of neurons per layer and systematically integrate out the parameters of the network. We will explain how the network simplifies at large width and how the propagation of signals from layer to layer can be understood in terms of a Wilsonian renormalization group flow. This will make manifest that deep networks have a tuning problem\, analogous to criticality\, that needs to be solved in order to make them useful. Ultimately we will find a “macroscopic” description for wide and deep networks in terms of weakly-interacting statistical models\, with the strength of the interactions between the neurons growing with depth-to-width aspect ratio of the network. Time permitting\, we will explain how the interactions induce representation learning. \nThis talk is based on a book\, The Principles of Deep Learning Theory\, co-authored with Sho Yaida and based on research also in collaboration with Boris Hanin. It will be published next year by Cambridge University Press.
URL:https://cmsa.fas.harvard.edu/event/12-1-21-new-technologies-in-mathematics-seminar-series/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-12.01.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211201T160000
DTEND;TZID=America/New_York:20211201T170000
DTSTAMP:20260511T000502
CREATED:20240214T080447Z
LAST-MODIFIED:20240301T112740Z
UID:10002578-1638374400-1638378000@cmsa.fas.harvard.edu
SUMMARY:Lagrangians and mirror symmetry in the Higgs bundle moduli space
DESCRIPTION:Abstract: The talk concerns recent work with Tamas Hausel in asking how SYZ mirror symmetry works for the moduli space of Higgs bundles. Focusing on C^*-invariant Lagrangian submanifolds\, we use the notion of virtual multiplicity as a tool firstly to examine if the Lagrangian is closed\, but  also to open up new features involving finite-dimensional algebras which are deformations of cohomology algebras. Answering some of the questions raised  requires revisiting basic constructions of stable bundles on curves.
URL:https://cmsa.fas.harvard.edu/event/2-1-2021-joint-harvard-cuhk-ymsc-differential-geometry-seminar/
LOCATION:MA
CATEGORIES:Joint Harvard-CUHK-YMSC Differential Geometry
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211202T103000
DTEND;TZID=America/New_York:20211202T120000
DTSTAMP:20260511T000502
CREATED:20240213T070448Z
LAST-MODIFIED:20240213T070448Z
UID:10002156-1638441000-1638446400@cmsa.fas.harvard.edu
SUMMARY:12/2/21 Quantum Matter in Mathematics and Physics
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/12-2-21-quantum-matter-in-mathematics-and-physics/
LOCATION:MA
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211202T103000
DTEND;TZID=America/New_York:20211202T120000
DTSTAMP:20260511T000502
CREATED:20240301T083755Z
LAST-MODIFIED:20240301T083839Z
UID:10002887-1638441000-1638446400@cmsa.fas.harvard.edu
SUMMARY:Symmetry in quantum field theory and quantum gravity 2
DESCRIPTION:Speaker: Daniel Harlow (MIT) \nTitle: Symmetry in quantum field theory and quantum gravity 2 \nAbstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence.  These conjectures are 1) that there are no global symmetries in quantum gravity\, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist\, and 3) all internal gauge symmetries must be compact.  Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity\, which leads to interesting applications in various related fields.  These definitions will be the focus of the first talk\, while the second will apply them to AdS/CFT to prove conjectures 1-3).
URL:https://cmsa.fas.harvard.edu/event/12-2-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:MA
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-12.02.21-1544x2048-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211202T130000
DTEND;TZID=America/New_York:20211202T140000
DTSTAMP:20260511T000502
CREATED:20240214T075408Z
LAST-MODIFIED:20240304T053731Z
UID:10002571-1638450000-1638453600@cmsa.fas.harvard.edu
SUMMARY:Kerr Geodesics and Self-consistent match between Inspiral and Transition-to-merger
DESCRIPTION:Abstract: The two-body motion in General Relativity can be solved perturbatively in the small mass ratio expansion. Kerr geodesics describe the leading order motion. After a short summary of the classification of polar and radial Kerr geodesic motion\, I will consider the inspiral motion of a point particle around the Kerr black hole subjected to the self-force. I will describe its quasi-circular inspiral motion in the radiation timescale expansion. I will describe in parallel the transition-to-merger motion around the last stable circular orbit and prove that it is controlled by the Painlevé transcendental equation of the first kind. I will then prove that one can consistently match the two motions using the method of asymptotically matched expansions.
