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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:20250416T120000
DTEND;TZID=America/New_York:20250416T130000
DTSTAMP:20260504T090337
CREATED:20250306T144613Z
LAST-MODIFIED:20250306T145201Z
UID:10003719-1744804800-1744808400@cmsa.fas.harvard.edu
SUMMARY:CMSA Q&A Seminar: Noah Golowich
DESCRIPTION:CMSA Q&A Seminar \nSpeaker: Noah Golowich (MIT) \nTopic: What is length generalization in large language models?
URL:https://cmsa.fas.harvard.edu/event/cmsaqa_41625/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:CMSA Q&A Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Q-A-Seminar-4.16.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250417T160000
DTEND;TZID=America/New_York:20250417T170000
DTSTAMP:20260504T090337
CREATED:20250108T143958Z
LAST-MODIFIED:20250422T182732Z
UID:10003655-1744905600-1744909200@cmsa.fas.harvard.edu
SUMMARY:Fifth Annual Yip Lecture | Scott Aaronson (UT Austin): How Much Math Is Knowable?
DESCRIPTION:Speaker: Scott Aaronson\, Department of Computer Science\, University of Texas\, Austin \nScott Aaronson is the founding director at the Quantum Information Center at the University of Texas at Austin. \nDate: April 17\, 2025 \nTime: 4:00-5:00 pm ET  (Reception following in the Math Common Room) \nLocation: Harvard Science Center Hall A \n  \nTitle: How Much Math Is Knowable? \nAbstract: Theoretical computer science has over the years sought more and more refined answers to the question of which mathematical truths are knowable by finite beings like ourselves\, bounded in time and space and subject to physical laws.  I’ll tell a story that starts with Gödel’s Incompleteness Theorem and Turing’s discovery of uncomputability.  I’ll then introduce the spectacular Busy Beaver function\, which grows faster than any computable function.  Work by me and Yedidia\, along with recent improvements by O’Rear and Riebel\, has shown that the value of BB(745) is independent of the axioms of set theory; on the other end\, an international collaboration proved last year that BB(5) = 47\,176\,870.  I’ll speculate on whether BB(6) will ever be known\, by us or our AI successors.  I’ll next discuss the P!=NP conjecture and what it does and doesn’t mean for the limits of machine intelligence.  As my own specialty is quantum computing\, I’ll summarize what we know about how scalable quantum computers\, assuming we get them\, will expand the boundary of what’s mathematically knowable.  I’ll end by talking about hypothetical models even beyond quantum computers\, which might expand the boundary of knowability still further\, if one is able (for example) to jump into a black hole\, create a closed timelike curve\, or project oneself onto the holographic boundary of the universe. \n  \nThe Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip. \n  \n\nThe previous Yip Lecture featured Josh Tenenbaum (MIT) who spoke on How to grow a mind from a brain: From guessing and betting to thinking and talking \n 
URL:https://cmsa.fas.harvard.edu/event/yip-2025/
LOCATION:Harvard Science Center\, 1 Oxford Street\, Cambridge\, MA\, 02138
CATEGORIES:Event,Public Lecture,Special Lectures,Yip Lecture Series
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Yip_2025.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250418T120000
DTEND;TZID=America/New_York:20250418T130000
DTSTAMP:20260504T090337
CREATED:20241211T195316Z
LAST-MODIFIED:20250218T160819Z
UID:10003647-1744977600-1744981200@cmsa.fas.harvard.edu
SUMMARY:Member Seminar
DESCRIPTION:Member Seminar \nSpeaker: Han Shao \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-41825/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250421T163000
DTEND;TZID=America/New_York:20250421T173000
DTSTAMP:20260504T090337
CREATED:20241209T163847Z
LAST-MODIFIED:20250418T142045Z
UID:10003636-1745253000-1745256600@cmsa.fas.harvard.edu
SUMMARY:Modeling the emergence of complex cortical structure from simple precursors in the brain: maps\, hierarchies\, and modules
