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SUMMARY:Program on Classical\, quantum\, and probabilistic integrable systems - novel interactions and applications
DESCRIPTION:Program on Classical\, quantum\, and probabilistic integrable systems – novel interactions and applications \nDates: March 24–May 24\, 2025  \nLocation: CMSA\, 20 Garden Street\, Cambridge MA 02138 \nExactly solvable models have played pivotal roles in mathematics and physics throughout their history. The program is dedicated to exploring and developing a more recent wave of their influence in stochastic models together with accompanying combinatorial\, classical\, and quantum integrable systems. Topics will include: \n\nColored and uncolored interacting particle systems with associated vertex models and line ensembles\nYang-Baxter integrability and its applications in algebraic combinatorics\, quantum systems\, and conformal field theory\nQuantum stochastic models\, quantum exclusion processes\, and free probability\nEmerging new aspects of classical and quantum integrable systems – hydrodynamics\, large deviations of stochastic models\, and random surface models\n\nOrganizers: \n\nAmol Aggarwal\, Columbia University & Clay Mathematics Institute\nGuillaume Barraquand\, École normale supérieure\, Paris\nAlexei Borodin\, MIT\nIvan Corwin\, Columbia University\nPierre Le Doussal\, École normale supérieure\, Paris\nMichael Wheeler\, University of Melbourne\n\nParticipants \n\nDenis Bernard\, Ecole Normale Supérieure Paris\nAlexey Bufetov\, University of Leipzig\nPasquale Calabrese\, SISSA Trieste\nSylvie Corteel\, UC Berkeley\nCesar Cuenca\, Ohio State University\nJan De Gier\, University of Melbourne\nAndrea De Luca\, CNRS\, Cergy Paris University\nBenjamin Doyon\, King’s College London\nPatrik Ferrari\, University of Bonn\nVadim Gorin\, UC Berkeley\nTamara Grava\, SISSA\nJimmy He\, Ohio State University\nJiaoyang Huang\, University of Pennsylvania\nKurt Johansson\, KTH Stockholm\nRichard Kenyon\, Yale\nAlexandre Krajenbrink\, Cambridge Quantum Computing & Quantinuum\nAtsuo Kuniba\, University of Tokyo\nMatteo Mucciconi\, National University of Singapore\nGreta Panova\, University of Southern California\nLeonid Petrov\, University of Virginia\nSylvain Prolhac\, Université Paul Sabatier\, Toulouse\nTomaž Prosen\, University of Ljubljana\nTomohiro Sasamoto\, Tokyo Institute of Technology\nHerbert Spohn\, Technical University of Munich\nLi-Cheng Tsai\, University of Utah\n\nSchedule \nWeek 1\nMonday\, March 24th \n11:00am – 12:00pm Room G-10\, Lecture 1 of 4: Denis Bernard\, École normale supérieure de Paris: Quantum Exclusion Processes for (and by) Amateurs \n12:00 – 2:00pm Common Room: Program Lunch \n4:00 – 4:30pm Common Room: CMSA colloquium tea \n4:30 – 5:30pm Common Room\, CMSA colloquium: Amol Aggarwal\, Columbia University: The Toda Lattice as a Soliton Gas \n  \nTuesday\, March 25th \n3:30 – 4:00pm Common Room: Program tea \n4:00 – 5:00pm Room G-10\, Seminar: Patrik Ferrari\, Universität Bonn: Decoupling and decay of two-point functions in a two-species TASEP \n  \nWednesday\, March 26th \n11:00am – 12:00pm Room G-10\, Lecture 1 of 3: Atsuo Kuniba\, University of Tokyo: Multispecies ASEP and t-PushTASEP on a ring and a strange five vertex model \n3:00 – 4:00pm Room G-10\, Lecture 2 of 4: Denis Bernard\, École normale supérieure de Paris: Quantum Exclusion Processes for (and by) Amateurs \n4:30 – 5:30pm Common Room: Program wine and cheese reception \n  \nThursday\, March 27th \n11:00am – 12:00pm Room G-10\, Lecture 1 of 2: Benjamin Doyon\, King’s College London: The equations of generalised hydrodynamics\, and their unusual diffusve corrections \nAbstract: I will discuss the hydrodynamics of one-dimensional many-body integrable models. At the Euler scale\, this is given by “generalised hydrodynamics”\, whose equations only depend on the asymptotic state content and the two-body scattering shift of the model. I will explain how these equations arise\, and mention some of their properties: Hamiltonian structure\, exact solutions\, absence of shocks. At the diffusive scale\, generic one-dimensional models with state-dependent currents display super-diffusion. However\, integrable models are in a special class of “linearly degenerate systems”\, where there is no superdiffusion\, and one might expect a standard derivative expansion. I will explain how the diffusive corrections to the Euler equations are not given by a derivative expansion\, but instead governed by long-range correlations coming from an Euler-scale fluctuation theory. I will give the general ideas behind this fluctuation theory\, where initial fluctuations are deterministically transported by the Euler equation. I will finally provide arguments for the conjecture that\, once long-range correlations are accounted for\, there is no emergent stochasticity at all scales of hydrodynamics in integrable systems. \n3:30 – 4:00pm Common Room: Program tea \n4:00 – 5:00pm Room G-10\, Seminar: Sylvie Corteel\, University of California at Berkeley: Crystal Skeletons \n  \nFriday\, March 28th \n12:00 – 1:00 pm Common Room: Lunch with CMSA Member Seminar \n2:00 – 3:00pm Room G-10\, Lecture 3 of 4 : Denis Bernard\, École normale supérieure de Paris: Quantum Exclusion Processes for (and by) Amateurs \n3:30 – 4:00 pm Common Room: Program tea \n  \n\n \nWeek 2\nMonday\, March 31 \n11:00am – 12:00pm Room G-10\, Lecture 2 of 2: Benjamin Doyon\, King’s College London: The equations of generalised hydrodynamics\, and their unusual diffusve corrections \nAbstract: I will discuss the hydrodynamics of one-dimensional many-body integrable models. At the Euler scale\, this is given by “generalised hydrodynamics”\, whose equations only depend on the asymptotic state content and the two-body scattering shift of the model. I will explain how these equations arise\, and mention some of their properties: Hamiltonian structure\, exact solutions\, absence of shocks. At the diffusive scale\, generic one-dimensional models with state-dependent currents display super-diffusion. However\, integrable models are in a special class of “linearly degenerate systems”\, where there is no superdiffusion\, and one might expect a standard derivative expansion. I will explain how the diffusive corrections to the Euler equations are not given by a derivative expansion\, but instead governed by long-range correlations coming from an Euler-scale fluctuation theory. I will give the general ideas behind this fluctuation theory\, where initial fluctuations are deterministically transported by the Euler equation. I will finally provide arguments for the conjecture that\, once long-range correlations are accounted for\, there is no emergent stochasticity at all scales of hydrodynamics in integrable systems. \n12:00 – 2:00pm Common Room: Program Lunch \n2:00 – 3:00pm Room G-10\, Lecture 2 of 3: Atsuo Kuniba\, University of Tokyo: Solutions of tetrahedron and 3D reflection equations from quantum cluster algebras \n\nAbstract: Tetrahedron and 3D equations are three-dimensional generalizations of the Yang-Baxter and the reflection equations. I will explain how quantum cluster algebras lead to solutions that generalize and unify many known solutions.  \n\n3:30 – 4:00pm Program tea \n  \nTuesday\, April 1 \n11:00am – 12:00pm Room G-10\, Lecture 1 of 2: Kurt Johansson\, KTH Stockholm: Extremal particles in uniform random Gelfand-Tsetlin patterns \nAbstract: I will report on joint work with Elnur Emrah on edge fluctuations in uniform random interlacing patterns with fixed top configuration. The goal is to describe all possible limit processes that can occur\, and the conditions under which they occur. \n3:30pm – 4:00pm\, Common Room: Program tea \n  \nWednesday\, April 2 \n11:00am – 12:00pm Room G-10\, Lecture 4 of 4: Denis Bernard\, École normale supérieure de Paris: Quantum Exclusion Processes for (and by) Amateurs \n3:00 – 4:00pm Room G-10\, Lecture 3 of 3: Atsuo Kuniba\, University of Tokyo: Box-ball systems \nAbstract: Box-ball systems are one-dimensional integrable cellular automata introduced in 1990. This talk surveys major developments that have unfolded consistently over the decades\, enriching the scope of the theory. Topics include ultradiscretization\, crystal theory in quantum groups\, the combinatorial and thermodynamic Bethe ansatz\, as well as generalized hydrodynamics. \n4:30 – 5:30pm Common Room: Program wine and cheese reception \n  \nThursday\, April 3 \n11:00am – 12:00pm Room G-10\, Lecture 2 of 2: Kurt Johansson\, KTH Stockholm: Extremal particles in uniform random Gelfand-Tsetlin patterns \nAbstract: I will report on joint work with Elnur Emrah on edge fluctuations in uniform random interlacing patterns with fixed top configuration. The goal is to describe all possible limit processes that can occur\, and the conditions under which they occur. \n3:30pm – 4:00pm Common Room: Program tea \n  \nFriday\, April 4 \n12:00 – 1:00pm Common Room: CMSA Member Seminar and Lunch \n3:30 – 4:00pm Common Room: Program tea \n  \n\n \nWeek 3\nMonday\, April 7 \n12:00 – 2:00pm Common Room: Program lunch \n4:00 – 4:30pm Tea with CMSA colloquium \n4:30 – 5:30pm CMSA Colloquium: Ben Webster\, University of Waterloo and Perimeter Institute: 3-D Mirror Symmetry \n  \nTuesday\, April 8 \n11:00am – 2:00pm Room G-10\, Pierre Le Doussal\, École normale supérieure de Paris: Exact results for the macroscopic fluctuation theory of the 1D weakly asymmetric exclusion process. \n3:30 – 4:00pm Common Room: Program tea  \n  \nWednesday\, April 9 \n12:00 – 1:00pm Common Room\, CMSA Q&A Seminar and lunch: Eric Maskin\, Harvard Economics: The Mathematics of Voting \n4:30 – 5:30pm Common Room: Program wine and cheese reception \n  \nThursday\, April 10 \n3:30 – 4:00pm Common Room: Program tea  \n  \nFriday\, April 11 \n12:00 – 1:00pm Common Room: CMSA member seminar and lunch \n3:30 – 4:00pm Common Room: Program tea \n  \n\nWeek 4\nMonday\, April 14 \n12:00 – 2:00pm Common Room: Program lunch \n4:00 – 4:30pm Tea with CMSA colloquium \n4:30 –5:30pm CMSA colloquium: Andrey Smirnov\, University of North Carolina at Chapel Hill: Quantum K-theory at roots of unity \n  \nTuesday\, April 15 \n11:00 am – 12:00pm Room G-10\, Ivan Corwin\, Columbia University: How Yang-Baxter unravels Kardar-Parisi-Zhang \nAbstract: Over the past few decades\, physicists and then mathematicians have sought to uncover the (conjecturally) universal long time and large space scaling limit for the so-called Kardar-Parisi-Zhang (KPZ) class of stochastically growing interfaces in (1+1)-dimensions. Progress has been marked by several breakthroughs\, starting with the identification of a few free-fermionic integrable models in this class and their single-point limiting distributions\, widening the field to include non-free-fermionic integrable representatives\, evaluating their asymptotics distributions at various levels of generality\, constructing the conjectural full space-time scaling limit\, known as the directed landscape\, and checking convergence to it for a few of the free-fermion representatives. \nIn this talk\, I will describe a method that should prove convergence for all known integrable representatives of the KPZ class to this universal scaling limit. The method has been fully realized for the Asymmetric Simple Exclusion Process and the Stochastic Six Vertex Model. It relies on the Yang-Baxter equation as its only input and unravels the rich complexity of the KPZ class and its asymptotics from first principles. This is based on a few works involving Amol Aggarwal\, Alexei Borodin\, Milind Hegde\, Jiaoyang Huang and me. \n3:30 – 4:00pm Common Room: Program tea  \n  \nWednesday\, April 16 \n11:00am – 12:00pm Room G-10\, Tamara Grava\, University of Bristol: Random solitons and soliton gas \nAbstract: A soliton is a localised travelling wave solution of a nonlinear dispersive equation. When the equation is integrable the interaction of many solitons is elastic. We study the behaviour of a set of N solitons for the Korteweg de Vries equation in the limit N goes to infinity (soliton gas) and the interaction of the soliton gas with a distinct soliton that we call a tracer soliton. We show that the average velocity of the tracer soliton satisfies the Zakharov-El kinetic equations. We then consider a set of random N soliton solution q_N(x\,t) and its limiting soliton gas q(x\,t). We prove a central limit theorem for the difference q_N(x\,t)-q(x\,t) for values of x and t that are bounded by log(N). \n12:00 – 1:00pm Common Room: CMSA Q&A seminar and lunch: Noah Golowich\, MIT: What is length generalization in large language models? \n4:30 – 5:30pm Common Room: Program wine and cheese reception \n  \nThursday\, April 17 \n11:00am – 12:00pm Room G-10\, Guillaume Barraquand\, École normale supérieure de Paris: Large time cumulants of the open KPZ equation \n12:00 – 1:00pm Common Room: lunch with featured Yip Lecture speaker Scott Aaronson and CMSA residents \n3:30pm Common Room: Program tea  \n4:00 – 5:00pm Science Center Hall A: Fifth Annual Yip Lecture\, Scott Aaronson: How Much Math is Knowable? \n5:00 – 6:00pm Math Department Common Room at the Harvard Science Center: Yip Lecture reception \n  \nFriday\, April 18 \n12:00 – 1:00pm Common Room: CMSA Member Seminar and lunch: Han Shao\, Harvard CMSA\, Topic TBD \n3:30 – 4:00pm Common Room: Program tea \n  \n\nWeek 5\n  \nMonday\, April 21 \n11:00am – 12:00pm Room G-10\, Tomaz Prosen\, University of Ljubljana\, Lecture 1 of 3: On Integrable Quantum and Classical Circuits (with Stochastic Boundaries) \nAbstract: I will introduce Yang-Baxter integrable brickwork quantum circuit models and discuss their integrability structure\, specifically\, the transfer matrix\, conservation laws etc. A paradigmatic example\, XXZ or unitary 6-vertex circuits exhibit an unusual link to KPZ scaling at the isotropic (SU(2) symmetric) point. I will establish the link to corresponding classical integrable Landau-Lifshitz circuits and discuss some aspects of transport and full counting statistics. \n12:00 – 2:00pm Common Room: Program Lunch \n4:00 – 4:30pm Common Room: CMSA colloquium tea \n4:30 – 5:30pm  Common Room\, CMSA colloquium: Ila Fiete\, MIT: Modeling the emergence of complex cortical structure from simple precursors in the brain: maps\, hierarchies\, and modules \n  \nTuesday\, April 22 \n11:00am – 12:00pm Room G-10\, Tomohiro Sasamoto\, Tokyo Institute of Technology: Large deviation of symmetric models through classical integrable systems \n3:30pm Common Room: Program tea  \n  \nWednesday\, April 23 \n11:00am – 12:00pm Room G-10\, Tomaz Prosen\, University of Ljubljana: On Integrable Quantum and Classical Circuits (with Stochastic Boundaries) \nAbstract: I will discuss explicit matrix product solutions for quantum many-body Markov chains\, defined for a Yang-Baxter integrable quantum circuit with specific stochastic Kraus processes at its boundaries. In the continuous time limit\, these solutions correspond to steady states of boundary driven Lindbladian dynamics and often yield non-trivial quasi-local conservation laws of integrable spin chains. The specific case of XXZ and Hubbard chain will be discussed. \n12:00 – 1:00pm Common Room: CMSA Q&A seminar and lunch: Alexei Borodin\, MIT: Connections between physics and probability \n4:30 – 5:30pm Common Room: Program wine and cheese reception \n  \nThursday\, April 24 \n11:00am – 12:00pm Room G-10\, Sylvain Prolhac\, Université Paul Sabatier\, Toulouse: Approach to stationarity for KPZ fluctuations in finite volume \nAbstract: At late times $t$\, the cumulants of the height for the KPZ fixed point in finite volume behave as affine functions of time $c_k(t) = a_k t+b_k$\, up to exponentially small corrections. The constant term $b_k$ is the last remaining information about the initial state observable at long enough times. Two approaches allow us to compute this constant from the totally asymmetric exclusion process\, a discrete version of the