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SUMMARY:Geometry and Physics Seminar
DESCRIPTION:During the summer of 2020\, the CMSA will be hosting a new Geometry Seminar. Talks will be scheduled on Mondays at 9:30pm or Tuesdays at 9:30am\, depending on the location of the speaker. This seminar is organized by Tsung-Ju Lee\, Yoosik Kim\, and Du Pei. \nTo learn how to attend this seminar\, please contact Tsung-Ju Lee (tjlee@cmsa.fas.harvard.edu). \n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n\n\n6/2/2020\n9:30am ET\nSiu-Cheong Lau\nBoston University\nThis meeting will be taking place virtually on Zoom. \nSpeaker: Equivariant Floer theory and SYZ mirror symmetry \nAbstract: In this talk\, we will first review a symplectic realization of the SYZ program and some of its applications. Then I will explain some recent works on equivariant Lagrangian Floer theory and disc potentials of immersed SYZ fibers. They are joint works with Hansol Hong\, Yoosik Kim and Xiao Zheng.\n\n\n6/8/2020\n9:30pm ET\nYoungjin Bae (KIAS)\nThis meeting will be taking place virtually on Zoom. \nTitle: Legendrian graphs and their invariants \nAbstract: Legendrian graphs naturally appear in the study of Weinstein manifolds with a singular Lagrangian skeleton\, and a tangle decomposition of Legendrian submanifolds. I will introduce various invariant of Legendrian graphs including DGA type\, polynomial type\, sheaf theoretic one\, and their relationship. This is joint work with Byunghee An\, and partially with Tamas Kalman and Tao Su.\n\n\n6/16/2020\n9:30am ET\nMichael McBreen (CMSA)\nThis meeting will be taking place virtually on Zoom. \nTitle: Loops in hypertoric varieties and symplectic duality \nAbstract: Hypertoric varieties are algebraic symplectic varieties associated to graphs\, or more generally certain hyperplane arrangements. They make many appearances in modern geometric representation theory. I will discuss certain infinite dimensional or infinite type generalizations of hypertoric varieties which occur in the study of enumerative invariants\, focusing on some elementary examples. Joint work with Artan Sheshmani and Shing-Tung Yau.\n\n\n6/22/2020\n9:30pm ET\nZiming Ma (CUHK)\nThis meeting will be taking place virtually on Zoom. \nTitle: The geometry of Maurer–Cartan equation near degenerate Calabi–Yau varieties \nAbstract: In this talk\, we construct a \(dgBV algebra PV*(X)\) associated to a possibly degenerate Calabi–Yau variety X equipped with local thickening data. This gives a version of the Kodaira–Spencer dgLa which is applicable to degenerated spaces including both log smooth or maximally degenerated Calabi–Yau. We use this to prove an unobstructedness result about the smoothing of degenerated Log Calabi–Yau varieties X satisfying Hodge–deRham degeneracy property for cohomology of X\, in the spirit of Kontsevich–Katzarkov–Pantev. This is a joint work with Kwokwai Chan and Naichung Conan Leung.\n\n\n6/30/2020\n9:30pm ET\nSunghyuk Park (Caltech)\nThis meeting will be taking place virtually on Zoom. \nTitle: 3-manifolds\, q-series\, and topological strings \nAbstract: \(\hat{Z}\) is an invariant of 3-manifolds valued in q-series (i.e. power series in q with integer coefficients)\, which has interesting modular properties. While originally from physics\, this invariant has been mathematically constructed for a big class of 3-manifolds\, and conjecturally it can be extended to all 3-manifolds. In this talk\, I will give a gentle introduction to \(\hat{Z}\) and what is known about it\, as well as highlighting some recent developments\, including the use of R-matrix\, generalization to higher rank\, large N-limit and interpretation as open topological string partition functions.\n\n\n7/7/2020\n9:30am ET\nJeremy Lane  (McMaster University)\nThis meeting will be taking place virtually on Zoom. \nTitle: Collective integrable systems and global action-angle coordinates \nAbstract: A “collective integrable system” on a symplectic manifold is a commutative integrable system constructed from a Hamiltonian action of a non-commutative Lie group. Motivated by the example of Gelfand-Zeitlin systems\, we give a construction of collective integrable systems that generate a Hamiltonian torus action on a dense subset of any Hamiltonian K-manifold\, where K is any compact connected Lie group. In the case where the Hamiltonian K-manifold is compact and multiplicity free\, the resulting Hamiltonian torus action is completely integrable and yields global action angle coordinates.  Moreover\, the image of the moment map is a (non-simple) convex polytope.\n\n\n7/13/2020\n9:30pm ET\nPo-Shen Hsin (Caltech)\nThis meeting will be taking place virtually on Zoom. \nTitle: Berry phase in quantum field theory \nAbstract: We will discuss Berry phase in family of quantum field theories using effective field theory. The family is labelled by parameters which we promote to be spacetime-dependent sigma model background fields. The Berry phase is equivalent to Wess-Zumino-Witten action for the sigma model. We use Berry phase to study diabolic points in the phase diagram of the quantum field theory and discuss applications to deconfined quantum criticality and new tests for boson/fermion dualities in \((2+1)d\).\n\n\n7/20/2020\n9:30pm ET\nSangwook Lee (KIAS)\nThis meeting will be taking place virtually on Zoom. \nTitle: A geometric construction of orbifold Jacobian algebras \nAbstract: We review the definition of a twisted Jacobian algebra of a Landau-Ginzburg orbifold due to Kaufmann et al. Then we construct an A-infinity algebra of a weakly unobstructed Lagrangian submanifold in a symplectic orbifold. We work on an elliptic orbifold sphere and see that above two algebras are isomorphic\, and furthermore their structure constants are related by a modular identity which was used to prove the mirror symmetry of closed string pairings. This is a joint work with Cheol-Hyun Cho.\n\n\n7/27/2020 9:30pm ET\nMao Sheng (USTC)\nThis meeting will be taking place virtually on Zoom. \nTitle: Parabolic de Rham bundles: motivic vs periodic \nAbstract: Let \($C$\) be a complex smooth projective curve. We consider the set of parabolic de Rham bundles over \($C$\) (with rational weights in parabolic structure). Many examples arise from geometry: let \($f: X\to U$\) be a smooth projective morphism over some nonempty Zariski open subset \($U\subset C$\). Then the Deligne–Iyer–Simpson canonical parabolic extension of the Gauss–Manin systems associated to \($f$\) provides such examples. We call a parabolic de Rham bundle \emph{motivic}\, if it appears as a direct summand of such an example of geometric origin. It is a deep question in the theory of linear ordinary differential equations and in Hodge theory\, to get a characterization of motivic parabolic de Rham bundles. In this talk\, I introduce another subcategory of parabolic de Rham bundles\, the so-called \emph{periodic} parabolic de Rham bundles. It is based on the work of Lan–Sheng–Zuo on Higgs-de Rham flows\, with aim towards linking the Simpson correspondence over the field of complex numbers and the Ogus–Vologodsky correspondence over the finite fields. We show that motivic parabolic de Rham bundles are periodic\, and conjecture that they are all periodic parabolic de Rham bundles. The conjecture for rank one case follows from the solution of Grothendieck–Katz p-curvature conjecture\, and for some versions of rigid cases should follow from Katz’s work on rigid local systems. The conjecture implies that in a spread-out of any complex elliptic curve\, there will be infinitely many supersingular primes\, a result of N. Elkies for rational elliptic curves. Among other implications of the conjecture\, we would like to single out the conjectural arithmetic Simpson correspondence\, which asserts that the grading functor is an equivalence of categories from the category of periodic parabolic de Rham bundles to the category of periodic parabolic Higgs bundles. This is a joint work in progress with R. Krishnamoorthy.