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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:20201120T150200
DTEND;TZID=America/New_York:20210101T150200
DTSTAMP:20260405T051328
CREATED:20240209T015737Z
LAST-MODIFIED:20240307T111352Z
UID:10001789-1605884520-1609513320@cmsa.fas.harvard.edu
SUMMARY:Members’ Seminar
DESCRIPTION:The CMSA Members’ Seminar will occur every Friday at 9:30am ET on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars\, as well as the weekly CMSA Colloquium series. Please email the seminar organizers to obtain a link. This year’s seminar is organized by Tianqi Wu. The Schedule will be updated below. \nPrevious seminars can be found here. \nSpring 2021:\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n\n\n1/29/2021\nCancelled\n\n\n\n2/5/2021\nItamar Shamir\nTitle: Boundary CFT and conformal anomalies \nAbstract: Boundary and defects in quantum field theory play an important role in many recent developments in theoretical physics. I will discuss such objects in the setting of conformal field theories\, focusing mainly on conformal anomalies. Boundaries or defects can support various kinds of conformal anomalies on their world volume. Perhaps the one which is of greatest theoretical importance is associated with the Euler density in even dimensions. I will show how this anomaly is related to the one point function of exactly marginal deformations and how it arises explicitly from various correlation functions.\n\n\n2/12/2021\nLouis Fan\nTitle:  Joint distribution of Busemann functions in corner growth models \nAbstract: The 1+1 dimensional corner growth model with exponential weights is a centrally important exactly solvable model in the Kardar-Parisi-Zhang class of statistical mechanical models. While significant progress has been made on the fluctuations of the growing random shape\, understanding of the optimal paths\, or geodesics\, is less developed. The Busemann function is a useful analytical tool for studying geodesics. We present the joint distribution of the Busemann functions\, simultaneously in all directions of growth\, in terms of mappings that represent FIFO (first-in-first-out) queues. As applications of this description we derive a marked point process representation for the Busemann function across a single lattice edge and point out its implication on structure of semi-infinite  geodesics. This is joint work with Timo Seppäläinen.\n\n\n2/19/2021\nDaniel Junghans\nTitle: Control issues of the KKLT scenario in string theory \nAbstract: The simplest explanation for the observed accelerated expansion of the universe is that we live in a 4-dimensional de Sitter space. We analyze to which extent the KKLT proposal for the construction of such de Sitter vacua in string theory is quantitatively controlled. As our main finding\, we uncover and quantify an issue which one may want to call the “singular-bulk problem”. In particular\, we show that\, generically\, a significant part of the manifold on which string theory is compactified in the KKLT scenario becomes singular. This implies a loss of control over the supergravity approximation on which the construction relies.\n\n\n2/26/2021\nTsung-Ju Lee\nTitle: SYZ fibrations and complex affine structures \nAbstract: Strominger–Yau–Zaslow conjecture has been a guiding principle in mirror symmetry. The conjecture predicts the existence of special Lagrangian torus fibrations of a Calabi–Yau manifold near a large complex structure limit point. Moreover\, the mirror is given by the dual fibrations and the Ricci-flat metric is obtained from the semi-flat metric with corrections from holomorphic discs whose boundaries lie in a special Lagrangian fiber. By a result of Collins–Jacob–Lin\, the complement of a smooth elliptic curve in the projective plane admits a SYZ fibration. In this talk\, I will explain how to compute the complex affine structure induced from this SYZ fibration and show that it agrees with the affine structure used in Carl–Pumperla–Siebert. This is based on a joint work with Siu-Cheong Lau and Yu-Shen Lin.\n\n\n3/5/2021\nCancelled\n\n\n\n3/11/2021 \n9:00pm ET\nRyan Thorngren\nTitle:  Symmetry protected topological phases\, anomalies\, and their classification \nAbstract: I will give an overview of some mathematical aspects of the subject of symmetry protected topological phases (SPTs)\, especially as their theory relates to index theorems in geometry\, cobordism of manifolds\, and group cohomology.\n\n\n3/18/2021 \n9:00pm ET\nRyan Thorngren\nTitle:  Symmetry protected topological phases\, anomalies\, and their classification\nAbstract: I will give an overview of some mathematical aspects of the subject of symmetry protected topological phases (SPTs)\, especially as their theory relates to index theorems in geometry\, cobordism of manifolds\, and group cohomology.\n\n\n3/26/2021 \n8:30am ET\nAghil Alaee\nTitle:  Rich extra dimensions are hidden inside black holes \nAbstract: In this talk\, I present an argument that shows why it is difficult to see rich extra dimensions in the Universe.\n\n\n4/2/2021\n8:30am ET\nEnno Keßler\nTitle: Super Stable Maps of Genus Zero \nAbstract: I will report on a supergeometric generalization of J-holomorphic curves. Supergeometry is a mathematical theory of geometric spaces with anti-commuting coordinates and functions which is motivated by the concept of supersymmetry from theoretical physics. Super J-holomorphic curves and super stable maps couple the equations of classical J-holomorphic curves with a Dirac equation for spinors and might\, in the future\, lead to a supergeometric generalization of Gromov-Witten invariants.