URL:https://cmsa.fas.harvard.edu/event/12-2-2021-general-relativity-seminar/
LOCATION:MA
CATEGORIES:General Relativity Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211202T131500
DTEND;TZID=America/New_York:20211202T143000
DTSTAMP:20260511T000502
CREATED:20240213T113157Z
LAST-MODIFIED:20240304T084850Z
UID:10002504-1638450900-1638455400@cmsa.fas.harvard.edu
SUMMARY:Hydrodynamics and multi-scale order in confluent epithelia
DESCRIPTION:Abstract: In this talk I will review our ongoing theoretical and experimental efforts toward deciphering the hydrodynamic behavior of confluent epithelia. The ability of epithelial cells to collectively flow lies at the heart of a myriad of processes that are instrumental for life\, such as embryonic morphogenesis and wound healing\, but also of life-threatening conditions\, such as metastatic cancer. Understanding the physical origin of these mechanisms requires going beyond the current hydrodynamic theories of complex fluids and introducing a new theoretical framework\, able to account for biomechanical activity as well as for scale-dependent liquid crystalline order.
URL:https://cmsa.fas.harvard.edu/event/hydrodynamics-and-multi-scale-order-in-confluent-epithelia/
LOCATION:MA
CATEGORIES:Active Matter Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211202T142800
DTEND;TZID=America/New_York:20211202T152800
DTSTAMP:20260511T000502
CREATED:20240215T094151Z
LAST-MODIFIED:20240301T110349Z
UID:10002725-1638455280-1638458880@cmsa.fas.harvard.edu
SUMMARY:12/2/2021 Interdisciplinary Science Seminar
DESCRIPTION:Title: Polyhomogeneous expansions and Z/2-harmonic spinors branching along graphs \nAbstract: In this talk\, we will first reformulate the linearization of the moduli space of Z/2-harmonic spinorsv branching along a knot. This formula tells us that the kernel and cokernel of the linearization are isomorphic to the kernel and cokernel of the Dirac equation with a polyhomogeneous boundary condition. In the second part of this talk\, I will describe the polyhomogenous expansions for the Z/2-harmonic spinors branching along graphs and formulate the Dirac equation with a suitable boundary condition that can describe the perturbation of graphs with some restrictions. This is joint work with Andriy Haydys and Rafe Mazzeo.
URL:https://cmsa.fas.harvard.edu/event/12-2-2021-interdisciplinary-science-seminar/
LOCATION:MA
CATEGORIES:Interdisciplinary Science Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211203T093000
DTEND;TZID=America/New_York:20211203T103000
DTSTAMP:20260511T000502
CREATED:20240214T072504Z
LAST-MODIFIED:20240301T110847Z
UID:10002558-1638523800-1638527400@cmsa.fas.harvard.edu
SUMMARY:Black Holes\, 2D Gravity\, and Random Matrices
DESCRIPTION:Member Seminar \nSpeaker: Dan Kapec \nTitle: Black Holes\, 2D Gravity\, and Random Matrices \nAbstract: I will discuss old and new connections between black hole physics\, 2D quantum gravity\, and random matrix theory. Black holes are believed to be very complicated\, strongly interacting quantum mechanical systems\, and certain aspects of their Hamiltonians should be well approximated by random matrix theory. The near-horizon effective dynamics of near-extremal black holes is two-dimensional\, and many theories of 2D quantum gravity are known to have random matrix descriptions. All of these expectations were recently borne out in surprising detail with the solution of the Jackiw-Teitelboim (JT) model\, but this result raises more questions than it answers. If time permits\, I will discuss some extensions of these results and possible future directions.