KPZ fixed point. First\, an iterated version of the matrix product representation for the stationary state leads\, for arbitrary initial conditions\, to expressions involving extreme value statistics of Brownian paths. On the other hand\, Bethe ansatz leads to rather explicit expressions for simple initial conditions. Comparison between the two approaches then provides conjectures for some generating functions of Brownian paths. \n3:30pm Common Room: Program tea  \n  \nFriday\, April 25 \n11:00am – 12:00pm Room G-10\, Tomaz Prosen\, University of Ljubljana\, Lecture 3 of 3: On Integrable Quantum and Classical Circuits (with Stochastic Boundaries) \nAbstract: In the last lecture I will discuss the possibility of quantum integrability of many-body quantum Markov chain generators\, such as Lindbladians with bulk or boundary dissipation\, and the corresponding circuit (Kraus) counterparts. The paradigmatic example is the XX model with dephasing noise which can be mapped to a Hubbard model with imaginary interaction\, both in the Hamiltonian and circuit formulation. \n3:30 – 4:00pm Common Room: Program tea \n  \n\nWeek 6\n  \nMonday\, April 28 \n11:00am – 12:00pm Room G-10\, Herbert Spohn\, Technische Universitaet Muenchen\, Lecture 1 of 3: Integral many-body systems and GHD \n12:00 – 2:00pm Common Room: Program Lunch \n2:00 – 3:00 pm Room G-10\, Tomohiro Sasamoto\, Tokyo Institute of Technology\, Exact density profile and current fluctuations in a tight-binding chain with dephasing noise \nAbstract: We consider a tight-binding chain with dephasing noise\, whose time evolution is described by the quantum master equation called the Gorini-Kossakowski-Sudarhan-Lindblad (GKSL) equation. By using a connection of this model to the Hubbard model with imaginary coupling [1]\, we study the density profile [2] and the variance of the current [3] exactly for the model on the infinite line by writing down contour integral formulas using Bethe ansatz. The talk is based on collaborations with Taiki Ishiyama and Kazuya Fujimoto.  \n4:00 – 4:30pm Common Room: CMSA colloquium tea \n4:30 –5:30pm Room G-10\, CMSA colloquium: Peter Sarnak\, IAS and Princeton University\, Bass-Note Spectra of locally uniform geometries \n  \nTuesday\, April 29 \n11:00 am – 12:00pm Room G-10\, Pasquale Calabrese\, SISSA Trieste\, Lecture 1 of 3: Quantum Mpemba effect \n2:00 – 3:00 pm Room G-10\, Greta Panova\, University of Southern California\, Grothendieck shenanigans: permutons from pipe dreams via integrable probability \nAbstract: Pipe dreams are tiling models originally introduced to study objects related to the Schubert calculus and K-theory of the Grassmannian. They can also be viewed as ensembles of random lattice walks with various interaction constraints. In our quest to understand what the maximal and typical algebraic objects look like\, we revealed some interesting permutons. The proofs use the theory of the Totally Asymmetric Simple Exclusion Process (TASEP). Deeper connections with domino tilings of the Aztec diamond and its frozen boundary allow us to describe the extreme cases of the original algebraic problem. This is based on joint work with A. H. Morales\, L. Petrov\, D. Yeliussizov. \n3:30 – 4:00pm Common Room: Program tea  \n  \nWednesday\, April 30 \n11:00am – 12:00pm Herbert Spohn\, Technische Universitaet Muenchen\, Lecture 2 of 3: Integral many-body systems and GHD \n12:00 – 1:00pm (tentative) Common Room: CMSA Q&A seminar and lunch \n3:00 – 4pm Room G-10\, Pasquale Calabrese\, SISSA Trieste\, Entanglement evolution and quasiparticle picture 1 \n4:30 – 5:30pm Common Room: Program wine and cheese reception \n  \nThursday\, May 1 \n11:00am – 12:00pm Room G-10\, Herbert Spohn\, Technische Universitaet Muenchen\, Lecture 3 of 3: Integral many-body systems and GHD \n2:00 – 3:00 pm Room G-10\, Li-Cheng Tsai\, University of Utah\, Stochastic heat flow by moments \nAbstract: The Stochastic Heat Flow (SHF) is the scaling limit of the directed polymers in random environments and the noise-mollified Stochastic Heat Equation (SHE)\, at the critical dimension of two and near the critical temperature. The finite-dimensional distributions of the SHF was obtained by Caravenna\, Sun\, and Zygouras (2023) by proving that the discrete polymers converge to a universal (model-independent) limit. In this talk\, I will report a new approach based on axioms. We formulate the SHF as a two-parameter continuous measure-valued process that satisfies a set of axioms\, and prove the uniqueness in law under these axioms. The key feature of the axioms concerns the matching of the first four moments. As an application\, we prove the convergence of the noise-mollified SHE to the SHF\, which only requires moment estimates. \n3:30pm Common Room: Program tea  \n  \nFriday\, May 2 \n11:00am – 12:00pm Room G-10\, Pasquale Calabrese\, SISSA Trieste\, Lecture 3 of 3: Entanglement evolution and quasiparticle picture 2 \n12:00 – 1:00pm Common Room\, CMSA Member seminar and lunch \n2:00 – 3:00 pm Room G-10\, Leonid Petrov\, University of Virginia: Random Fibonacci Words \nAbstract: Fibonacci words are words of 1’s and 2’s\, graded by the total sum of the digits. They form a differential poset YF which is an estranged cousin of the Young lattice powering irreducible representations of the symmetric group. We introduce families of “coherent” measures on YF depending on many parameters\, which come from the theory of clone Schur functions (Okada 1994). We characterize parameter sequences ensuring positivity of the measures\, and we describe the large-scale behavior of some ensembles of random Fibonacci words. The subject has connections to total positivity of tridiagonal matrices\, Stieltjes moment sequences\, orthogonal polynomials from the (q-)Askey scheme\, and residual allocation (stick-breaking) models. Based on a joint work with Jeanne Scott. \n3:30 – 4:00pm Common Room: Program tea \n\nWeek 7\n  \nMonday\, May 5 \n11:00am – 12:00pm Room G-10\, Jan De Gier\, University of Melbourne\, Lecture 1 of 3: Pfaffian point process for TASEP on the half line \n12:00 – 2:00pm Common Room: Program Lunch \n2:00 – 3:00 pm  Jiaoyang Huang\, University of Pennsylvania: Ramanujan Property and Edge Universality of Random Regular Graphs \nAbstract: Extremal eigenvalues of graphs are of particular interest in theoretical computer science and combinatorics. Specifically\, the spectral gap—the difference between the largest and second-largest eigenvalues—measures the expansion properties of a graph. In this talk\, I will focus on random d-regular graphs.I will begin by providing background on the eigenvalues of random d-regular graphs and their connections to random matrix theory. In the second part of the talk\, I will discuss our recent results on eigenvalue rigidity and edge universality for these graphs. Eigenvalue rigidity asserts that\, with high probability\, each eigenvalue concentrates around its classical location as predicted by the Kesten-McKay distribution. Edge universality states that the second-largest eigenvalue and the smallest eigenvalue of random d-regular graphs converge to the Tracy-Widom distribution from the Gaussian Orthogonal Ensemble. Consequently\, approximately 69% of d-regular graphs are Ramanujan graphs. This work is based on joint work with Theo McKenzie and Horng-Tzer Yau. \n  \n4:00 – 4:30pm Common Room: CMSA colloquium tea \n4:30 –5:30pm Common Room\, CMSA colloquium: Ariel Procaccia\, Harvard University\, Thinking Outside the Ballot Box \n  \nTuesday\, May 6 \n11:00 am – 12:00pm Room G-10\, Jan De Gier\, University of Melbourne\, Lecture 2 of 3: Pfaffian point process for TASEP on the half line \n2:00 – 3:00 Richard Kenyon\, Yale University\, Multinomial dimers and 3d limit shapes \nAbstract: The “multinomial dimer model” on a graph G is the dimer model on the N-fold blow up of G (the graph obtained by replacing each vertex with N vertices and each edge with a complete bipartite graph K_{N\,N}). In the large N limit this model