\n\n\n8/4/2020\n9:30am Et\nPavel Safronov (University of Zurich)\nThis meeting will be taking place virtually on Zoom. \nTitle: Kapustin–Witten TFT on 3-manifolds and skein modules\n\nAbstract: Kapustin and Witten have studied a one-parameter family of topological twists of \(4d N=4\) super Yang–Mills. They have shown that the categories of boundary conditions on a surface are exactly the categories participating in the geometric Langlands program of Beilinson and Drinfeld. Moreover\, S-duality is manifested as a quantum geometric Langlands duality after the topological twist. In this talk I will describe some mathematical formalizations of Hilbert spaces of states on a 3-manifold. I will outline an equivalence between two such possible formalizations: complexified Floer homology of Abouzaid–Manolescu and skein modules. This is a report on work in progress joint with Sam Gunningham.\n\n\n8/11/2020\n9:30am\nXujia Chen (Stonybrook)\nThis meeting will be taking place virtually on Zoom. \nTitle: Lifting cobordisms and Kontsevich-type recursions for counts of real curves \nAbstract: Kontsevich’s recursion\, proved in the early 90s\, is a recursion formula for the counts of rational holomorphic curves in complex manifolds. For complex fourfolds and sixfolds with a real structure (i.e. a conjugation)\, signed invariant counts of real rational holomorphic curves were defined by Welschinger in 2003. Solomon interpreted Welschinger’s invariants as holomorphic disk counts in 2006 and proposed Kontsevich-type recursions for them in 2007\, along with an outline of a potential approach of proving them. For many symplectic fourfolds and sixfolds\, these recursions determine all invariants from basic inputs. We establish Solomon’s recursions by re-interpreting his disk counts as degrees of relatively oriented pseudocycles from moduli spaces of stable real maps and lifting cobordisms from Deligne-Mumford moduli spaces of stable real curves (which is different from Solomon’s approach).\n\n\n8/18/2020\n9:30am ET\nDongmin Gang (Asia Pacific Center for Theoretical Physics)\nThis meeting will be taking place virtually on Zoom. \nTitle: M-theoretic genesis of topological phases \nAbstract:  I will talk about a novel way of constructing \((2+1)d\) topological phases using M-theory. They emerge as macroscopic world-volume theories of M5-branes wrapped on non-hyperbolic 3-manifolds. After explaining the algorithm of extracting modular structures of the topological phase  from topological data of the 3-manifold\, I will discuss the possibility of full classification of topological orders via the geometrical construction.\n\n\n8/25/2020\n9:30pm ET\nMykola Dedushenko (Caltech)\nThis meeting will be taking place virtually on Zoom. \nTitle: Algebras and traces at the boundary of \(4d N=4\) SYM \nAbstract: I will describe how the structure of supersymmetric boundary correlators in \(4d N=4\) SYM can be encoded in a class of associative algebras equipped with twisted traces. In the case of interfaces\, this yields a new connection to integrability.
URL:https://cmsa.fas.harvard.edu/event/geometry-and-physics-seminar/
CATEGORIES:Geometry and Physics Seminar
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SUMMARY:Strongly Correlated Quantum Materials and High-Temperature Superconductors Series
DESCRIPTION:In the 2020-2021 academic year\, the CMSA will be hosting a lecture series on Strongly Correlated Materials and High Tc Superconductor. All talks will take place from 10:30-12:00pm ET virtually on Zoom. \nCuprate high-temperature superconductors are a classic quantum material system to demonstrate the beauty of “Emergence and Entanglement” in the quantum phases of matter. Merely by adding more holes into an antiferromagnetic insulator\, several fascinating phases emerge\, including a d-wave superconductor\, a pseudo-gap metal\, and strange metal. After intensive studies from experimental\, theoretical\, and numerical communities for more than three decades\, remarkable progress has been made\, but basic questions remain: \n\nWhat is the origin of the superconductivity? What are the relative contributions of electron-phonon coupling\, spin fluctuations\, or resonating-valence-bonds?\nHow do we explain the pseudo-gap and the Fermi arc in the underdoped region above the critical temperature? Are they from some symmetry breaking order parameters\, or do we need an unconventional picture involving fractionalization?\nIs the strange metal at optimal doping associated with a quantum critical point? And if so\, what is the driving force of this phase transition?\n\nThe cuprate quantum materials have been a major source for many new concepts in modern condensed matter physics\, such as quantum spin liquids\, topological order\, and non-Fermi liquids. In the coming years\, it is clear that the study of the cuprates will continually motivate new concepts and development of new techniques. In this seminar series\, we hope to accelerate this process by bringing together deeper conversations between experimental\, theoretical\, and numerical experts with different backgrounds and perspectives. \nThe Strongly Correlated Quantum Materials and High-Temperature Superconductors series is a part of the Quantum Matter in Mathematics and Physics seminar. \nSeminar organizers: Juven Wang (Harvard CMSA) and Yahui Zhang (Harvard). \nScientific program advisors: Professor Subir Sachdev (Harvard)\, Professor Patrick Lee (MIT). \nIn order to learn how to attend this series\, please fill out this form. \nFor more information\, please contact Juven Wang (jw@cmsa.fas.harvard.edu) and Yahui Zhang (yahui_zhang@g.harvard.edu) \nSpring 2022\nApril 20\, 2022 | 11:30 – 1:00 pm ET \nHarold Y. Hwang (Stanford University & SLAC National Accelerator Laboratory) \nTitle: Superconductivity in infinite-layer nickelates \nAbstract: Since its discovery\, unconventional superconductivity in cuprates has motivated the search for materials with analogous electronic or atomic structure. We have used soft chemistry approaches to synthesize superconducting infinite layer nickelates from their perovskite precursor phase. We will present the synthesis and transport properties of the nickelates\, observation of a doping-dependent superconducting dome\, and our current understanding of their electronic and magnetic structure. \n\nFebruary 3\, 2022 | 11:30 – 1:00 pm ET \nLu Li (U Michigan) \nTitle: Quantum Oscillations of Electrical Resistivity in an Insulator \nAbstract: In metals\, orbital motions of conduction electrons are quantized in magnetic fields\, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators\, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12\, despite much larger than that of usual metals\, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems. \n2020 – 2021\nSeptember 2\, 2020 | 10:30am ET\n\n\n\n\n\n\n\nSubir Sachdev (Harvard) \nTitle: Metal-to-metal quantum phase transitions not described by symmetry-breaking orders \nAbstract: Numerous experiments have explored the phases of the cuprates with increasing doping density p from the antiferromagnetic insulator. There is now strong evidence that the small p region is a novel phase of matter\, often called the pseudogap metal\, separated from conventional Fermi liquid at larger p by a quantum phase transition. Symmetry-breaking orders play a spectator role\, at best\, at this quantum phase transition. I will describe trial wavefunctions across this metal-metal transition employing hidden layers of ancilla qubits (proposed by Ya-Hui Zhang). Quantum fluctuations are described by a gauge theory  of ghost fermions that