URL:https://cmsa.fas.harvard.edu/event/12-3-2021-member-seminar/
LOCATION:MA
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211206T130000
DTEND;TZID=America/New_York:20211206T140000
DTSTAMP:20260511T000502
CREATED:20240214T112042Z
LAST-MODIFIED:20240301T074922Z
UID:10002695-1638795600-1638799200@cmsa.fas.harvard.edu
SUMMARY:Extremal Black Hole Corrections from Iyer-Wald
DESCRIPTION:Abstract: Extremal black holes play a key role in our understanding of various swampland conjectures and in particular the WGC. The mild form of the WGC states that higher-derivative corrections should decrease the mass of extremal black holes at fixed charge. Whether or not this conjecture is satisfied depends on the sign of the combination of Wilson coefficients that control corrections to extremality. Typically\, corrections to extremality need to be computed on a case-by-case basis\, but in this talk I will present a universal derivation of extremal black hole corrections using the Iyer-Wald formalism. This leads to a formula that expresses general corrections to the extremality bound in terms of the stress tensor of the perturbations under consideration\, clarifying the relation between the WGC and energy conditions. This shows that a necessary condition for the mild form of the WGC to be satisfied is a violation of the Dominant Energy Condition. This talk is based on 2111.04201.
URL:https://cmsa.fas.harvard.edu/event/12-6-2021-swampland-seminar/
LOCATION:MA
CATEGORIES:Swampland Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211207T093000
DTEND;TZID=America/New_York:20211207T103000
DTSTAMP:20260511T000502
CREATED:20230818T050741Z
LAST-MODIFIED:20240122T054102Z
UID:10001286-1638869400-1638873000@cmsa.fas.harvard.edu
SUMMARY:2d N=(0\,1) gauge theories\, Spin(7) orientifolds and triality
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/12-7-21-algebraic-geometry-in-string-theory/
LOCATION:Virtual
CATEGORIES:Algebraic Geometry in String Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211207T093000
DTEND;TZID=America/New_York:20211207T103000
DTSTAMP:20260511T000502
CREATED:20240213T070713Z
LAST-MODIFIED:20240213T070713Z
UID:10002160-1638869400-1638873000@cmsa.fas.harvard.edu
SUMMARY:The singularity probability of random symmetric matrices
DESCRIPTION:Abstract: Let M_n be drawn uniformly from all n by n symmetric matrices with entries in {-1\,1}. In this talk I’ll consider the following basic question: what is the probability that M_n is singular? I’ll discuss recent joint work with Marcelo Campos\, Marcus Michelen and Julian Sahasrabudhe where we show that this probability is exponentially small. I hope to make the talk accessible to a fairly general audience.
URL:https://cmsa.fas.harvard.edu/event/the-singularity-probability-of-random-symmetric-matrices/
LOCATION:MA
CATEGORIES:Combinatorics Physics and Probability
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Combinatorics-Physics-and-Probability-Seminar-12.07.2021.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211208T093000
DTEND;TZID=America/New_York:20211208T103000
DTSTAMP:20260511T000502
CREATED:20240214T042604Z
LAST-MODIFIED:20240502T154649Z
UID:10002528-1638955800-1638959400@cmsa.fas.harvard.edu
SUMMARY:Induced subgraphs and tree decompositions
DESCRIPTION:Speaker: Maria 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.
URL:https://cmsa.fas.harvard.edu/event/induced-subgraphs-and-tree-decompositions/
LOCATION:MA
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-12.08.21-791x1024-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211208T103000
DTEND;TZID=America/New_York:20211208T120000
DTSTAMP:20260511T000502
CREATED:20240214T094451Z
LAST-MODIFIED:20240301T083428Z
UID:10002644-1638959400-1638964800@cmsa.fas.harvard.edu
SUMMARY:Defects\, link invariants and exact WKB
DESCRIPTION:Speaker: Fei Yan (Rutgers) \nTitle: Defects\, link invariants and exact WKB \nAbstract: I will describe some of my recent work on defects in supersymmetric field theories. The first part of my talk is focused on line defects in certain large classes of 4d N=2 theories and 3d N=2 theories. I will describe geometric methods to compute the ground states spectrum of the bulk-defect system\, as well as implications on the construction of link invariants. In the second part I will talk about some perspectives of surface defects in 4d N=2 theories and related applications on the exact WKB method for ordinary differential equations. This talk is based on past joint work with A. Neitzke\, various work in progress with D. Gaiotto\, S. Jeong\, A. Khan\, G. Moore\, as well as work by myself.