DESCRIPTION:Colloquium \nSpeaker: Ila Fiete\, MIT \nTitle: Modeling the emergence of complex cortical structure from simple precursors in the brain: maps\, hierarchies\, and modules \nAbstract: Modular and hierarchical structures are ubiquitous in the brain. Two distinct hypotheses for such morphogenesis involve genetic specification (the positional information hypothesis) or spontaneous structure emergence from symmetry breaking (the pattern formation hypothesis). Indeed\, there is rich evidence supporting both hypotheses in different systems\, and more recently evidence that both systems might interact\, for instance with genetic specification providing an initial but relatively low-information scaffold of positional guidance and pattern formation constructing sharper structures by bootstrapping from this guidance. In this talk\, I will consider the emergence of two systems in the brain: the visual processing hierarchy with topographic structure\, and a modular cognitive circuit consisting of functionally independent grid cell networks that compute spatial location from velocity cues as animals move and navigate the world. I will describe how simple activity-driven growth and competition rules can lead to the emergence of topographically ordered sensory processing hierarchies\, and how genetically specified smooth gradients with purely local recurrent interactions on two scales can lead to global module emergence. In sum\, simple growth rules\, local interactions and smooth gradients can interact to produce rich emergent order on multiple scales in the form of maps\, modules\, and hierarchies\, with predictions that bridge scales from genes to connectivity to function.
URL:https://cmsa.fas.harvard.edu/event/colloquium-42125/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-4.21.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250422T110000
DTEND;TZID=America/New_York:20250422T120000
DTSTAMP:20260504T090337
CREATED:20250128T213711Z
LAST-MODIFIED:20250418T204712Z
UID:10003704-1745319600-1745323200@cmsa.fas.harvard.edu
SUMMARY:Hyperbolic equations in a double null gauge
DESCRIPTION:General Relativity Seminar \nSpeaker: Christopher Stith\, University of Michigan \nTitle: Hyperbolic equations in a double null gauge \nAbstract: The hyperbolic nature of the Einstein equations is well-known and has been used in many different contexts. More recently\, the double null gauge has proven to be a powerful tool for quantitative analysis of the Einstein equations. It has the advantage of reducing the equations for many dynamical quantities to ODEs along null curves\, and the Bianchi equations to a first-order hyperbolic system. The double null gauge has been used extensively and to great effect in analyzing the structure of spacetime for many purposes\, including (for instance) stability problems and trapped surface formation. However\, the local existence problem for the Einstein equations in a double null gauge has never been treated in full in its own right. In this talk\, we discuss how to formulate a general procedure for solving the linearized problem\, namely\, the local existence theory for systems of first-order hyperbolic equations in a double null gauge.
URL:https://cmsa.fas.harvard.edu/event/general-relativity-seminar-42225/
LOCATION:CMSA G102\, 20 Garden Street\, Cambridge\, MA\, 02138
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-4.22.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250422T161500
DTEND;TZID=America/New_York:20250422T181500
DTSTAMP:20260504T090337
CREATED:20250421T132929Z
LAST-MODIFIED:20250421T134309Z
UID:10003736-1745338500-1745345700@cmsa.fas.harvard.edu
SUMMARY:Classifying Space for Phases of Matrix Product States
DESCRIPTION:Geometry and Quantum Theory Seminar \nSpeakers: Bryan Wang Peng Jun (Harvard) and Bowen Yang (CMSA) \nTitle: Classifying Space for Phases of Matrix Product States \nAbstract: In this talk we will introduce recent work of Beaudry-Hermele-Pflaum-Qi-Spiegel-Stephen (arXiv:2501.14241)\, on constructing a classifying space for phases of matrix product states (MPS).