carry neither spin nor charge. I will also\ndescribe a separate approach to this transition in a t-J model with random exchange interactions in the limit of large dimensions. This approach leads to a partly solvable SYK-like critical theory of holons and spinons\, and a linear in temperature resistivity from time reparameterization fluctuations. Near criticality\, both approaches have in common emergent fractionalized excitations\, and a significantly larger entropy than naively expected. \nVideo\n\n\n\n\nSeptember 23\, 2020 | 10:30am ET\n\n\n\n\n\n\n\nSubir Sachdev (Harvard) \nTitle: Metal-to-metal quantum phase transitions not described by symmetry-breaking orders II \nAbstract: In this second talk\, I will focus on (nearly) solvable models of metal-metal transition in random systems. The t-J model with random and all-to-all hopping and exchange can be mapped onto a quantum impurity model coupled self-consistently to an environment (the mapping also applies to a t-J model in a large dimension lattice\,  with random nearest-neighbor exchange). Such models will be argued to exhibit metal-metal quantum phase transitions in the universality class of the SYK model\, accompanied by a linear-in-T resistivity from time reparameterization  fluctuations. I will also present the results of exact diagonalization of random t-J clusters\, obtained recently with Henry Shackleton\, Alexander Wietek\, and Antoine Georges. \nVideo\n\n\n\n\nSeptember 24\, 2020 | 12:00pm ET\n\n\n\n\n\n\n\nInna Vishik (University of California\, Davis)\n\nTitle: Universality vs materials-dependence in cuprates: ARPES studies of the model cuprate Hg1201Abstract: The cuprate superconductors exhibit the highest ambient-pressure superconducting transition temperatures (T c )\, and after more than three decades of extraordinary research activity\, continue to pose formidable scientific challenges. A major experimental obstacle has been to distinguish universal phenomena from materials- or technique-dependent ones. Angle-resolved photoemission spectroscopy (ARPES) measures momentum-dependent single-particle electronic excitations and has been invaluable in the endeavor to determine the anisotropic momentum-space properties of the cuprates. HgBa 2 CuO 4+d (Hg1201) is a single-layer cuprate with a particularly high optimal T c and a simple crystal structure; yet there exists little information from ARPES about the electronic properties of this model system. I will present recent ARPES studies of doping-\, temperature-\, and momentum-dependent systematics of near-nodal dispersion anomalies in Hg1201. The data reveal a hierarchy of three distinct energy scales which establish several universal phenomena\, both in terms of connecting multiple experimental techniques for a single material\, and in terms of connecting comparable spectral features in multiple structurally similar cuprates.Video\n\n\n\n\nOctober 15\, 2020 | 10:30am ET\n\n\n\n\n\n\n\nLouis Taillefer (Université de Sherbrooke) \nTitle: New signatures of the pseudogap phase of cuprate superconductors \nAbstract: The pseudogap phase of cuprate superconductors is arguably the most enigmatic phase of quantum matter. We aim to shed new light on this phase by investigating the non- superconducting ground state of several cuprate materials at low temperature across a wide doping range\, suppressing superconductivity with a magnetic field. Hall effect measurements across the pseudogap critical doping p* reveal a sharp drop in carrier density n from n = 1 + p above p* to n = p below p\, signaling a major transformation of the Fermi surface. Angle-dependent magneto-resistance (ADMR) directly reveals a change in Fermi surface topology across p. From specific heat measurements\, we observe the classic thermodynamic signatures of quantum criticality: the electronic specific heat C el shows a sharp peak at p\, where it varies in temperature as C el ~ – T logT. At p and just above\, the electrical resistivity is linear in T at low T\, with an inelastic scattering rate that obeys the Planckian limit. Finally\, the pseudogap phase is found to have a large negative thermal Hall conductivity\, which extends to zero doping. We show that the pseudogap phase makes phonons become chiral. Understanding the mechanisms responsible for these various new signatures will help elucidate the nature of the pseudogap phase. \nVideo\n\n\n\n\nOctober 28\, 2020 | 10:30am ET\n\n\n\n\n\n\n\nPatrick Lee (MIT) \nTitle: The not-so-normal normal state of underdoped Cuprate \nAbstract: The underdoped Cuprate exhibits a rich variety of unusual properties that have been exposed after years of experimental investigations. They include a pseudo-gap near the anti-nodal points and “Fermi arcs” of gapless excitations\, together with a variety of order such as charge order\, nematicity and possibly loop currents and time reversal and inversion breaking. I shall argue that by making a single assumption of strong pair fluctuations at finite momentum (Pair density wave)\, a unified description of this phenomenology is possible. As an example\, I will focus on a description of the ground state that emerges when superconductivity is suppressed by a magnetic field which supports small electron pockets. [Dai\, Senthil\, Lee\, Phys Rev B101\, 064502 (2020)] There is some support for the pair density wave hypothesis from STM data that found charge order at double the usual wave-vector in the vicinity of vortices\, as well as evidence for a fragile form of superconductivity persisting to fields much above Hc2. I shall suggest a more direct experimental probe of the proposed fluctuating pair density wave. \nVideo\n\n\n\n\nNovember 6\, 2020 |12:30pm ET\n\n\n\n\n\n\n\nZhi-Xun Shen (Stanford University) \nTitle: Essential Ingredients for Superconductivity in Cupper Oxide Superconductors \nAbstract: High‐temperature superconductivity in cupper oxides\, with critical temperature well above what wasanticipated by the BCS theory\, remains a major unsolved physics problem. The problem is fascinating because it is simultaneously simple ‐ being a single band and 1⁄2 spin system\, yet extremely rich ‐ boasting d‐wave superconductivity\, pseudogap\, spin and charge orders\, and strange metal phenomenology. For this reason\, cuprates emerge as the most important model system for correlated electrons – stimulating conversations on the physics of Hubbard model\, quantum critical point\, Planckian metal and beyond.\nCentral to this debate is whether the Hubbard model\, which is the natural starting point for the undoped\nmagnetic insulator\, contains the essential ingredients for key physics in cuprates. In this talk\, I will discuss our photoemission evidence for a multifaceted answer to this question [1‐3]. First\, we show results that naturally points to the importance of Coulomb and magnetic interactions\, including d‐wave superconducting gap structure [4]\, exchange energy (J) control of bandwidth in single‐hole dynamics [5]. Second\, we evidence effects beyond the Hubbard model\, including band dispersion anomalies at known phonon frequencies [6\, 7]\, polaronic spectral lineshape and the emergence of quasiparticle with doping [8]. Third\, we show properties likely of hybrid electronic and phononic origin\, including the pseudogap [9‐11]\, and the almost vertical phase boundary near the critical 19% doping [12]. Fourth\, we show examples of small q phononic coupling that cooperates with d‐wave superconductivity [13‐15]. Finally\, we discuss recent experimental advance in synthesizing and investigating doped one‐dimensional (1D) cuprates [16]. As theoretical calculations of the 1D Hubbard model are reliable\, a robust comparison can be carried out. The experiment reveals a near‐neighbor attractive interaction that is an order of magnitude larger than the attraction generated by spin‐superexchange in the Hubbard model. Addition of such an attractive term\, likely of phononic origin\, into the Hubbard model with canonical parameters provides a quantitative explanation for all important experimental observable: spinon and holon dispersions\, and holon‐ holon attraction. Given the structural similarity of the materials\, It is likely that an extended two‐dimensional\n(2D) Hubbard model with such an attractive term\, will connect the dots of the above four classes of\nexperimental observables and provide a holistic understanding of cuprates\, including the elusive d‐wave superconductivity in 2D Hubbard model. \n[1] A. Damascelli\, Z. Hussain\, and Z.