URL:https://cmsa.fas.harvard.edu/event/12-8-2021-quantum-matter-in-mathematics-and-physics/
LOCATION:Virtual
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-12.08.21-1544x2048-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211208T140000
DTEND;TZID=America/New_York:20211208T150000
DTSTAMP:20260511T000502
CREATED:20230808T175752Z
LAST-MODIFIED:20240515T203917Z
UID:10001201-1638972000-1638975600@cmsa.fas.harvard.edu
SUMMARY:Hierarchical Transformers are More Efficient Language Models
DESCRIPTION:Speaker: Piotr Nawrot\, University of Warsaw \nTitle: Hierarchical Transformers are More Efficient Language Models \nAbstract: Transformer models yield impressive results on many NLP and sequence modeling tasks. Remarkably\, Transformers can handle long sequences which allows them to produce long coherent outputs: full paragraphs produced by GPT-3 or well-structured images produced by DALL-E. These large language models are impressive but also very inefficient and costly\, which limits their applications and accessibility. We postulate that having an explicit hierarchical architecture is the key to Transformers that efficiently handle long sequences. To verify this claim\, we first study different ways to upsample and downsample activations in Transformers so as to make them hierarchical. We use the best performing upsampling and downsampling layers to create Hourglass – a hierarchical Transformer language model. Hourglass improves upon the Transformer baseline given the same amount of computation and can yield the same results as Transformers more efficiently. In particular\, Hourglass sets new state-of-the-art for Transformer models on the ImageNet32 generation task and improves language modeling efficiency on the widely studied enwik8 benchmark.
URL:https://cmsa.fas.harvard.edu/event/12-8-21-new-technologies-in-mathematics/
LOCATION:Virtual
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-12.08.21.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211209T093000
DTEND;TZID=America/New_York:20211209T143000
DTSTAMP:20260511T000502
CREATED:20230705T082223Z
LAST-MODIFIED:20250328T200233Z
UID:10000072-1639042200-1639060200@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture - Karen Uhlenbeck
DESCRIPTION:Karen Uhlenbeck (Institute for Advanced Study) \nTitle: The Noether Theorems in Geometry: Then and Now \nAbstract: The 1918 Noether theorems were a product of the general search for energy and momentum conservation in Einstein’s newly formulated theory of general relativity. Although widely referred to as the connection between symmetry and conservation laws\, the theorems themselves are often not understood properly and hence have not been as widely used as they might be. In the first part of the talk\, I outline a brief history of the theorems\, explain a bit of the language\, translate the first theorem into coordinate invariant language and give a few examples. I will mention only briefly their importance in physics and integrable systems. In the second part of the talk\, I describe why they are still relevant in geometric analysis: how they underlie standard techniques and why George Daskalopoulos and I came to be interested in them for our investigation into the best Lipschitz maps of Bill Thurston. Some applications to integrals on a domain a hyperbolic surface leave open possibilities for applications to integrals on domains which are locally symmetric spaces of higher dimension. The talk finishes with an example or two from the literature. \nTalk Chair: Laura DeMarco \nVIDEO
URL:https://cmsa.fas.harvard.edu/event/12-9-21-math-science-literature-lecture-karen-uhlenbeck/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Lecture_Uhlenbeck_12921.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20211209T142900
DTEND;TZID=America/New_York:20211209T152900
DTSTAMP:20260511T000502
CREATED:20240215T093828Z
LAST-MODIFIED:20240215T093828Z
UID:10002723-1639060140-1639063740@cmsa.fas.harvard.edu
SUMMARY:12/9/21 Interdisciplinary Science Seminar
DESCRIPTION:Title: Numerical Higher Dimensional Geometry \nAbstract: In 1977\, Yau proved that a Kahler manifold with zero first Chern class admits a Ricci flat metric\, which is uniquely determined by certain “moduli” data. These metrics have been very important in mathematics and in theoretical physics\, but despite much subsequent work we have no analytical expressions for them. But significant progress has been made on computing numerical approximations. We give an introduction (not assuming knowledge of complex geometry) to these problems and describe these methods.
URL:https://cmsa.fas.harvard.edu/event/12-9-21-interdisciplinary-science-seminar/
LOCATION:MA
CATEGORIES:Interdisciplinary Science Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Interdisciplinary-Science-Seminar-12.09.21-1583x2048-1.png
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