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June  June  June  1  2  3  4 
5  6  7  CMSA Geometry and Physics Seminar: Collective integrable systems and global actionangle coordinates
9:30 AM10:30 AM July 7, 2020 A “collective integrable system” on a symplectic manifold is a commutative integrable system constructed from a Hamiltonian action of a noncommutative Lie group. Motivated by the example of GelfandZeitlin systems, we give a construction of collective integrable systems that generate a Hamiltonian torus action on a dense subset of any Hamiltonian Kmanifold, where K is any compact connected Lie group. In the case where the Hamiltonian Kmanifold 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 (nonsimple) convex polytope. Zoom: https://harvard.zoom.us/j/94717938264  Decay estimates and complete BakryEmry theory
10:00 AM11:00 AM July 7, 2020 The connection between decay estimates for entropy and logarithmic Sobolev inequalities is wellestablished for dynamical systems on commutative systems. I will explain how to extend this to matrixvalued functions, and then apply these techniques to Lindbladians on quantum systems interacting with an environment. In fact, some Lindbladian on small quantum systems seems to contain all the relevant information of dynamical systems on groups. This is joint work with Haojian Li and Nick LaRacuente. Zoom: https://harvard.zoom.us/j/779283357
 8  9  CMSA Condensed Matter/Math Seminar: Deconfined metallic quantum criticalityI
9:00 AM10:30 AM July 9, 2020 A number of strongly correlated electronic materials exhibit quantum criticality that does not fit into the conventional LandauGinzburgWilson paradigm of continuous phase transitions. Inspired by these experimental examples, I will discuss a new class of quantum phase transitions that describe a continuous transition between a Fermi liquid metal with a generic electronic Fermi surface and electrical insulators without Fermi surface of neutral excitations. Such phase transitions are described in terms of a finite density of fractionalized excitations coupled to emergent gauge fields. I will discuss various concrete examples of such gauge theories and describe their associated phase transitions using a renormalization group framework. Remarkably, we find examples of continuous phase transitions between Landau Fermi liquid metals and insulators, where the quantum critical point hosts a nonFermi liquid with a sharp Fermi surface but no longlived quasiparticles. I will comment on the relevance of this new theoretical framework for some of the most pressing questions in the field of quantum matter. Zoom: https://harvard.zoom.us/j/977347126
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12  13  CMSA Social Science Applications Forum: Convergence of Large Population Games to Mean Field Games with Interaction Through the Controls
10:00 AM11:00 AM July 13, 2020 This work considers stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. We develop a framework to prove convergence of finiteplayer games to the asymptotic mean field game. Our approach is based on the concept of propagation of chaos for forward and backward weakly interacting particles which we investigate by fully probabilistic methods, and which appear to be of independent interest. These propagation of chaos arguments allow to derive moment and concentration bounds for the convergence of both Nash equilibria and social optima in noncooperative and cooperative games, respectively. Incidentally, we also obtain convergence of a system of second order parabolic partial differential equations on finite dimensional spaces to a second order parabolic partial differential equation on the Wasserstein space. For security reasons, you will have to show your full name to join the meeting. Zoom: https://harvard.zoom.us/j/95475021655  CMSA Geometry and Physics Seminar: Berry phase in quantum field theory
9:00 PM10:00 PM July 13, 2020 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 spacetimedependent sigma model background fields. The Berry phase is equivalent to WessZuminoWitten 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. Zoom: https://harvard.zoom.us/j/94717938264
 14  Integrability and Braided Tensor Categories
10:00 AM11:00 AM July 14, 2020 Many integrable critical classical statistical mechanical models and the corresponding quantum spin chains possess a fractionalspin conserved current. Such currents have been constructed by utilizing quantumgroup algebras, fermionic and parafermionic operators, and ideas from “discrete holomorphicity”. I define them generally and naturally using a braided tensor category, a topological structure familiar from the study of knot invariants, anyons and conformal field theory. I derive simple constraints on the Boltzmann weights necessary and sufficient for such a current to exist, generalizing those found using quantumgroup algebras. I find many solutions, in both geometric and local models. In all cases, the resulting weights are those of an integrable lattice model, giving a linear construction for “Baxterising”, i.e. building a solution of the YangBaxter equation out of topological data. Zoom: https://harvard.zoom.us/j/779283357
 15  CMSA Quantum Matter/Quantum Field Theory Seminar: Interplay between two boundary effects
10:30 AM12:00 PM July 15, 2020 We study the interplay between two nontrivial boundary effects: (1) the d1 dimensional edge states of ddimensional strongly interacting symmetry protected topological states, and (2) the boundary fluctuations of ddimensional bulk quantum criticality. We also discuss states localized at an interface in a higher dimensional bulk, when the bulk undergoes a quantum phase transition. Using controlled analytical methods, we demonstrate that the interplay between the two different boundary effects leads to rich physics at the d1 dimensional boundary, including new stable fixed points, and also an exotic quantum phase transition which cannot happen in a local d1 dimensional system alone. Our analytical calculation is qualitatively consistent with recent numerical works on nonlocal quantum many body systems.