‐X. Shen\, Review of Modern Physics\, 75\, 473 (2003)\n[2] M. Hashimoto et al.\, Nature Physics 10\, 483 (2014)\n[3] JA Sobota\, Y He\, ZX Shen ‐ arXiv preprint arXiv:2008.02378\, 2020; submitted to Rev. of Mod. Phys.\n[4] Z.‐X. Shen et al.\, Phys. Rev. Lett. 70\, 1553 (1993)\n[5] B.O. Wells et al.\, Phys. Rev. Lett. 74\, 964 (1995)\n[6] A. Lanzara et al.\, Nature 412\, 510 (2001)\n[7] T. Cuk et al.\, Phys. Rev. Lett.\, 93\, 117003 (2004)\n[8] K.M. Shen et al.\, Phys. Rev. Lett.\, 93\, 267002 (2004)\n[9] D.M. King et al.\, J. of Phys. & Chem of Solids 56\, 1865 (1995)\n[10] D.S. Marshall et al.\, Phy. Rev. Lett. 76\, 484 (1996)\n[11] A.G. Loeser et al.\, Science 273\, 325 (1996)\n[12] S. Chen et al.\, Science\, 366\, 6469 (2019)\n[13] T.P. Devereaux\, T. Cuk\, Z.X. Shen\, N. Nagaosa\, Phys. Rev. Lett.\, 93\, 117004 (2004)\n[14] S. Johnston et al.\, Phys. Rev. Lett. 108\, 166404 (2012)\n[15] Yu He et al.\, Science\, 362\, 62 (Oct. 2018)\n[16] Z. Chen\, Y. Wang et al.\, preprint\, 2020 \nVideo\n\n\n\n\nNovember 12\, 2020 |10:30am ET\n\n\n\n\n\n\n\nChandra Varma (Visting Professor\, University of California\, Berkeley.\nEmeritus Distinguished Professor\, University of California\, Riverside.)Title: Loop-Current Order and Quantum-Criticality in CupratesThis talk is organized as follows:\n1. Physical Principles leading to Loop-current order and quantum criticality as the central feature in the physics of Cuprates.\n2. Summary of the essentially exact solution of the dissipative xy model for Loop-current fluctuations.\n3. Quantitative comparison of theory for the quantum-criticality with a variety of experiments.\n4. Topological decoration of loop-current order to understand ”Fermi-arcs” and small Fermi-surface magneto-oscillations.Time permitting\,\n(i) Quantitative theory and experiment for fluctuations leading to d-wave superconductivity.\n(ii) Extensions to understand AFM quantum-criticality in heavy-fermions and Fe-based superconductors.\n(iii) Problems.Video\n\n\n\n\nNovember 18\, 2020 |10:30am ET\n\n\n\n\n\n\n\nAntoine Georges (Collège de France\, Paris and Flatiron Institute\, New York) \nTitle: Superconductivity\, Stripes\, Antiferromagnetism and the Pseudogap: What Do We Know Today about the 2D Hubbard model? \nAbstract: Simplified as it is\, the Hubbard model embodies much of the complexity of the `strong correlation problem’ and has established itself as a paradigmatic model in the field. In this talk\, I will argue that several key aspects of its physics in two dimensions can now be established beyond doubt\, thanks to the development of controlled and accurate computational methods. These methods implement different and complementary points of view on the quantum many-body problem. Along with pushing forward each method\, the community has recently embarked into a major effort to combine and critically compare these approaches\, and in several instances a consistent picture of the physics has emerged as a result. I will review in this perspective our current understanding of the emergence of a pseudogap in both the weak and strong coupling regimes. I will present recent progress in understanding how the pseudogap phase may evolve into a stripe-dominated regime at low temperature\, and briefly address the delicate question of the competition between stripes and superconductivity. I will also emphasize outstanding questions which are still open\, such as the possibility of a Fermi surface reconstruction without symmetry breaking. Whenever possible\, connections to the physics of cuprate superconductors will be made. If time permits\, I may also address the question of Planckian transport and bad metallic transport at high temperature. \nVideo\n\n\n\n\nNovember 19\, 2020 |10:30am ET\n\n\n\n\n\n\n\nEduardo Fradkin (University of Illinois at Urbana-Champaign) \nTitle: Pair Density Waves and Intertwined Orders in High Tc Superconductors\n\nAbstract: I will argue that the orders that are present in high temperature superconductors naturally arise with the same strength and are better regarded as intertwined rather than competing. I illustrate this concept in the context of the orders that are present in the pair-density-wave state and the phase diagrams that result from this analysis. \nVideo\n\n\n\n\nNovember 25\, 2020 |10:30am ET\n\n\n\n\n\n\n\nQimiao Si (Rice University) \nTitle: Bad Metals and Electronic Orders – Nematicity from Iron Pnictides to Graphene Moiré Systems \nAbstract: Strongly correlated electron systems often show bad-metal behavior\, as operationally specified in terms of a resistivity at room temperature that reaches or exceeds the Mott-Ioffe-Regel limit. They display a rich landscape of electronic orders\, which provide clues to the underlying microscopic physics. Iron-based superconductors present a striking case study\, and have been the subject of extensive efforts during the past decade or so. They are well established to be bad metals\, and their phase diagrams prominently feature various types of electronic orders that are essentially always accompanied by nematicity. In this talk\, I will summarize these characteristic features and discuss our own efforts towards understanding the normal state through the lens of the electronic orders and their fluctuations. Implications for superconductivity will be briefly discussed. In the second part of the talk\, I will consider the nematic correlations that have been observed in the graphene-based moiré narrow-band systems. I will present a theoretical study which demonstrates nematicity in a “fragile insulator”\, predicts its persistence in the bad metal regime and provides an overall perspective on the phase diagram of these correlated systems.\n\n\n\n\nDecember 2\, 2020 |10:30am ET\n\n\n\n\n\n\n\nAndrey Chubukov (University of Minnesota) \nTitle: Interplay between superconductivity and non-Fermi liquid at a quantum critical point in a metal \n\nAbstract:  I discuss the interplay between non-Fermi liquid behaviour and pairing near a quantum-critical point (QCP) in a metal. These tendencies are intertwined in the sense that both originate from the same interaction mediated by gapless fluctuations of a critical order parameter. The two tendencies compete because fermionic incoherence destroys the Cooper logarithm\, while the pairing eliminates scattering at low energies and restores fermionic coherence. I discuss this physics for a class of models with an effective dynamical interaction V (Ω) ~1/|Ω|^γ (the γ-model). This model describes\, in particular\, the pairing at a 2D Ising-nematic critical point in (γ=1/3)\, a 2D antiferromagnetic critical point (γ=1/2) and the pairing by an Einstein phonon with vanishing dressed Debye frequency (γ=2). I argue the pairing wins\, unless the pairing component of the interaction is artificially reduced\, but because of fermionic incoherence in the normal state\, the system develops a pseudogap\, preformed pairs behaviour in the temperature range between the onset of the pairing at Tp and the onset of phase coherence at the actual superconducting Tc. The ratio Tc/Tp decreases with γ and vanishes at γ =2. I present two complementary arguments of why this happens. One is the softening of longitudinal gap fluctuations\, which become gapless at γ =2. Another is the emergence of a 1D array of dynamical vortices\, whose number diverges at γ =2. I argue that once the number of vortices becomes infinite\, quasiparticle energies effectively get quantized and do not get re-arranged in the presence of a small phase variation. I show that a new non-superconducting ground state emerges at γ >2.