URL:https://cmsa.fas.harvard.edu/event/quantumgeo_42225/
LOCATION:Science Center 507\, 1 Oxford Street\, Cambridge\, 02138
CATEGORIES:Geometry and Quantum Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Geometry-Quantum-Theory-4.22.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250423T120000
DTEND;TZID=America/New_York:20250423T130000
DTSTAMP:20260504T090337
CREATED:20241125T204235Z
LAST-MODIFIED:20250407T150818Z
UID:10003624-1745409600-1745413200@cmsa.fas.harvard.edu
SUMMARY:CMSA Q&A Seminar: Alexei Borodin
DESCRIPTION:CMSA Q&A Seminar \nSpeaker: Alexei Borodin (MIT) \nTopic: Connections between physics and probability
URL:https://cmsa.fas.harvard.edu/event/cmsaqa_42325/
LOCATION:Common Room\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:CMSA Q&A Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Q-A-Seminar-4.23.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250423T140000
DTEND;TZID=America/New_York:20250423T150000
DTSTAMP:20260504T090337
CREATED:20250128T214818Z
LAST-MODIFIED:20250311T184354Z
UID:10003709-1745416800-1745420400@cmsa.fas.harvard.edu
SUMMARY:Machine learning for analytic calculations in theoretical physics
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Matthias Wilhelm (University of Southern Denmark) \nTitle: Machine learning for analytic calculations in theoretical physics \nAbstract: In this talk\, we will present recent progress on applying machine-learning techniques to improve calculations in theoretical physics\, in which we desire exact and analytic results. One example are so-called integration-by-parts reductions of Feynman integrals\, which pose a frequent bottleneck in state-of-the-art calculations in theoretical particle and gravitational-wave physics. These reductions rely on heuristic approaches for selecting a finite set of linear equations to solve\, and the quality of the heuristics heavily influences the performance. In this talk\, we investigate the use of machine-learning techniques to find improved heuristics. We use funsearch\, a genetic programming variant based on code generation by a Large Language Model\, in order to explore possible approaches\, then use strongly typed genetic programming to zero in on useful solutions. Both approaches manage to re-discover the state-of-the-art heuristics recently incorporated into integration-by-parts solvers\, and in one example find a small advance on this state of the art.
URL:https://cmsa.fas.harvard.edu/event/newtech_42325/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-4.23.2025.docx-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250424T100000
DTEND;TZID=America/New_York:20250424T110000
DTSTAMP:20260504T090337
CREATED:20250128T191347Z
LAST-MODIFIED:20250421T140604Z
UID:10003686-1745488800-1745492400@cmsa.fas.harvard.edu
SUMMARY:Mass gap in AdS space
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Ziming Ji\, Northeastern University \nTitle: Mass gap in AdS space \nAbstract: AdS space can be used as an IR regulator of QFT. The asymptotic conformal boundary in AdS space provides rich\, unique observables. We study asymptotic free theories in two-dimensional AdS space. By changing the AdS curvature scale \Lambda L\, we observe boundary signals of quantum phase transitions where mass gaps are dynamically generated in the bulk. We also utilize supersymmetry to study gauge theories in AdS4. We argue a connection between the AdS partition function and the prepotential and use the F-maximization of the Nekrasov partition function to study supersymmetric boundary conditions and its connection to the Seiberg-Witten theory. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/mathphys_42425/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-4.24.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250425T030000
DTEND;TZID=America/New_York:20250425T160000
DTSTAMP:20260504T090337
CREATED:20250422T134510Z
LAST-MODIFIED:20250422T140503Z
UID:10003713-1745550000-1745596800@cmsa.fas.harvard.edu
SUMMARY:Adversarial KA
DESCRIPTION:Freedman CMSA Seminar \nSpeaker: Slava Dzhenzher\, MIPT \nTitle: Adversarial KA \nAbstract: Regarding the representation theorem of Kolmogorov and Arnold (KA) as an algorithm for representing or «expressing» functions\, we test its robustness by analyzing its ability to withstand adversarial attacks. We find KA to be robust to countable collections of continuous adversaries\, but unearth a question about the equi-continuity of the outer functions that\, so far\, obstructs taking limits and defeating continuous groups of adversaries. This question on the regularity of the outer functions is relevant to the debate over the applicability of KA to the general theory of NNs. Based on  https://arxiv.org/abs/2504.05255 \n  \n 
URL:https://cmsa.fas.harvard.edu/event/freedman_42525/
LOCATION:Virtual
CATEGORIES:Freedman Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Freedman-Seminar-4.25.25.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250428T163000
DTEND;TZID=America/New_York:20250428T173000
DTSTAMP:20260504T090337
CREATED:20241209T171137Z
LAST-MODIFIED:20250423T174326Z
UID:10003637-1745857800-1745861400@cmsa.fas.harvard.edu
SUMMARY:Bass-Note Spectra of locally uniform geometries
DESCRIPTION:Colloquium \nSpeaker: Peter Sarnak\, IAS & Princeton University \nTitle: Bass-Note Spectra of locally uniform geometries \nAbstract: We formulate and report on the problem of the Bass-Note Spectrum of an invariant operator as one varies over locally uniform geometries. In the Euclidean setting this recasts classical problems of Mahler from the geometry of numbers in a new light. For certain operators homogeneous dynamics can be used decisively. In the non-Euclidean setting of hyperbolic manifolds we review some recent developments using the conformal bootstrap method and of random covers to study the Bass-Note spectra. We highlight the theme and impact of rigidity.