is tractable for general graphs: we find formulas for the partition function and limit shapes in some natural settings\, including a three-dimensional version of the Aztec Diamond. This is joint work with Catherine Wolfram (Yale). \n3:30 – 4:00pm Common Room: Program tea  \n  \nWednesday\, May 7 \n3:00 – 4pm Room G-10\, Jan De Gier\, University of Melbourne\, Lecture 3 of 3: Pfaffian point process for TASEP on the half line \n4:30 – 5:30pm Common Room: Program wine and cheese reception \n  \nThursday\, May 8: \n2:00 – 3:00 pm Room G-10\, Andrea De Luca\, CNRS Cergy Paris University\, Monitored quantum systems\, product of random matrices and permutations \n3:30pm Common Room: Program tea  \n  \nFriday\, May 9: \n12:00 – 1:00pm Common Room: CMSA Member Seminar and lunch\, Sergiy Verstyuk\, Harvard CMSA\, Title TBD \n2:00 – 3:00 pm Room G-10\, Cesar Cuenca\, Ohio State University\, Random partitions at high temperature \nAbstract: By using Fourier transforms based on Jack symmetric polynomials\, we study discrete particle ensembles x_1>x_2>…>x_N with the inverse temperature beta in the regime where beta tends to zero\, as the number of particles tends to infinity. We prove the LLN and characterize the limiting measure in terms of a moment problem. For fixed-time distributions of special Markov chains\, the limiting measures can be expressed in terms of the eigenvalues of certain Jacobi operators. \n3:30 – 4:00pm Common Room: Program tea \n\nWeek 8\n  \nMonday\, May 12 \n11:00am – 12:00pm Room G-10\, Jimmy He\, Ohio State University\, Symmetries of periodic and free boundary measures on partitions \nAbstract: The periodic and free boundary q-Whittaker measures are probability measures on partitions defined in terms of q-Whittaker functions and an additional parameter $u$ controlling the behavior of the system at the boundary. I will explain a hidden distributional symmetry of this model which exchanges the $u$ and $q$ parameters\, as well as related results on Hall-Littlewood measures. As a special case\, we recover identities of Imamura–Mucciconi–Sasamoto. This is joint work with Michael Wheeler. \n12:00 – 2:00pm Common Room: Program Lunch \n4:00 – 4:30pm Common Room: CMSA colloquium tea \n4:30 – 5:30pm Common Room\, CMSA colloquium: Anna Seigal\, Harvard University\, Factorizations for data analysis \n  \nTuesday\, May 13 \n3:30pm Common Room: Program tea  \n  \nWednesday\, May 14 \n12:00 – 1:00pm Common Room: CMSA Conference Reports seminar and lunch: Hugo Cui\, Harvard CMSA\, reporting on the Perimeter Institute Theory+AI Workshop \n3:00 – 4:00pm Room G-10\, Alexandre Krajenbrink\, Cambridge Quantum Computing and Quantinuum\, Unveiling the classical integrable structure of the weak noise theory of the KPZ class: example of the matrix Log–Gamma polymer and the q-TASEP \n4:30 – 5:30pm Common Room: Program wine and cheese reception \n  \nThursday\, May 15 \n11:00am – 12:00pm Room G-10: Roger Van Peski\, Columbia University\, Integrability in discrete random matrix theory \n\nAbstract: Integrable structure has been well-used in classical random matrix theory\, and recently is also enjoying application in the parallel world of discrete random matrices (over integers\, p-adic integers\, and finite fields). In this talk I will try to cover—at least briefly—the following:\n\n\nSome favorite probabilistic results (convergence of discrete random matrix local limits to a new integrable interacting particle system\, the ‘reflecting Poisson sea’)\,\nSome exact formulas with Hall-Littlewood polynomials that make these results possible\, and \nSome intriguing newer formulas (joint with Jiahe Shen) for Hermitian and antisymmetric p-adic matrices\, which naturally feature ‘formal’ Hall-Littlewood processes with negative t parameter.\n\n\n\n2:00 – 3:00 pm Room G-10\, Matteo Mucciconi\, National University Singapore\, Orthogonality of spin q-Whittaker polynomials \nAbstract: Spin q-Whittaker polynomials are a family of symmetric polynomials that can be defined as partition functions of a solvable lattice model. Their study reveals that they possess mysterious properties such as additional “unorthodox” symmetries\, eigenrelations with respect to difference operators and a self orthogonality that I will prove in the talk. A particular case of these results include a novel orthogonality for the Grothendieck polynomials from K-theory of Grassmannian. I will also discuss applications to exact solutions of directed random polymer models with Beta weights. \n3:30pm Common Room: Program tea  \n  \nFriday\, May 16 \n12:00 – 1:00pm Common Room: CMSA Member Seminar  and lunch: Samy Jelassi\, Echo Chamber: RL Post-training Amplifies Behaviors Learned in Pretraining \n3:30 – 4:00pm Common Room: Program tea \n\nVideos are available on the Youtube Playlist. \n\n 
URL:https://cmsa.fas.harvard.edu/event/integrablesystems2025/
LOCATION:CMSA 20 Garden Street Cambridge\, Massachusetts 02138 United States
CATEGORIES:Event,Programs
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/featured_Classical-quantum-probabalistic-2.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250130T160000
DTEND;TZID=America/New_York:20250130T173000
DTSTAMP:20260716T134322
CREATED:20240710T194728Z
LAST-MODIFIED:20241218T212836Z
UID:10003399-1738252800-1738258200@cmsa.fas.harvard.edu
SUMMARY:CMSA/MATH Welcome Back Gathering
DESCRIPTION:Thursday\, Jan. 30\, 2025 \n4:00 pm \nAll CMSA and Math affiliates are invited. \n 
URL:https://cmsa.fas.harvard.edu/event/cmsa-math_13025/
LOCATION:CMSA 20 Garden Street Cambridge\, Massachusetts 02138 United States
CATEGORIES:Event
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250121T090000
DTEND;TZID=America/New_York:20250124T170000
DTSTAMP:20260716T134322
CREATED:20240710T140404Z
LAST-MODIFIED:20250213T211311Z
UID:10003397-1737450000-1737738000@cmsa.fas.harvard.edu
SUMMARY:Workshop on Symmetries and Gravity
DESCRIPTION:Workshop on Symmetries and Gravity \nDates: January 21-24\, 2025 \nLocation: Harvard CMSA\, 20 Garden Street\, Cambridge\, MA 02138 \nOrganizers: Ibrahima Bah (Johns Hopkins University)\, Patrick Jefferson (Johns Hopkins University)\, Yiming Chen (Stanford University) \nDescription: There is a widespread belief\, that has its origins in work from the 70s\, that a theory of quantum gravity cannot admit global symmetries. Traditionally\, this was seen only as a qualitative statement about ordinary symmetries\, but there have since been a number of developments that have both widened its scope and sharpened its implications. Recent work has greatly broadened the definition of global symmetries\, and characterizes them in terms of topological operators in quantum systems. Concurrently\, insights from quantum gravity have suggested ways to quantify the extent of global symmetry violation. Additionally\, advances in the swampland program\, along with amplitudes and bootstrap techniques\, have shown ways to turn high-energy statements into constraints on low-energy effective field theories. In string theory\, there are more concrete statements on charge violation in gravity\, with proofs in limited context. In general\, however\, “no global symmetries in quantum gravity” continues to be an open conjecture with broad implications on the nature of quantum gravity and low-energy effective field theory. The main goal of the meeting is to bring together experts in the various arenas of research above\, to reassess and develop new strategies for making progress on this long-standing open problem. Some objectives include understanding the violation of various generalized and categorical symmetries in gravity more cohesively\, and putting concrete bounds on global charge-violating amplitudes at low energies. \nPartially funded by the Simons Collaboration on Global Categorical Symmetries. \n  \nConfirmed Participants \n\nTom Banks\, Rutgers\nFederico Bonetti\, Durham University\nChristian Copetti\, Oxford\nHector Parra De Freitas\, Harvard\nDamian van de Heisteeg\, Harvard CMSA\nMatilda