\n\n\n\n\nDecember 9\, 2020 |10:30am ET\n\n\n\n\n\n\n\nDavid Hsieh (Caltech) \nTitle:  Signatures of anomalous symmetry breaking in the cuprates   \nAbstract: The temperature versus doping phase diagram of the cuprate high-Tc superconductors features an enigmatic pseudogap region whose microscopic origin remains a subject of intensive study. Experimentally resolving its symmetry properties is imperative for narrowing down the list of possible explanations. In this talk I will give an overview of how optical second harmonic generation (SHG) can be used as a sensitive probe of symmetry breaking\, and recap the ways it has been used to solve outstanding problems in condensed matter physics. I will then describe how we have been applying SHG polarimetry and spectroscopy to interrogate the cuprate pseudogap. In particular\, I will discuss our data on YBa2Cu3Oy [1]\, which show an order parameter-like increase in SHG intensity below the pseudogap temperature T* across a broad range of doping levels. I will then focus on our more recent results on a model parent cuprate Sr2CuO2Cl2 [2]\, where evidence of anomalous broken symmetries surprisingly also exists. Possible connections between these observations will be speculated upon.\n[1] L. Zhao\, C. A. Belvin\, R. Liang\, D. A. Bonn\, W. N. Hardy\, N. P. Armitage and D. Hsieh\, “A global inversion-symmetry-broken phase inside the pseudogap region of YBa2Cu3Oy\,” Nature Phys. 13\, 250 (2017). \n[2] A. de la Torre\, K. L. Seyler\, L. Zhao\, S. Di Matteo\, M. S. Scheurer\, Y. Li\, B. Yu\, M. Greven\, S. Sachdev\, M. R. Norman and D. Hsieh. “Anomalous mirror symmetry breaking in a model insulating cuprate Sr2CuO2Cl2\,” Preprint at https://arxiv.org/abs/2008.06516\n\n\n\n\nDecember 16\, 2020 |10:30am ET\n\n\n\n\n\n\n\nZheng-Yu Weng (Tsinghua University) \nTitle: Organizing Principle of Mottness and Complex Phenomenon in High Temperature Superconductors\n\nAbstract: The complex phenomenon in the high-Tc cuprate calls for a microscopic understanding based on general principles. In this Lecture\, an exact organizing principle for a typical doped Mott insulator will be presented\, in which the fermion sign structure is drastically reduced to a mutual statistics. Its nature as a long-range spin-charge entanglement of many-body quantum mechanics will be exemplified by exact numerical calculations. The phase diagram of the cuprate may be unified in a “bottom-up” fashion by a “parent” ground state ansatz with hidden orders constructed based on the organizing principle. Here the pairing mechanism will go beyond the “RVB” picture and the superconducting state is of non-BCS nature with modified London equation and novel elementary excitations. In particular\, the Bogoliubov/Landau quasiparticle excitation are emerging with a two-gap structure in the superconducting state and the Fermi arc in a pseudogap regime. A mathematic framework of fractionalization and duality transformation guided by the organizing principle will be introduced to describe the above emergent phenomenon.\n\n\n\n\nDecember 17\, 2020 |10:30am ET\n\n\n\n\n\n\n\nSteven Kivelson (Stanford University) \nTitle: What do we know about the essential physics of high temperature superconductivity after one third of a century? \nAbstract: Despite the fact that papers submitted to glossy journals universally start by bemoaning the absence of theoretical understanding\, I will argue that the answer to the title question is “quite a lot.” To focus the discussion\, I will take the late P.W. Anderson’s “Last Words on the Cuprates” (arXiv:1612.03919) as a point of departure\, although from a perspective that differs from his in many key points.\n\n\n\n\nJanuary 20\, 2021 |10:30am ET\n\n\n\n\n\n\n\nThomas Peter Devereaux (Stanford University) \nTitle:  Numerical investigations of models of the cuprates\n\nAbstract: Richard Feynman once said “Anyone who wants to analyze the properties of matter in a real problem might want to start by writing down the fundamental equations and then try to solve them mathematically. Although there are people who try to use such an approach\, these people are the failures in this field. . . ” \nI will summarize efforts to solve microscopic models of the cuprates using quantum Monte Carlo and density matrix renormalization group computational methods\, with emphasis on how far one can get before failing to describe the real materials. I will start with an overview of the quantum chemistry of the cuprates that guides our choices of models\, and then I will discuss “phases” of these models\, both realized and not. I will lastly discuss the transport properties of the models in the “not-so-normal” regions of the phase diagram.\n\n\n\n\nFebruary 3\, 2021 |10:30am ET\n\n\n\n\n\n\n\nPhilip Phillips (University of Illinois Urbana-Champaign) \nTitle: Beyond BCS: An Exact Model for Superconductivity and Mottness\n\nAbstract: High-temperature superconductivity in the cuprates remains an unsolved problem because the cuprates start off their lives as Mott insulators in which no organizing principle such a Fermi surface can be invoked to treat the electron interactions. Consequently\, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity. Part of the problem is that the basic model for a Mott insulator\, namely the Hubbard model is unsolvable in any dimension we really care about. To address this problem\, I will start by focusing on the overlooked Z_2 emergent symmetry of a Fermi surface first noted by Anderson and Haldane. Mott insulators break this emergent symmetry. The simplest model of this type is due to Hatsugai/Kohmoto. I will argue that this model can be thought of a fixed point for Mottness. I will then show exactly[1] that this model when appended with a weak pairing interaction exhibits not only the analogue of Cooper’s instability but also a superconducting ground state\, thereby demonstrating that a model for a doped Mott insulator can exhibit superconductivity. The properties of the superconducting state differ drastically from that of the standard BCS theory. The elementary excitations of this superconductor are not linear combinations of particle and hole states but rather are superpositions of doublons and holons\, composite excitations signaling that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state. Additional unexpected features of this model are that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies and a suppression of the superfluid density as seen in the cuprates.\n[1] PWP\, L. Yeo\, E. Huang\, Nature Physics\, 16\, 1175-1180 (2020).\n\n\n\n\nFebruary 10\, 2021 |10:30am ET\n\n\n\n\n\n\n\nSenthil Todadri (MIT) \nTitle: Strange metals as ersatz Fermi liquids: emergent symmetries\, general constraints\, and experimental tests \nAbstract: The strange metal regime is one of the most prominent features of the cuprate phase diagram but yet has remained amongst the most mysterious. Seemingly similar metallic behavior is seen in a few other metals. In this talk\, I will discuss\, in great generality\, some properties of `strange metals’ in an ideal clean system. I will discuss general constraints[1] on the emergent low energy symmetries of any such strange metal. These constraints may be viewed as a generalization of the Luttinger theorem of ordinary Fermi liquids. Many\, if not all\, non-Fermi liquids will have the same realization of emergent symmetry as a Fermi liquid (even though they could have very different dynamics). Such phases – dubbed ersatz Fermi liquids – share some (but not all) universal properties with Fermi liquids. I will discuss the implications for understanding the strange metal physics observed in experiments . Combined with a few experimental observations\, I will show that these general model-independent considerations lead to concrete predictions[2] about a class of strange metals. The most striking of these is a divergent susceptibility of an observable that has the same symmetries as the loop current order parameter.