URL:https://cmsa.fas.harvard.edu/event/colloquium-42825/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-4.28.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250429T161500
DTEND;TZID=America/New_York:20250429T181500
DTSTAMP:20260504T090337
CREATED:20250414T213151Z
LAST-MODIFIED:20250428T143404Z
UID:10003740-1745943300-1745950500@cmsa.fas.harvard.edu
SUMMARY:Algebraic approach to the bow construction
DESCRIPTION:Geometry and Quantum Theory Seminar \nSpeakers: Anadil Saeed Rao (Northeastern) and Vasily Krylov (CMSA/Harvard) \nTitle: Algebraic approach to the bow construction \nAbstract: Anadil will finish his part of the talk. Vasily will then explain how to understand moduli spaces of instantons on R^4\, monopoles on R^3\, and instantons on Taub-NUT spaces algebraically as so-called bow varieties. We will see how affine type A Nakajima quiver varieties and Slodowy slices arise as special cases of bow varieties. Time permitting\, we will also discuss applications to 3D mirror symmetry and Coulomb branches.
URL:https://cmsa.fas.harvard.edu/event/quantumgeo_42925-2/
LOCATION:Science Center 507\, 1 Oxford Street\, Cambridge\, 02138
CATEGORIES:Geometry and Quantum Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Geometry-Quantum-Theory-4.29.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250501T100000
DTEND;TZID=America/New_York:20250501T110000
DTSTAMP:20260504T090337
CREATED:20250128T172012Z
LAST-MODIFIED:20250428T143252Z
UID:10003681-1746093600-1746097200@cmsa.fas.harvard.edu
SUMMARY:From superspace to twisted supergravity
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Fabian Hahner\, University of Washington \nTitle: From superspace to twisted supergravity \nAbstract: In this talk\, I will present a geometric perspective on the pure spinor superfield formalism\, which proves fruitful for studying twisted supergravity. For eleven-dimensional supergravity\, we use this technique to construct the full interacting theory together with all its twists in a uniform and geometric way as homotopy Poisson–Chern–Simons theories. In addition to simplifying the computation of twists immensely\, this also provides fresh insights into the supergeometric origin of supergravity. Building on these ideas\, we further construct local dg Lie algebras that recover conformal supergravity multiplets and their twists in terms of a geometric moduli problem on superspace. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/mathphys_5125/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-5.1.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250502T120000
DTEND;TZID=America/New_York:20250502T130000
DTSTAMP:20260504T090337
CREATED:20241211T195435Z
LAST-MODIFIED:20250428T151202Z
UID:10003650-1746187200-1746190800@cmsa.fas.harvard.edu
SUMMARY:Incentives for data sharing in federated learning
DESCRIPTION:Member Seminar \nSpeaker: Han Shao\, Harvard CMSA \nTitle: Incentives for data sharing in federated learning \nAbstract: Federated learning has recently emerged as a powerful approach for enabling collaboration across large populations of learning agents. However\, agents may have incentives to defect from the collaboration—that is\, to withdraw or contribute less data than expected—due to the costs of data curation and privacy concerns. This raises several key questions: What happens when agents defect\, and how can we prevent such defections? \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-5225/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-5.2.25.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250505T150000
DTEND;TZID=America/New_York:20250505T160000
DTSTAMP:20260504T090337
CREATED:20250226T173940Z
LAST-MODIFIED:20250226T173940Z