Delgado\, IFT\nMichele Del-Zotto\, Uppsala University\nMuldrow Etheredge\, UMass Amherst\nIñaki Garcia-Etxebarria\, Durham University\nEduardo Garcia-Valdecasas\, SISSA\, Trieste\nNaomi Gendler\, Harvard\nKelian Haring\, CERN\nDaniel Harlow\, MIT\nJonathan Heckman\, University of Pennsylvania\nBen Heidenreich\, UMass Amherst\nAidan Herderschee\, IAS\nMax Huebner\, Uppsala University\nJesús Huertas\, Instituto de Física Teórica\nTheo Johnson-Freyd\, Dalhousie University\nHo Tat Lam\, MIT\nAdam Levine\, MIT\nYue-Zhou Li\, Princeton\nJacob McNamara\, Caltech\nRuben Minasian\, Institute of Theoretical Physics Saclay\nAmineh Mohseni\, Harvard\nMiguel Montero\, IFT\nGregory Moore\, Rutgers\nLeonardo Rastelli\, Stony Brook\nMatt Reece\, Harvard University\nGrant Remmen\, New York University\nDiego Rodriguez-Gomez\, University of Oviedo\nKonstantinos Roumpedakis\, Johns Hopkins\nTom Rudelius\, Durham University\nVivek Saxena\, Stony Brook and Rutgers\nEdgar Shaghoulian\, UC Santa Cruz\nShu-Heng Shao\, Stony Brook and MIT\nAdar Sharon\, Simons Center for Geometry and Physics\, Stony Brook\nIrene Valenzuela\, IFT and CERN\nThomas Waddleton\, Johns Hopkins\nHao Xu\, University of Göttingen\nXingyang Yu\, Virginia Tech\n\n  \nSchedule  \nTuesday\, Jan. 21\, 2025 \n9:00 – 9:30 am\nBreakfast \n9:30 – 11:00 am\nReview\nLeonardo Rastelli\, Stony Brook University\nYoutube Video \n11:00 – 11:15 am\nBreak \n11:15 am– 12:00 pm\nKelian Haring\, CERN\nTitle: S-matrix bootstrap and black hole production\nAbstract: I will review the expected effects of black hole production in scattering amplitudes. I will consider both symmetry-breaking and elastic amplitudes. I will argue that\, in the elastic case\, this input can be computationally useful. Then\, I will discuss an example of a symmetry-breaking Wilson coefficient as a concrete target for the bootstrap.\nYoutube Video \n12:00 – 1:45 pm\nLunch Break \n1:45 – 2:30 pm\nHo Tat Lam\, MIT\nTitle: Global Aspects of Exactly Marginal Current-Current Deformations\nAbstract: Conformal field theories connected by exactly marginal deformations form conformal manifolds. In two dimensions\, a large class of conformal manifolds is generated by bilinears of currents\, known as current-current deformations. In this talk\, we will revisit these deformations and prove that a dense set of points on the conformal manifolds are related to the seed theory through discrete gauging. This perspective enables us to connect the topology of the conformal manifolds with the anomalies of the currents and to show that enhanced invertible symmetries reorganized into non-invertible symmetries away from the symmetry enhanced points. We will also discuss how current-current deformation can be understood from the recently proposed continuous abelian symmetry topological field theory.\nYoutube Video \n2:30 – 3:15 pm\nTom Banks\, Rutgers University\nTitle: Symmetries in the Hilbert Bundle Formulation of Quantum Gravity\nAbstract: Results of Jacobson\, Carlip and Solodukhin from the 1990s\, as extended by Banks and Zurek in 2021\, point to a solution of Einstein’s equations as a hydrodynamic approximation to a quantum gravitational system\, which determines the density matrix assigned to each subsystem corresponding to a hydrodynamic causal diamond in terms of the Virasoro generator of a cut off 1 + 1 dimensional CFT. The full quantum system can be viewed as a Hilbert bundle over the space of timelike geodesics on the hydrodynamic background. Isometries of the background generically map one fiber of the bundle to another and don’t act on a fixed Hilbert space. Time evolution along each geodesic is given by an analog of “one sided modular flow in QFT”\, which in this context is a sequence of unitary embeddings of smaller diamond Hilbert spaces into larger ones. A full unitary map on the entire Hilbert space of a fiber requires a “Quantum Principle of Relativity” equating the entanglement spectrum of the density matrix of the largest diamond in the overlap between diamonds on different geodesics. In principle\, this implies asymptotic symmetries for spacetimes which have them. For the case of asymptotically AdS space\, this can be worked out in a hand waving way by using the Tensor Network Renormalization Group of Evenbly and Vidal. For asymptotically flat space we probably require a better non-perturbative definition of the space of asymptotic states to understand the action of the Poincare group. For de Sitter space there is no sense in which the de Sitter group acts on any set of asymptotic observables. Ironically\, there IS an approximate de Sitter invariance of at least low point inflationary correlation functions\, but I will not have time to discuss that.\nYoutube Video \n3:15 – 3:45 pm\nBreak \n3:45 – 4:30 pm\nChristian Copetti\, Oxford University\nTitle: Non-Invertible Symmetries\, Generalized Gauging and Factorization\nAbstract: We analyze a toy model for low dimensional holography\, in which the dual theory is an ensemble over 2d RCFTs. This simple model lacks factorization on multi-boundary geometries and at the same time has a (generalized) bulk global symmetry. We show that both problems are solved if the path integral prescription is modified by a generalized gauging operation\, which can also be interpreted as the insertion of (topological) EOW branes.\nYoutube Video \n4:30 – 5:00 pm\nFree Discussion \nWednesday\, Jan. 22\, 2025 \n9:00 – 9:30 am\nBreakfast \n9:30 – 11:00 am\nReview\nDaniel Harlow\, MIT\nYoutube Video \n11:00 – 11:15 am\nBreak \n11:15 am– 12:00 pm\nJacob McNamara\, Caltech\nTitle: Conserved Charges of Closed Universes\nAbstract: In quantum gravity\, while our standard notions of symmetry operator become hard to define\, the notion of conserved charge continues to make sense. After a general discussion of conserved charges in quantum gravity\, I will present a new kinematic invariant of a gravitational path integral that refines the cobordism groups of quantum gravity: the (higher) category of closed universe charges. By categorifying an argument of Coleman\, Giddings\, and Strominger\, I will argue that conserved charges in quantum gravity of any form degree arise only due to a categorical version of ensemble holography.\nYoutube Video \n12:00 – 1:45 pm\nLunch Break \n1:45 – 2:30 pm\nFederico Bonetti\, Durham University\nTitle: Aspects of Categorical Symmetries for Branes\nYoutube Video \n2:30 – 3:15 pm\nKonstantinos Roumpedakis\, Johns Hopkins University\nTitle: Symmetry Operators and Gravity\nAbstract: It is widely believed that there are no conserved charges in a theory of gravity\, based on arguments involving black holes. Moreover\, the modern approach to study global symmetries is the language of topological operators. In this talk\, I will revisit the absence of global symmetries in a theory of gravity from the perspective of topological operators. More specifically\, I will argue that topological operators for continuous symmetries written in terms of currents need regularization\, which effectively gives them a small but finite width. The regulated operator is a finite tension object which fluctuates. In the zero-width limit these fluctuations freeze\, recovering the properties of a topological operator. When gravity is turned on\, the zero-width limit becomes ill-defined\, thereby prohibiting the existence of topological operators. This talk is based on work in collaboration with Ibrahima Bah\, Patrick Jefferson\, and Thomas Waddleton.\nYoutube Video \n3:15 – 3:45 pm\nBreak \n3:45 – 4:30 pm\nIñaki Garcia-Etxebarria\, Durham University\nTitle: Some aspects of symmetry descent\nAbstract: SymTFTs allow us to encode the symmetry structure of Quantum Field Theories in a convenient way. For those QFTs that arise in geometric engineering\, or holography\, we expect to be able to derive the SymTFT from the geometric data of the string background. This talk will describe some recent progress in this direction\, together with S. Hosseini and with F. Gagliano.