\n[1]. Dominic Else\, Ryan Thorngren\, T. Senthil\, https://arxiv.org/abs/2007.07896\n[2]. Dominic Else\, T. Senthil\, https://arxiv.org/abs/2010.10523\n\n\n\n\nApril 1\, 2021 |9:00am ET\n\n\n\n\n\n\n\nNaoto Nagaosa (University of Tokyo) \nTitle: Applied physics of high-Tc theories \nAbstract: Since the discovery of high temperature superconductors in cuprates in 1986\, many theoretical ideas have been proposed which have enriched condensed matter theory. Especially\, the resonating valence bond (RVB) state for (doped) spin liquids is one of the most fruitful idea. In this talk\, I would like to describe the development of RVB idea to broader class of materials\, especially more conventional magnets. It is related to the noncollinear spin structures with spin chirality and associated quantal Berry phase applied to many phenomena and spintronics applications. It includes the (quantum) anomalous Hall effect\, spin Hall effect\, topological insulator\, multiferroics\, various topological spin textures\, e.g.\, skyrmions\, and nonlinear optics. I will show that even though the phenomena are extensive\, the basic idea is rather simple and common in all of these topics.\n\n\n\n\nApril 22\, 2021 |10:30am ET\n\n\n\n\n\n\n\nDung-Hai Lee (UC Berkeley) \nTitle: “Non-abelian bosonization in two and three spatial dimensions and some applications” \nAbstract: In this talk\, we generalize Witten’s non-abelian bosonization in $(1+1)$-D to two and three spatial dimensions. Our theory applies to fermions with relativistic dispersion. The bosonized theories are non-linear sigma models with level-1 Wess-Zumino-Witten terms. As applications\, we apply the bosonization results to the $SU(2)$ gauge theory of the $\pi$ flux mean-field theory of half-filled Hubbard model\, critical spin liquids of “bipartite-Mott insulators” in 1\,2\,3 spatial dimensions\, and twisted bilayer graphene.\n\n\n\n\nMay 12\, 2021 |10:30am ET\n\n\n\n\n\n\n\nAndré-Marie Tremblay (Université de Sherbrooke) \nTitle: A unified theoretical perspective on the cuprate phase diagram \nAbstract: Many features of the cuprate phase diagram are a challenge for the usual tools of solid state physics. I will show how a perspective that takes into account both the localized and delocalized aspects of conduction electrons can explain\, at least qualitatively\, many of these features. More specifically\, I will show that the work of several groups using cluster extensions of dynamical mean-field theory sheds light on the pseudogap\, on the quantum-critical point and on d-wave superconductivity. I will argue that the charge transfer gap and oxygen hole content are the best indicators of strong superconductivity and that many observations are a signature of the influence of Mott physics away from half-filling. I will also briefly comment on what information theoretic measures tell us about this problem.\n\n\n\n\nAugust 11\, 2021 |10:30am ET\n\n\n\n\n\n\n\nPiers Coleman (Rutgers) \nTitle: Order Fractionalization* \nAbstract: I will discuss the interplay of spin fractionalization with broken\nsymmetry. When a spin fractionalizes into a fermion\, the resulting particle\ncan hybridize or pair with the mobile electrons to develop a new kind of\nfractional order parameter. The concept of “order fractionalization” enables\nus to extend the concept of off-diagonal order to encompass the formation of\nsuch order parameters with fractional quantum numbers\, such as spinorial\norder[1].\nA beautiful illustration of this phenomenon is provided by a model\nwhich incorporates the Yao-Lee-Kitaev model into a Kondo lattice[2]. This\nmodel explicitly exhibits order fractionalization and is expected to undergo a\ndiscrete Ising phase transition at finite temperature into an\norder-fractionalized phase with gapless Majorana excitations.\nThe broader implications of these considerations for Quantum\nMaterials and Quantum Field Theory will be discussed.\nWork done in collaboration with Yashar Komijani\, Anna Toth and Alexei\nTsvelik.\n[1] Order Fractionalization\, Yashar Komijani\, Anna Toth\, Premala Chandra\, Piers Coleman\, (2018).\n[2] Order Fractionalization in a Kitaev Kondo model\, Alexei Tsvelik and Piers Coleman\, (2021).\n\n\n\n\nSeptember 15\, 2021 |10:30am ET\n\n\n\n\n\n\n\nLiang Fu (MIT) \nTitle: Three-particle mechanism for pairing and superconductivity \nAbstract: I will present a new mechanism and an exact theory of electron pairing due to repulsive interaction in doped insulators. When the kinetic energy is small\, the dynamics of adjacent electrons on the lattice is strongly correlated. By developing a controlled kinetic energy expansion\, I will show that two doped charges can attract and form a bound state\, despite and because of the underlying repulsion. This attraction by repulsion is enabled by the virtual excitation of a third electron in the filled band. This three-particle pairing mechanism leads to a variety of novel phenomena at finite doping\, including spin-triplet superconductivity\, pair density wave\, BCS-BEC crossover and Feshbach resonance involving “trimers”. Possible realizations in moire materials\, ZrNCl and WTe2 will be discussed. \n[1] V. Crepel and L. Fu\, Science Advances 7\, eabh2233 (2021)\n[2] V. Crepel and L. Fu\, arXiv:2103.12060\n[3] K. Slagle and L. Fu\,  Phys. Rev. B 102\, 235423 (2020)\n\n\n\n\nSeptember 29\, 2021 |11:30am ET (special time)\n\n\n\n\n\n\n\nNai Phuan Ong (Princeton University)\n\nTitle:.Abstract: The layered honeycomb magnet alpha-RuCl3 orders below 7 K in a zigzag phase in zero field. An in-plane magnetic field H||a suppresses the zigzag order at 7 Tesla\, leaving a spin-disordered phase widely believed to be a quantum spin liquid (QSL) that extends to ~12 T. We have observed oscillations in the longitudinal thermal conductivity Kxx vs. H from 0.4 to 4 K. The oscillations are periodic in 1/H (with a break-in-slope at 7 T). The amplitude function is maximal in the QSL phase (7 –11.5 T). I will describe a benchmark for crystalline disorder\, the reproducibility and intrinsic nature of the oscillations\, and discuss implications for the QSL state. I will also show detailed data on the thermal Hall conductivity Kxy measured from 0.4 K to 10 K and comment on recent half-quantization results.*Czajka et al.\, Nature Physics 17\, 915 (2021).Collaborators: Czajka\, Gao\, Hirschberger\, Lampen Kelley\, Banerjee\, Yan\, Mandrus and Nagler.\n\n\n\n\nDate TBA |10:30am ET\n\n\n\n\n\n\n\nSuchitra Sebastian (University of Cambridge) \nTitle: TBA\n\n\n\n\nDate TBA |10:30am ET\n\n\n\n\n\n\n\nJenny Hoffman (Harvard University) \nTitle: TBA
URL:https://cmsa.fas.harvard.edu/event/strongly-correlated-quantum-materials-and-high-temperature-superconductors-series/
CATEGORIES:Event,Strongly Correlated Quantum Materials and High-Temperature Superconductors
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/unnamed-3-600x338-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201001T103000
DTEND;TZID=America/New_York:20201001T120000
DTSTAMP:20260404T221413
CREATED:20240209T013427Z
LAST-MODIFIED:20240209T013427Z
UID:10001774-1601548200-1601553600@cmsa.fas.harvard.edu