 16  CMSA Condensed Matter/Math Seminar: Deconfined metallic quantum criticality – II
10:30 AM12:00 PM July 16, 2020 The main goal of this talk is to discuss in detail a concrete setup for deconfined metallic quantum criticality. In particular, we propose that certain quantum Hall bilayers can host examples of a deconfined metalinsulator transition (DMIT), where a Fermi liquid (FL) metal with a generic electronic Fermi surface evolves into a gapped insulator (or, an insulator with Goldstone modes) through a continuous quantum phase transition. The transition can be accessed by tuning a single parameter, and its universal critical properties can be understood using a controlled framework. At the transition, the two layers are effectively decoupled, where each layer undergoes a continuous transition from a FL to a generalized composite Fermi liquid (gCFL). The thermodynamic and transport properties of the gCFL are similar to the usual CFL, while its spectral properties are qualitatively different. The FLgCFL quantum critical point hosts a sharply defined Fermi surface without longlived electronic quasiparticles. Immediately across the transition, the two layers of gCFL are unstable to forming an insulating phase. We discuss the topological properties of the insulator and various observable signatures associated with the DMIT. Some key ingredients of this proposal include DiracChernSimons theory, color superconductivity, dimensional decoupling, etc. Zoom: https://harvard.zoom.us/j/977347126
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19  20  CMSA Geometry and Physics Seminar: A geometric construction of orbifold Jacobian algebras
9:30 PM10:30 PM July 20, 2020 We review the definition of a twisted Jacobian algebra of a LandauGinzburg orbifold due to Kaufmann et al. Then we construct an Ainfinity 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 CheolHyun Cho. Zoom: https://harvard.zoom.us/j/94717938264
 21  Applied von Neumann Algebra
10:00 AM11:00 AM July 21, 2020 We are interested in mathematical results which are stated entirely without reference to von Neumann algebras but whose proofs use von Neumann algebras in an essential way. The first stunning example is the Kaplansky result that ab=1 iff ba=1 in a group algebra over a field of characteristic zero. Connes’ noncommutative integration theory yields other examples. We will concentrate on a new example in the theory of zero sets of Bergman spaces where we are able to calculate a certain density of orbits of Fuchsian groups. Zoom: https://harvard.zoom.us/j/779283357
 22  23  24  2020 Big Data Conference
All day July 24, 2020July 25, 2020 Please note: the 2020 Big Data Conference will take place virtually. More information to follow.On August 2425, 2020 the CMSA will be hosting our sixth annual Conference on Big Data. The Conference will feature many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. Organizers: ShingTung Yau, William Caspar Graustein Professor of Mathematics, Harvard University Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business HorngTzer Yau, Professor of Mathematics, Harvard University Sergiy Verstyuk, CMSA, Harvard University Speakers:
Sanjeev Arora, Princeton University Joseph Dexter, Dartmouth University Nicole Immorlica, Microsoft Amin Saberi, Stanford University Vira Semenova, University of California, Berkeley Varda Shalev, Tel Aviv University Elizabeth Sibert, Harvard University Information about last year’s conference can be found here: cmsa.fas.harvard.edu/2019bigdata/
 25  2020 Big Data Conference
All day July 25, 2020July 25, 2020 Please note: the 2020 Big Data Conference will take place virtually. More information to follow.On August 2425, 2020 the CMSA will be hosting our sixth annual Conference on Big Data. The Conference will feature many speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. Organizers: ShingTung Yau, William Caspar Graustein Professor of Mathematics, Harvard University Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business HorngTzer Yau, Professor of Mathematics, Harvard University Sergiy Verstyuk, CMSA, Harvard University Speakers:
Sanjeev Arora, Princeton University Joseph Dexter, Dartmouth University Nicole Immorlica, Microsoft Amin Saberi, Stanford University Vira Semenova, University of California, Berkeley Varda Shalev, Tel Aviv University Elizabeth Sibert, Harvard University Information about last year’s conference can be found here: cmsa.fas.harvard.edu/2019bigdata/

26  27  28  29  CMSA Quantum Matter/Quantum Field Theory Seminar: Higgsconfinement phase transitions with fundamental representation matter
9:30 AM11:00 AM July 29, 2020 I will discuss the conditions under which Higgs and confining regimes in gauge theories with fundamental representation matter fields can be sharply distinguished. It is widely believed that these regimes are smoothly connected unless they are distinguished by the realization of global symmetries. However, I will show that when a U(1) global symmetry is spontaneously broken in both the confining and Higgs regimes, the two phases can be separated by a phase boundary. The phase transition between the two regimes may be detected by a novel topological vortex order parameter. I’ll illustrate these ideas by explicit calculations in gauge theories in three spacetime dimensions, and then explain the generalization to four dimensions. One important implication of our results is that nuclear matter and quark matter are sharply distinct phases of QCD with an approximate SU(3) flavor symmetry. Zoom: https://harvard.zoom.us/j/977347126
 30  31  August 