\n\n\n4/9/2021\nJuven Wang \nVideo\nTitle: Ultra Unification \nAbstract: Strong\, electromagnetic\, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). In this work\, we propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly matching and cobordism constraints (especially from the baryon minus lepton number B − L and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension\, whose low energy contains unitary topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase)\, or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase)\, or right-handed neutrinos\, or their combinations. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects\, etc.\, whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math\, QFT\, and condensed matter terminology\, and elaborate more on the nonperturbative global anomalies of Z2\, Z4\, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860\, arXiv:2008.06499\, arXiv:2006.16996\, arXiv:1910.14668.\n\n\n4/16/2021\nSergiy Verstyuk\nTitle: Deep learning methods for economics \nAbstract: The talk discusses some recent developments in neural network models and their applicability to problems in international economics as well as macro-via-micro economics. Along the way\, interpretability of neural networks features prominently.\n\n\n4/23/2021\nYifan Wang\nTitle: Virtues of Defects in Quantum Field Theories \nAbstract: Defects appear ubiquitously in many-body quantum systems as boundaries and impurities. They participate inextricably in the quantum dynamics and give rise to novel phase transitions and critical phenomena. Quantum field theory provides the natural framework to tackle these problems\, where defects define extended operators over sub-manifolds of the spacetime and enrich the usual operator algebra. Much of the recent progress in quantum field theory has been driven by the exploration of general structures in this extended operator algebra\, precision studies of defect observables\, and the implications thereof for strongly coupled dynamics. In this talk\, I will review selected developments along this line that enhance our understanding of concrete models in condensed matter and particle physics\, and that open new windows to nonperturbative effects in quantum gravity.\n\n\n4/30/2021\nYun Shi\nTitle: D-critical locus structure for local toric Calabi-Yau 3-fold \nAbstract: Donaldson-Thomas (DT) theory is an enumerative theory which produces a count of ideal sheaves of 1-dimensional subschemes on a Calabi-Yau 3-fold. Motivic Donaldson-Thomas theory\, originally introduced by Kontsevich-Soibelman\, is a categorification of the DT theory. This categorification contains more refined information of the moduli space. In this talk\, I will give a brief introduction to motivic DT theory following the definition of Bussi-Joyce-Meinhardt\, in particular the role of d-critical locus structure in the definition of motivic DT invariant. I will also discuss results on this structure on the Hilbert schemes of zero dimensional subschemes on local toric Calabi-Yau threefolds. This is based on joint work in progress with Sheldon Katz.\n\n\n5/7/2021\nThérèse Yingying Wu\nTitle: Topological aspects of Z/2Z eigenfunctions for the Laplacian on S^2 \nAbstract: In this talk\, I will present recent work with C. Taubes on an eigenvalue problem for the Laplacian on the round 2-sphere associated with a configuration of an even number of distinct points on that sphere\, denoted as C_2n. I will report our preliminary findings on how eigenvalues and eigenfunctions change as a function of the configuration space. I will also discuss how the compactification of C_2n is connected to the moduli space of algebraic curves (joint work with S.-T. Yau). There is a supergeometry tie-in too.\n\n\n5/14/2021\nDu Pei\nTitle: Three applications of TQFTs \nAbstract: Topological quantum field theories (TQFTs) often serve as a bridge between physics and mathematics. In this talk\, I will illustrate how TQFTs that arise in physics can help to shed light on 1) the quantization of moduli spaces 2) quantum invariants of 3-manifolds\, and 3) smooth structures on 4-manifolds.\n\n\n5/21/2021\nFarzan Vafa\nTitle: Active nematic defects and epithelial morphogenesis \nAbstract: Inspired by recent experiments that highlight the role of topological defects in morphogenesis\, we develop a minimal framework to study the dynamics of an active curved surface driven by its nematic texture (a rank 2 symmetric traceless tensor). Allowing the surface to evolve via relaxational dynamics (gradient flow) leads to a theory linking nematic defect dynamics\, cellular division rates\, and Gaussian curvature. Regions of large positive (negative) curvature and positive (negative) growth are colocalized with the presence of positive (negative) defects\, and cells accumulate at positive defects and are depleted at negative defects.  We also show that activity stabilizes a bound $+1$ defect state by creating an incipient tentacle\, while a bound $+1$ defect state surrounded by two $-1/2$ defects can create a stationary ring configuration of tentacles\, consistent with experimental observations. The talk is based on a recent paper with L Mahadevan [arXiv:2105.0106].