SUMMARY:10/1/2020 Quantum Matter seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/10-1-2020-quantum-matter-seminar/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201002T104500
DTEND;TZID=America/New_York:20201002T121500
DTSTAMP:20260404T221413
CREATED:20230707T112042Z
LAST-MODIFIED:20250328T200723Z
UID:10000143-1601635500-1601640900@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture: Birational geometry
DESCRIPTION:Vyacheslav V. Shokurov (Johns Hopkins University) \nTitle: Birational geometry \nAbstract: About main achievements in birational geometry during the last fifty years. \nTalk chair: Caucher Birkar \nVideo
URL:https://cmsa.fas.harvard.edu/event/cmsa-math-science-literature-lecture_shokurov/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Lecture_Shokurov-pdf.jpeg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201005T080000
DTEND;TZID=America/New_York:20201005T093000
DTSTAMP:20260404T221413
CREATED:20230707T112316Z
LAST-MODIFIED:20250328T200738Z
UID:10000144-1601884800-1601890200@cmsa.fas.harvard.edu
SUMMARY:CMSA Math-Science Literature Lecture: Kunihiko Kodaira and complex manifolds
DESCRIPTION:Yujiro Kawamata (University of Tokyo) \nTitle: Kunihiko Kodaira and complex manifolds \nAbstract: Kodaira’s motivation was to generalize the theory of Riemann surfaces in Weyl’s book to higher dimensions.  After quickly recalling the chronology of Kodaira\, I will review some of Kodaira’s works in three sections on topics of harmonic analysis\, deformation theory and compact complex surfaces.  Each topic corresponds to a volume of Kodaira’s collected works in three volumes\, of which I will cover only tiny parts. \nTalk chair: Baohua Fu \nVideo 
URL:https://cmsa.fas.harvard.edu/event/cmsa-math-science-literature-lecture_kawamata/
LOCATION:Virtual
CATEGORIES:Event,Math Science Literature Lecture Series,Public Lecture,Special Lectures
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Lecture_Kawamata-pdf.jpeg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201005T103000
DTEND;TZID=America/New_York:20201005T120000
DTSTAMP:20260404T221413
CREATED:20240201T023640Z
LAST-MODIFIED:20240201T023640Z
UID:10001527-1601893800-1601899200@cmsa.fas.harvard.edu
SUMMARY:10/05/2020 Math Physics Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/10-05-2020-math-physics-seminar/
CATEGORIES:Mathematical Physics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201005T103000
DTEND;TZID=America/New_York:20201005T120000
DTSTAMP:20260404T221413
CREATED:20240209T104813Z
LAST-MODIFIED:20240209T104813Z
UID:10001831-1601893800-1601899200@cmsa.fas.harvard.edu
SUMMARY:4/15/2020 Quantum Matter seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/4-15-2020-quantum-matter-seminar/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201006T113000
DTEND;TZID=America/New_York:20201006T123000
DTSTAMP:20260404T221413
CREATED:20240201T023837Z
LAST-MODIFIED:20240201T023837Z
UID:10001528-1601983800-1601987400@cmsa.fas.harvard.edu
SUMMARY:10/6/2020 Computer Science for Mathematicians
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/10-6-2020-computer-science-for-mathematicians/
CATEGORIES:Computer Science for Mathematicians Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201007T103000
DTEND;TZID=America/New_York:20201007T120000
DTSTAMP:20260404T221413
CREATED:20240201T022156Z
LAST-MODIFIED:20240201T022156Z
UID:10001525-1602066600-1602072000@cmsa.fas.harvard.edu
SUMMARY:10/7/2020 Quantum Matter Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/10-7-2020-quantum-matter-seminar/
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201008T103000
DTEND;TZID=America/New_York:20201008T120000
DTSTAMP:20260404T221413
CREATED:20240201T022038Z
LAST-MODIFIED:20240201T022038Z
UID:10001524-1602153000-1602158400@cmsa.fas.harvard.edu
SUMMARY:10/8/2020 Quantum Matter Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/10-8-2020-quantum-matter-seminar/
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201014T090000
DTEND;TZID=America/New_York:20201014T100000
DTSTAMP:20260404T221413
CREATED:20240127T031011Z
LAST-MODIFIED:20240507T194446Z
UID:10001499-1602666000-1602669600@cmsa.fas.harvard.edu
SUMMARY:Statistical\, mathematical\, and computational aspects of noisy intermediate-scale quantum computers 
DESCRIPTION:Speaker: Gil Kalai (Hebrew University and IDC Herzliya) \nTitle: Statistical\, mathematical\, and computational aspects of noisy intermediate-scale quantum computers \nAbstract: Noisy intermediate-scale quantum (NISQ) Computers hold the key for important theoretical and experimental questions regarding quantum computers. In the lecture I will describe some questions about mathematics\, statistics and computational complexity which arose in my study of NISQ systems and are related to \n\na) My general argument “against” quantum computers\,\nb) My analysis (with Yosi Rinott and Tomer Shoham) of the Google 2019 “quantum supremacy” experiment.\nRelevant papers:\nYosef Rinott\, Tomer Shoham and Gil Kalai\, Statistical aspects of the quantum supremacy demonstration\, https://gilkalai.files.wordpress.com/2019/11/stat-quantum2.pdf\nGil Kalai\, The Argument against Quantum Computers\, the Quantum Laws of Nature\, and Google’s Supremacy Claims\, https://gilkalai.files.wordpress.com/2020/08/laws-blog2.pdf\nGil Kalai\, Three puzzles on mathematics\, computations\, and games\, https://gilkalai.files.wordpress.com/2019/09/main-pr.pdf
URL:https://cmsa.fas.harvard.edu/event/10-14-2020-colloquium/
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.14.20-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201014T103000
DTEND;TZID=America/New_York:20201014T120000
DTSTAMP:20260404T221413
CREATED:20240127T031114Z
LAST-MODIFIED:20240127T031114Z
UID:10001500-1602671400-1602676800@cmsa.fas.harvard.edu
SUMMARY:10/14/2020 Quantum Matter Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/10-14-2020-quantum-matter-seminar/
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201014T140000
DTEND;TZID=America/New_York:20201014T150000
DTSTAMP:20260404T221413
CREATED:20240127T031227Z
LAST-MODIFIED:20240127T031227Z
UID:10001501-1602684000-1602687600@cmsa.fas.harvard.edu
SUMMARY:10/14/2020 RM&PT Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/10-14-2020-rmpt-seminar/
CATEGORIES:Random Matrix & Probability Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201014T150000
DTEND;TZID=America/New_York:20201014T160000
DTSTAMP:20260404T221413
CREATED:20240201T021720Z
LAST-MODIFIED:20240515T192014Z
UID:10001522-1602687600-1602691200@cmsa.fas.harvard.edu
SUMMARY:Triple Descent and a Fine-Grained Bias-Variance Decomposition
DESCRIPTION:Speaker: Jeffrey Pennington\, Google Brain \nTitle: Triple Descent and a Fine-Grained Bias-Variance Decomposition \nAbstract: Classical learning theory suggests that the optimal generalization performance of a machine learning model should occur at an intermediate model complexity\, striking a balance between simpler models that exhibit high bias and more complex models that exhibit high variance of the predictive function. However\, such a simple trade-off does not adequately describe the behavior of many modern deep learning models\, which simultaneously attain low bias and low variance in the heavily overparameterized regime. Recent efforts to explain this phenomenon theoretically have focused on simple settings\, such as linear regression or kernel regression with unstructured random features\, which are too coarse to reveal important nuances of actual neural networks. In this talk\, I will describe a precise high-dimensional asymptotic analysis of Neural Tangent Kernel regression that reveals some of these nuances\, including non-monotonic behavior deep in the overparameterized regime. I will also present a novel bias-variance decomposition that unambiguously attributes these surprising observations to particular sources of randomness in the training procedure.