\nYoutube Video \n4:30 – 5:00 pm\nFree Discussion \n6:00 pm\nDinner at Changsho Restaurant \nThursday\, Jan. 23\, 2025 \n9:00 – 9:30 am\nBreakfast \n9:30 – 11:00 am\nReview\nIrene Valenzuela\, IFT and CERN\nTitle: Breaking of Symmetries in Gravity\nAbstract: Global symmetries are expected to be broken (or gauged) in quantum gravity. However\, we can still learn a lot from understanding the mechanisms by which quantum gravity avoids them and quantifying their breaking. Remarkably\, several Swampland constraints can be reinterpreted as consequences of breaking global symmetries. I will first focus on quantifying the minimal symmetry violation of axionic shift symmetries\, and show how the bottom-up expectation based on black holes seems to hold in string theory examples. I will then discuss how this symmetry violation changes as we move in the moduli space\, implying a drop-off of the quantum gravity cut-off when the symmetry is approximate. Finally\, I will discuss the fate of non-invertible symmetries in string theory\, and how they are typically broken at loop level. Nevertheless\, these approximate non-invertible symmetries are still useful to fill in the gaps in the worldsheet proofs of some Swampland conjectures. \n11:00 – 11:15 am\nBreak \n11:15 am– 12:00 pm\nTom Rudelius\, Durham University\nTitle: A Symmetry-Centric Perspective on the Geometry of the Landscape and the Swampland\nAbstract: As famously observed by Ooguri and Vafa nearly twenty years ago\, scalar field moduli spaces in quantum gravity appear to exhibit various universal features. For instance\, they seem to be infinite in diameter\, have trivial fundamental group\, and feature towers of massive particles that become light in their asymptotic limits. In this talk\, I will explain how these features can be reformulated in more modern language using generalized notions of global symmetries. Such symmetries are ubiquitous in non-gravitational quantum field theories\, but it is widely believed that they must be either gauged or broken in quantum gravity. We will see that the observations of Ooguri and Vafa can be understood as consequences of such gauging or breaking. \n12:00 – 1:45 pm\nLunch Break \n1:45 – 2:30 pm\nMiguel Montero\, IFT\nTitle: Parity symmetry breaking and the membrane Weak Gravity Conjecture\nAbstract: Symmetries are expected to be broken or gauged in any consistent theory of quantum gravity\, and this also applies to spacetime symmetries such as parity. I will argue that\, in the context of 4d N=1 AdS vacua of string theory\, the Weak Gravity Conjecture for membranes case only holds if the vacuum has an exact (i.e. gauged) parity symmetry of Pin+ type. I will give top-down examples of M-theory vacua illustrating this\, and show that in the DGKT scenario (a putative massive IIA vacuum with scale separation\, whose full consistency is the subject of some debate in the literature) there is no parity symmetry\, and the membrane WGC is violated. Thus\, there is either a pathology in DGKT\, or the membrane WGC is wrong. Both possibilities would have interesting consequences\, and I will outline ongoing work to figure out which one is it. \n2:30 – 3:15 pm\nMatilda Delgado\, IFT\nTitle: Dualities\, Defects and Duality Defects\nAbstract: I will outline how duality symmetries in quantum gravity theories naturally predict the existence of defects associated with duality transformations. While some of these objects are well-understood and extensively studied\, others remain enigmatic; I will discuss this with examples. I will conclude by discussing the potential role of dualities in characterising the UV defects predicted by cobordism conjecture (and more generally by the no global symmetries conjecture). Based on: [2412.03640] \n3:15 – 3:45 pm\nBreak \n3:45 – 4:30 pm\nMax Hübner\, Uppsala University\nTitle: Metric Isometries\, Holography\, and Continuous Symmetry Operators\nAbstract: In the AdS/CFT correspondence\, a topological symmetry operator of the boundary CFT is dual to a dynamical brane in the gravitational AdS bulk. Said differently\, this predicts a dynamical brane for every global symmetry of the boundary CFT. We analyze this correspondence for continuous symmetries which arise from a consistent truncation of isometries on the “internal” factor X of AdS × X. We discuss how this perspective can be used to both derive properties of the topological symmetry operators and non-topological properties of their bulk duals. \n4:30 – 5:00 pm\nFree Discussion \n  \nFriday\, Jan. 24\, 2025 \n9:00 – 9:30 am\nBreakfast \n9:30 – 10:15 am\nJonathan Heckman\, University of Pennsylvania\nTitle: Cobordism Utopia\nAbstract: On general grounds one expects that global symmetries are absent in quantum gravity. We discuss some aspects of this issue\, focusing on the recently proposed Swampland Cobordism Conjecture\, and related conjectures connected with completeness of the spectrum of states charged under symmetries. In particular\, the U-dualities of M-theory provide an excellent arena both for testing aspects of these conjectures\, as well as predicting the existence of new dynamical objects. We also comment on how this approach connects to related top down and holographic approaches to constructing and studying gauging and breaking symmetries in quantum gravity. Based on joint work to appear with Braeger\, Debray\, Dierigl\, and Montero. \n10:15 – 11:00 am\nNaomi Gendler\, Harvard University \n11:00 – 11:15 am\nBreak \n11:15 am – 12:00 pm\nDiego Rodriguez-Gomez\, University of Oviedo\nTitle: Non-BPS branes as holographic symmetry operators\nAbstract: We propose a holographic description of the operators implementing continuous global symmetries that are dual to superstring gauge fields in terms of non-BPS D- branes\, and consider some possible further extensions. \n12:00 – 12:45 pm\nGreg Moore\, Rutgers University\nTitle: Summing Over Bordisms In 2d TQFT: Déjà Vu\nAbstract: This is basically a rerun of a talk I gave on zoom for the CMSA on March 16\, 2022. I will review the contents of a paper I wrote with Anindya Banerjee 2201.00903\, but including a few minor updates. I will describe a construction in Topological Field Theory (TFT) which was motivated by developments in the quantum gravity community. The goal is to provide an interpretation of a model discussed by D. Marolf and H. Maxfield 2002.08950 aimed at fitting their model within the functorial framework of Quantum Field Theory (QFT). Given a TFT one can consider – formally – the sum over all bordisms between fixed ingoing and outgoing spatial slices (with appropriate weight factors for the bordisms) of the amplitudes associated to the bordism by the TFT. This construction leads to convergent sums in d\leq 2 dimensions\, at least for for generic parameters of the TFT. I will describe a curious splitting property satisfied by the total amplitude. I view the splitting property as an alternative to ensemble-type interpretations. There will be a cameo appearance of a very interesting paper by Daniel Friedan 2306.00019 which purports to give an axiomatic framework for Euclidean Quantum Gravity (EQG) analogous to the functorial formalism of QFT. I will also note\, in passing\, that these extremely simple\, low-dimensional\, baby baby baby models of EQG admit global symmetries and continuous parameters. \n1:00 pm\nFarewell Lunch \n 
URL:https://cmsa.fas.harvard.edu/event/symmetries/
LOCATION:CMSA 20 Garden Street Cambridge\, Massachusetts 02138 United States
CATEGORIES:Workshop
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Poster_Workshop-on-Symmetries-and-Gravity_2.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240905T160000
DTEND;TZID=America/New_York:20240905T170000
DTSTAMP:20260716T134322
CREATED:20240710T192944Z
LAST-MODIFIED:20241212T195515Z
UID:10003398-1725552000-1725555600@cmsa.fas.harvard.edu
SUMMARY:CMSA/Math Fall Gathering
DESCRIPTION:September 5\, 2024 \n4:00 pm \nCMSA Common Room\, 20 Garden Street\, Cambridge MA \nAll CMSA and Math affiliates are invited.