\n\n\n\n\n\nFall 2020:\n\n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n\n\n9/11/2020\nMoran Koren\nTitle:  Observational Learning and Inefficiencies in Waitlists \nAbstract: Many scarce resources are allocated through waitlists without monetary transfers. We consider a model\, in which objects with heterogeneous qualities are offered to strategic agents through a waitlist in a first-come-first-serve manner. Agents\, upon receiving an offer\, accept or reject it based on both a private signal about the quality of the object and the decisions of agents ahead of them on the list. This model combines observational learning and dynamic incentives\, two features that have been studied separately. We characterize the equilibrium and quantify the inefficiency that arises due to herding and selectivity. We find that objects with intermediate expected quality are discarded while objects with a lower expected quality may be accepted. These findings help in understanding the reasons for the substantial discard rate of transplant organs of various qualities despite the large shortage of organ supply.\n\n\n9/18/2020\nMichael Douglas\nTitle: A talk in two parts\, on strings and on computers and math \nAbstract: I am dividing my time between two broad topics. The first is string theory\, mostly topics in geometry and compactification. I will describe my current work on numerical Ricci flat metrics\, and list many open research questions. The second is computation and artificial intelligence. I will introduce transformer models (Bert\,GPT) which have led to breakthroughs on natural language processing\, describe their potential for helping us do math\, and sketch some related theoretical problems.\n\n\n9/25/2020\nCancelled – Math Science Lecture\n\n\n\n10/2/2020\nCancelled – Math Science Lecture\n\n\n\n10/9/2020\nWai Tong (Louis) Fan\nTitle: Stochastic PDE as scaling limits of interacting particle systems \nAbstract: Interacting particle models are often employed to gain understanding of the emergence of macroscopic phenomena from microscopic laws of nature. These individual-based models capture fine details\, including randomness and discreteness of individuals\, that are not considered in continuum models such as partial differential equations (PDE) and integral-differential equations. The challenge is how to simultaneously retain key information in microscopic models as well as efficiency and robustness of macroscopic models.\nIn this talk\, I will discuss how this challenge can be overcome by elucidating the probabilistic connections between particle models and PDE. These connections also explain how stochastic partial differential equations (SPDE) arise naturally under a suitable choice of level of detail in modeling complex systems. I will also present some novel scaling limits including SPDE on graphs and coupled SPDE. These SPDE not only interpolate between particle models and PDE\, but also quantify the source and the order of magnitude of stochasticity. Scaling limit theorems and new duality formulas are obtained for these SPDE\, which connect phenomena across scales and offer insights about the genealogies and the time-asymptotic properties of the underlying population dynamics. Joint work with Rick Durrett.\n\n\n10/16/2020\nTianqi Wu\nTitle: Koebe circle domain conjecture and the Weyl problem in hyperbolic 3-space \nAbstract: In 1908\, Paul Koebe conjectured that every open connected set in the plane is conformally diffeomorphic to an open connected set whose boundary components are either round circles or points. The Weyl problem\, in the hyperbolic setting\, asks for isometric embedding of surfaces of curvature at least -1 into the hyperbolic 3-space. We show that there are close relationships among the Koebe conjecture\, the Weyl problem and the work of Alexandrov and Thurston on convex surfaces. This is a joint work with Feng Luo.\n\n\n10/23/2020\nChangji Xu\nTitle: Random Walk Among Bernoulli Obstacles \nAbstract: Place an obstacle with probability $1 – p$ independently at each vertex of $\mathbb Z^d$ and consider a simple symmetric random walk that is killed upon hitting one of the obstacles. This is called random walk among Bernoulli obstacles. The most prominent feature of this model is a strong localization effect: the random walk will be localized in a very small region conditional on the event that it survives for a long time. In this talk\, we will discuss some recent results about the behaviors of the conditional random walk\, in quenched\, annealed\, and biased settings.\n\n\n10/30/2020\nMichael Simkin\nTitle: The differential equation method in Banach spaces and the $n$-queens problem \nAbstract: The differential equation method is a powerful tool used to study the evolution of random combinatorial processes. By showing that the process is likely to follow the trajectory of an ODE\, one can study the deterministic ODE rather than the random process directly. We extend this method to ODEs in infinite-dimensional Banach spaces.