URL:https://cmsa.fas.harvard.edu/event/10-14-2020-new-technologies-seminar/
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-10.14.20.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201015T103000
DTEND;TZID=America/New_York:20201015T120000
DTSTAMP:20260404T221413
CREATED:20240201T021839Z
LAST-MODIFIED:20240201T021839Z
UID:10001523-1602757800-1602763200@cmsa.fas.harvard.edu
SUMMARY:10/15/2020 Quantum Matter Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/10-15-2020-quantum-matter-seminar/
LOCATION:Virtual
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201019T103000
DTEND;TZID=America/New_York:20201019T113000
DTSTAMP:20260404T221413
CREATED:20240127T030908Z
LAST-MODIFIED:20240127T030908Z
UID:10001498-1603103400-1603107000@cmsa.fas.harvard.edu
SUMMARY:10/19/2020 Math Physics Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/10-19-2020-math-physics-seminar/
CATEGORIES:Mathematical Physics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201020T113000
DTEND;TZID=America/New_York:20201020T123000
DTSTAMP:20260404T221413
CREATED:20240127T030632Z
LAST-MODIFIED:20240127T030632Z
UID:10001497-1603193400-1603197000@cmsa.fas.harvard.edu
SUMMARY:10/20/2020 Computer Science for Math
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/10-20-2020-computer-science-for-math/
CATEGORIES:Computer Science for Mathematicians Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201021T103000
DTEND;TZID=America/New_York:20201021T120000
DTSTAMP:20260404T221413
CREATED:20240127T023403Z
LAST-MODIFIED:20240127T023403Z
UID:10001495-1603276200-1603281600@cmsa.fas.harvard.edu
SUMMARY:10/21/2020 Quantum Matter Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/10-21-2020-quantum-matter-seminar/
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201022T103000
DTEND;TZID=America/New_York:20201022T120000
DTSTAMP:20260404T221413
CREATED:20240127T023302Z
LAST-MODIFIED:20240127T023302Z
UID:10001494-1603362600-1603368000@cmsa.fas.harvard.edu
SUMMARY:10/22/2020 Quantum Matter Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/10-22-2020-quantum-matter-seminar/
CATEGORIES:Quantum Matter
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201027T113000
DTEND;TZID=America/New_York:20201027T123000
DTSTAMP:20260404T221413
CREATED:20240127T022958Z
LAST-MODIFIED:20240127T022958Z
UID:10001491-1603798200-1603801800@cmsa.fas.harvard.edu
SUMMARY:10/27/2020 Computer Science for Mathematicians
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/10-27-2020-computer-science-for-mathematicians/
CATEGORIES:Computer Science for Mathematicians Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201028T103000
DTEND;TZID=America/New_York:20201028T120000
DTSTAMP:20260404T221413
CREATED:20240127T023513Z
LAST-MODIFIED:20240127T023513Z
UID:10001496-1603881000-1603886400@cmsa.fas.harvard.edu
SUMMARY:10/28/2020 Strongly Correlated Quantum Materials
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/10-28-2020-strongly-correlated-quantum-materials/
CATEGORIES:Strongly Correlated Quantum Materials and High-Temperature Superconductors
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201028T140000
DTEND;TZID=America/New_York:20201028T150000
DTSTAMP:20260404T221413
CREATED:20240127T023200Z
LAST-MODIFIED:20240127T023200Z
UID:10001493-1603893600-1603897200@cmsa.fas.harvard.edu
SUMMARY:10/28/2020 RM&PT seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/10-28-2020-rmpt-seminar/
CATEGORIES:Random Matrix & Probability Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201028T150000
DTEND;TZID=America/New_York:20201028T160000
DTSTAMP:20260404T221413
CREATED:20240127T031359Z
LAST-MODIFIED:20240515T201157Z
UID:10001502-1603897200-1603900800@cmsa.fas.harvard.edu
SUMMARY:Generalization bounds for rational self-supervised learning algorithms\, or "Understanding generalizations requires rethinking deep learning"
DESCRIPTION:Speakers: Boaz Barak and Yamini Bansal\, Harvard University Dept. of Computer Science \nTitle: Generalization bounds for rational self-supervised learning algorithms\, or “Understanding generalizations requires rethinking deep learning” \nAbstract: The generalization gap of a learning algorithm is the expected difference between its performance on the training data and its performance on fresh unseen test samples. Modern deep learning algorithms typically have large generalization gaps\, as they use more parameters than the size of their training set. Moreover the best known rigorous bounds on their generalization gap are often vacuous. In this talk we will see a new upper bound on the generalization gap of classifiers that are obtained by first using self-supervision to learn a complex representation of the (label free) training data\, and then fitting a simple (e.g.\, linear) classifier to the labels. Such classifiers have become increasingly popular in recent years\, as they offer several practical advantages and have been shown to approach state-of-art results. We show that (under the assumptions described below) the generalization gap of such classifiers tends to zero as long as the complexity of the simple classifier is asymptotically smaller than the number of training samples. We stress that our bound is independent of the complexity of the representation that can use an arbitrarily large number of parameters. Our bound assuming that the learning algorithm satisfies certain noise-robustness (adding small amount of label noise causes small degradation in performance) and rationality (getting the wrong label is not better than getting no label at all) conditions that widely (and sometimes provably) hold across many standard architectures. We complement this result with an empirical study\, demonstrating that our bound is non-vacuous for many popular representation-learning based classifiers on CIFAR-10 and ImageNet\, including SimCLR\, AMDIM and BigBiGAN. The talk will not assume any specific background in machine learning\, and should be accessible to a general mathematical audience. Joint work with Gal Kaplun. \n 
URL:https://cmsa.fas.harvard.edu/event/10-28-2020-new-technologies-in-mathematics-seminar/
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-New-Technologies-in-Mathematics-10.28.20.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201029T103000
DTEND;TZID=America/New_York:20201029T120000
DTSTAMP:20260404T221413
CREATED:20240127T023101Z
LAST-MODIFIED:20240127T023101Z
UID:10001492-1603967400-1603972800@cmsa.fas.harvard.edu
SUMMARY:10/29/2020 Quantum Matter Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/10-29-2020-quantum-matter-seminar/
CATEGORIES:Quantum Matter
END:VEVENT
END:VCALENDAR