URL:https://cmsa.fas.harvard.edu/event/fallgathering2024/
LOCATION:CMSA 20 Garden Street Cambridge\, Massachusetts 02138 United States
CATEGORIES:Event
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-2-600x338-1-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180827T090000
DTEND;TZID=America/New_York:20190505T170000
DTSTAMP:20260716T134322
CREATED:20230904T082011Z
LAST-MODIFIED:20250303T193339Z
UID:10000010-1535360400-1557075600@cmsa.fas.harvard.edu
SUMMARY:PROGRAM ON TOPOLOGICAL ASPECTS OF CONDENSED MATTER
DESCRIPTION:During Academic year 2018-19\, the CMSA will be hosting a Program on Topological Aspects of Condensed Matter. New ideas rooted in topology have recently had a big impact on condensed matter physics\, and have highlighted new connections with high energy physics\, mathematics and quantum information theory. Additionally\, these ideas have found applications in the design of photonic systems and of materials with novel mechanical properties. The aim of this program will be to deepen these connections by foster discussion and seeding new collaborations within and across disciplines. \nAs part of the Program\, the CMSA will be hosting two workshops: \n\nWorkshop on Topology and Quantum Phases of Matter (August 27-28\, 2018)\nWorkshop on Topological Aspects of Condensed Matter (September 10-11\, 2019)\n\n. \nAdditionally\, a weekly Topology Seminar will be held on Mondays from 10:00-11:30pm in CMSA room G10. \n\nHere is a partial list of the mathematicians who have indicated that they will attend part or all of this special program\n\n\n\n\n\nName\nTentative Visiting Dates\n\n\n\n\n\nJason Alicea \n\n11/12/2018-11/16/2018\n\n\nMaissam Barkeshli\n4/22/2019 – 4/26/2019\n\n\nXie Chen\n4/15-17/2019 4/19-21/2019 4/24-30/2019\n\n\n\nLukasz Fidkowski \n\n1/7/2019-1/11/2019\n\n\n\nZhengcheng Gu \n\n8/15/2018-8/30/2018 & 5/9/2019-5/19/2019\n\n\n\nYin Chen He \n\n10/14/2018-10/27/2018\n\n\nAnton Kapustin\n8/26/2018-8/30/2018 & 3/28/2019-4/5/2019\n\n\n\nMichael Levin \n\n3/11/2019-3/15/2019\n\n\nYuan-Ming Lu\n4/29/2019-6/01/2019\n\n\n\nAdam Nahum \n\n4/2/2019- 4/19/2019\n\n\n\nMasaki Oshikawa \n\n4/22/2019-5/22/2019\n\n\nChong Wang\n 10/22/2018-11/16/2018\n\n\n\nJuven Wang \n\n4/1/2019-4/16/2019\n\n\nCenke Xu\n 8/26/2018-10/1/2018\n\n\n\nYi-Zhuang You \n\n4/1/2019-4/19/2019\n\n\n\nMike Zaletel \n\n5/1/2019-5/10/2019
URL:https://cmsa.fas.harvard.edu/event/topological-aspects-of-condensed-matter/
LOCATION:CMSA 20 Garden Street Cambridge\, Massachusetts 02138 United States
CATEGORIES:Programs
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20170109T090000
DTEND;TZID=America/New_York:20170113T170000
DTSTAMP:20260716T134322
CREATED:20250305T194842Z
LAST-MODIFIED:20250305T194842Z
UID:10003717-1483952400-1484326800@cmsa.fas.harvard.edu
SUMMARY:Working Conference on Applications of Random Matrix Theory to Data Analysis\, January 9-13\, 2017
DESCRIPTION:The Center of Mathematical Sciences and Applications will be hosting a working Conference on Applications of Random Matrix Theory to Data Analysis\, January 9-13\, 2017.  The conference will be hosted in Room G10 of the CMSA Building located at 20 Garden Street\, Cambridge\, MA 02138. \nParticipants:\nGerard Ben Arous\, Courant Institute of Mathematical Sciences \nAlex Bloemendal\, Broad Institute \nArup Chakraburty\, MIT \n\n\n\nZhou Fan\, Stanford University \nAlpha Lee\, Harvard University \nMatthew R. McKay\, Hong Kong University of Science and Technology (HKUST) \nDavid R. Nelson\, Harvard University \nNick Patterson\, Broad Institute \nMarc Potters\, Capital Fund management \n\n\n\nYasser Roudi\, IAS \nTom Trogdon\, UC Irvine \nOrganizers: \n\n\n\nMichael Brenner\, Lucy Colwell\, Govind Menon\, Horng-Tzer Yau \nPlease click Program for a downloadable schedule with talk abstracts.\n\nSchedule: \n\n\n\nJanuary 9 – Day 1\n\n\n9:30am – 10:00am\nBreakfast & Opening remarks\n\n\n10:00am – 11:00am\nMarc Potters\, “Eigenvector overlaps and the estimation of large noisy matrices”\n\n\n11:00am – 12:00pm\nYasser Roudi\n\n\n12:00pm – 2:00pm\nLunch\n\n\n2:00pm\nAfternoon Discussion\n\n\nJanuary 10 – Day 2\n\n\n8:30am – 9:00am\nBreakfast\n\n\n9:00am – 10:00am\nArup Chakraburty\, “The mathematical analyses and biophysical reasons underlying why the prevalence of HIV strains and their relative fitness are simply correlated\, and pose the challenge of building a general theory that encompasses other viruses where this is not true.”\n\n\n10:00am – 11:00am\nTom Trogdon\, “On the average behavior of numerical algorithms”\n\n\n11:00am – 12:00pm\nDavid R. Nelson\, “Non-Hermitian Localization in Neural Networks”\n\n\n12:00pm – 2:00pm\nLunch\n\n\n2:00pm\nAfternoon Discussion\n\n\nJanuary 11 – Day 3\n\n\n8:30am – 9:00am\nBreakfast\n\n\n9:00am – 10:00am\nNick Patterson\n\n\n10:00am – 11:00am\nLucy Colwell\n\n\n11:00am – 12:00pm\nAlpha Lee\n\n\n12:00pm – 2:00pm\nLunch\n\n\n2:00pm-4:00pm\nAfternoon Discussion\n\n\n4:00pm\nGerard Ben Arous (Public Talk)\, “Complexity of random functions of many variables: from geometry to statistical physics and deep learning algorithms“\n\n\nJanuary 12 – Day 4\n\n\n8:30am – 9:00am\nBreakfast\n\n\n9:00am – 10:00am\nGovind Menon\n\n\n10:00am – 11:00am\nAlex Bloemendal\n\n\n11:00am – 12:00pm\nZhou Fan\, “Free probability\, random matrices\, and statistics”\n\n\n12:00pm – 2:00pm\nLunch\n\n\n2:00pm\nAfternoon Discussion\n\n\nJanuary 13 – Day 5\n\n\n8:30am – 9:00am\nBreakfast\n\n\n9:00am – 12:00pm\nFree for Working\n\n\n12:00pm – 2:00pm\nLunch\n\n\n2:00pm\nFree for Working\n\n\n\n\n* This event is sponsored by CMSA Harvard University.