\nWe apply this tool to the classical $n$-queens problem: Let $Q(n)$ be the number of placements of $n$ non-attacking chess queens on an $n \times n$ board. Consider the following random process: Begin with an empty board. For as long as possible choose\, uniformly at random\, a space with no queens in its row\, column\, or either diagonal\, and place on it a queen. We associate the process with an abstract ODE. By analyzing the ODE we conclude that the process almost succeeds in placing $n$ queens on the board. Furthermore\, we can obtain a complete $n$-queens placement by making only a few changes to the board. By counting the number of choices available at each step we conclude that $Q(n) \geq (n/C)^n$\, for a constant $C>0$ associated with the ODE. This is optimal up to the value of $C$.\n\n\n11/6/2020\nKenji Kawaguchi\nTitle: Deep learning: theoretical results on optimization and mixup \nAbstract: Deep neural networks have achieved significant empirical success in many fields\, including the fields of computer vision\, machine learning\, and artificial intelligence. Along with its empirical success\, deep learning has been theoretically shown to be attractive in terms of its expressive power. However\, the theory of the expressive power does not ensure that we can efficiently find an optimal solution in terms of optimization\, robustness\, and generalization\, during the optimization process of a neural network. In this talk\, I will discuss some theoretical results on optimization and the effect of mixup on robustness and generalization.\n\n\n11/13/2020\nOmri Ben-Eliezer\nTitle: Sampling in an adversarial environment \nAbstract: How many samples does one need to take from a large population in order to truthfully “represent” the population? While this cornerstone question in statistics is very well understood when the population is fixed in advance\, many situations in modern data analysis exhibit a very different behavior: the population interacts with and is affected by the sampling process. In such situations\, the existing statistical literature does not apply. \nWe propose a new sequential adversarial model capturing these situations\, where future data might depend on previously sampled elements; we then prove uniform laws of large numbers in this adversarial model. The results\, techniques\, and applications reveal close connections to various areas in mathematics and computer science\, including VC theory\, discrepancy theory\, online learning\, streaming algorithms\, and computational geometry. \nBased on joint works with Noga Alon\, Yuval Dagan\, Shay Moran\, Moni Naor\, and Eylon Yogev.\n\n\n11/20/2020\nCharles Doran\nTitle: The Calabi-Yau Geometry of Feynman Integrals \nAbstract: Over the past 30 years Calabi-Yau manifolds have proven to be the key geometric structures behind string theory and its variants. In this talk\, I will show how the geometry and moduli of Calabi-Yau manifolds provide a new framework for understanding and computing Feynman integrals. An important organizational principle is provided by mirror symmetry\, and specifically the DHT mirror correspondence. This is joint work with Andrey Novoseltsev and Pierre Vanhove.\n\n\n\nColloquia & Seminars\,Seminars
URL:https://cmsa.fas.harvard.edu/event/members-seminar/
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201216T103000
DTEND;TZID=America/New_York:20201216T120000
DTSTAMP:20260405T051328
CREATED:20240126T100017Z
LAST-MODIFIED:20240126T100017Z
UID:10001446-1608114600-1608120000@cmsa.fas.harvard.edu
SUMMARY:12/16/2020 Strongly Correlated Quantum Materials
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/12-16-2020-strongly-correlated-quantum-materials/
CATEGORIES:Strongly Correlated Quantum Materials and High-Temperature Superconductors
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20201216T120000
DTEND;TZID=America/New_York:20201216T130000
DTSTAMP:20260405T051328
CREATED:20240126T094639Z
LAST-MODIFIED:20250305T192329Z
UID:10001442-1608120000-1608123600@cmsa.fas.harvard.edu
SUMMARY:The Inside View: Raymarching and the Thurston Geometries
DESCRIPTION:On Wednesday\, December 16 at 12:00 p.m. EST\, WAM and CMSA will host a holiday seminar featuring Sabetta Matsumoto\, Georgia Institute of Technology who will present The Inside View: Raymarching and the Thurston Geometries. \nThe properties of euclidean space seem natural and obvious to us\, to the point that it took mathematicians over two thousand years to see an alternative to Euclid’s parallel postulate. The eventual discovery of hyperbolic geometry in the 19th century shook our assumptions\, revealing just how strongly our native experience of the world blinded us from consistent alternatives\, even in a field that many see as purely theoretical. Non-euclidean spaces are still seen as unintuitive and exotic\, but with direct immersive experiences we can get a better intuitive feel for them. The latest wave of virtual reality hardware\, in particular the HTC Vive\, tracks both the orientation and the position of the headset within a room-sized volume\, allowing for such an experience. We create realtime rendering to explore the three-dimensional geometries of the Thurston/Perelman geometrization theorem. In this talk\, we use the “inside view” of each manifold to try to understand its geometry and what life might be like on the inside. Joint work with Rémi Coulon\, Henry Segerman and Steve Trettel. \nVisit the event page
URL:https://cmsa.fas.harvard.edu/event/the-inside-view-raymarching-and-the-thurston-geometries/
CATEGORIES:Colloquia & Seminar,Seminars
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/image002-1-600x338-1.jpg
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END:VCALENDAR