URL:https://cmsa.fas.harvard.edu/event/working-conference-on-applications-of-random-matrix-theory-to-data-analysis-january-9-13-2017/
LOCATION:CMSA 20 Garden Street Cambridge\, Massachusetts 02138 United States
CATEGORIES:Conference,Event
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20151128T090000
DTEND;TZID=America/New_York:20161202T170000
DTSTAMP:20260716T134322
CREATED:20240212T084906Z
LAST-MODIFIED:20250304T172138Z
UID:10001895-1448701200-1480698000@cmsa.fas.harvard.edu
SUMMARY:Mini-workshop on SYZ and Homological Mirror Symmetry
DESCRIPTION:The Center of Mathematical Sciences and Applications will be hosting a 4-day workshop on SYZ and Homological Mirror Symmetry and related areas on November 28 – December 2\, 2016 at Harvard CMSA Building: Room G10\, 20 Garden Street\, Cambridge\, MA 02138. \nOrganizers:\nBong Lian (Brandeis University)\, Siu-Cheong Lau (Boston University)\, Shing-Tung Yau (Harvard University) \nSpeakers:\n\nConan Leung\, Chinese University of Hong Kong\nJunwu Tu\, University of Missouri\nJingyu Zhao\, Columbia University\nDavid Treumann\, Boston College\nHiro Lee Tanaka\, Harvard University\nFabian Haiden\, Harvard University\nHansol Hong\, Harvard CMSA/Brandeis University\nNetanel Blaier\, Harvard CMSA/Brandeis University\nGarret Alston\, The University of Oklahoma\n\nPlease click Workshop Program for a downloadable schedule with talk abstracts. \nConference Schedule:\n\n\n\nMonday\, November 28 – Day 1\n\n\n\n\n\n\n10:30am –11:30am\nHiro Lee Tanaka\, “Floer theory through spectra”\n\n\nLunch\n\n\n1:00pm – 2:30pm\nFabian Haiden\, “Categorical Kahler Geometry”\n\n\n 2:30pm-2:45pm\n Break\n\n\n2:45pm – 4:15pm\nFabian Haiden\, “Categorical Kahler Geometry”\n\n\n4:30pm – 5:15pm\nGarret Alston\, “Potential Functions of Non-exact fillings”\n\n\n\n\n\n\n\nTuesday\, November 29 – Day 2\n\n\n\n\n\n\n10:30am –11:30am\nConan Leung\, “Remarks on SYZ”\n\n\nLunch\n\n\n1:00pm – 2:30pm\nJingyu Zhao\, “Homological mirror symmetry for open manifolds and Hodge theoretic invariants”\n\n\n 2:30pm-2:45pm\n Break\n\n\n2:45pm – 4:15pm\nHiro Lee Tanaka\, “Floer theory through spectra”\n\n\n4:30pm – 5:15pm\nHansol Hong\, “Mirror Symmetry for punctured Riemann surfaces and gluing construction”\n\n\n\n\n\n\n\nWednesday\, November 30 – Day 3\n\n\n\n\n\n\n10:30am –11:30am\nJunwu Tu\, “Homotopy L-infinity spaces and mirror symmetry”\n\n\nLunch\n\n\n1:00pm – 2:30pm\nJingyu Zhao\, “Homological mirror symmetry for open manifolds and Hodge theoretic invariants”\n\n\n 2:30-2:45pm\n Break\n\n\n2:45pm – 4:15pm\nDavid Treumann\, “Invariants of Lagrangians via microlocal sheaf theory”\n\n\n\n\n\n\n\n\n\n\n\n\nThursday\, December 1 – Day 4\n\n\n\n\n\n\n10:30am –11:30am\nDavid Treumann\, “Some examples in three dimensions”\n\n\nLunch\n\n\n1:00pm – 2:30pm\nJunwu Tu\, “Homotopy L-infinity spaces and mirror symmetry”\n\n\n 2:30-2:45pm\n Break\n\n\n2:45pm – 3:30pm\nNetanel Blaier\, “The quantum Johnson homomorphism\, and the symplectic mapping class group of 3-folds”\n\n\n\n\n\n\n\n* This event is sponsored by the Simons Foundation and CMSA Harvard University.
URL:https://cmsa.fas.harvard.edu/event/mini-workshop-on-syz-and-homological-mirror-symmetry/
LOCATION:CMSA 20 Garden Street Cambridge\, Massachusetts 02138 United States
CATEGORIES:Event,Workshop
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20150102T090000
DTEND;TZID=America/New_York:20151231T170000
DTSTAMP:20260716T134322
CREATED:20230904T081503Z
LAST-MODIFIED:20250228T180655Z
UID:10000051-1420189200-1451581200@cmsa.fas.harvard.edu
SUMMARY:MATH-PHYSICS PROGRAM
DESCRIPTION:In the past thirty years there have been deep interactions between mathematics and theoretical physics which have tremendously enhanced both subjects. The focal points of these interactions include string theory\, general relativity\, and quantum many-body theory. \nString theory has been at the center of the ongoing effort to uncover the fundamental principles of nature and in particular to unify Einstein’s geometric theory of gravity with quantum theory. The development of this field has sparked a historically unprecedented synergy between mathematics and physics. Progress at the forefront of theoretical physics has relied crucially on very recent developments in pure mathematics. At the same time insights from physics have led to both new branches of pure mathematics as well as dramatic progress in old branches. \nSeveral examples from the recent past exemplifying this synergy include the prediction from string theory of mirror symmetry\, a highly unexpected mathematical equivalence between distinct pairs of Calabi-Yau manifolds. This fueled exciting developments in algebraic\, enumerative and symplectic geometry. At the same time the realization of string theory as a phenomenologically viable physical theory depends crucially on detailed mathematical properties of these manifolds. In Einstein’s theory of general relativity the proofs of the positive energy theorem and the stability of flat spacetime were accompanied by fundamental new results in functional analysis\, differential geometry and minimal surface theory. In the coming decades we expect many more important discoveries to arise from the interface of mathematics and physics. The Cheng Fund will foster these efforts. \n\n\nHere is a partial list of the mathematicians who have indicated that they will attend part or all of this special program \n\n\n\n\nName\nTentative Visiting Dates\n\n\n\n\nPo-Ning Chen\n2/1/15-4/30/15\n\n\nHong-Jian He\n3/5/15-5/5/15\n\n\nMonica Guica\n12/1/14-3/15/15\n\n\nAmer Iqbal\n1/8/15-4/8/15\n\n\nSuvrat Raju\n2/25/15-5/25/15\n\n\nMithat Ünsal\n9/1/15-12/31/15
URL:https://cmsa.fas.harvard.edu/event/math-physics-program/
LOCATION:CMSA 20 Garden Street Cambridge\, Massachusetts 02138 United States
CATEGORIES:Programs
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