UID:10003715-1746457200-1746460800@cmsa.fas.harvard.edu
SUMMARY:Quantum Field Theory and Physical Mathematics
DESCRIPTION:Quantum Field Theory and Physical Mathematics Seminar
URL:https://cmsa.fas.harvard.edu/event/qft_5525/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Field Theory and Physical Mathematics
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250505T163000
DTEND;TZID=America/New_York:20250505T173000
DTSTAMP:20260504T090337
CREATED:20250407T140808Z
LAST-MODIFIED:20250501T134436Z
UID:10003733-1746462600-1746466200@cmsa.fas.harvard.edu
SUMMARY:Thinking Outside the Ballot Box
DESCRIPTION:Colloquium \nSpeaker: Ariel Procaccia\, Harvard University \nTitle: Thinking Outside the Ballot Box \nAbstract: How should one design unprecedented democratic processes capable of handling enormous sets of alternatives like all possible policies\, bills\, or statements? I argue that this challenge can be addressed through a framework called generative social choice\, which fuses the rigor of social choice theory with the flexibility and power of large language models. I then explore an application of generative social choice to the problem of identifying a proportionally representative slate of opinion statements. This includes a discussion of desired properties\, an algorithm that provably achieves them\, an implementation using GPT\, and insights from an end-to-end pilot. By providing guarantees\, generative social choice could alleviate concerns about AI-driven democratic innovation and help unlock its potential.
URL:https://cmsa.fas.harvard.edu/event/colloquium-5525/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-5.5.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250506T161500
DTEND;TZID=America/New_York:20250506T181500
DTSTAMP:20260504T090337
CREATED:20250407T174129Z
LAST-MODIFIED:20250407T174129Z
UID:10003738-1746548100-1746555300@cmsa.fas.harvard.edu
SUMMARY:Geometry and Quantum Theory Seminar
DESCRIPTION:Geometry and Quantum Theory Seminar
URL:https://cmsa.fas.harvard.edu/event/quantumgeo_5625/
LOCATION:Science Center 507\, 1 Oxford Street\, Cambridge\, 02138
CATEGORIES:Geometry and Quantum Theory Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250508T100000
DTEND;TZID=America/New_York:20250508T110000
DTSTAMP:20260504T090337
CREATED:20250312T185317Z
LAST-MODIFIED:20250501T191129Z
UID:10003728-1746698400-1746702000@cmsa.fas.harvard.edu
SUMMARY:Residues and homotopy Lie algebras
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Zhenping Gui\, Shanghai Institute for Mathematics and Interdisciplinary Sciences \nTitle: Residues and homotopy Lie algebras \nAbstract: I will introduce the notion of a chiral operad for any compact Riemann surface. This operad consists of compositions of residue operations\, which give rise to the Chevalley-Cousin complex and lead to the definition of chiral homology (derived conformal blocks). I will explain how to use this machinery to rigorously define certain Feynman integrals in 2D chiral CFTs. Subsequently\, I will present a polysimplicial construction of a series of chain models for the configuration space of points in an affine space and study residue operations. These residue operations can be described by a homotopy Lie algebra structure\, and the latter defines a higher-dimensional analog of the Chevalley-Cousin complex. This is based on joint work in progress with Charles Young and Laura Felder. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/mathphys_5825/
LOCATION:Virtual
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-5.8.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250509T120000
DTEND;TZID=America/New_York:20250509T130000
DTSTAMP:20260504T090337
CREATED:20241211T195446Z
LAST-MODIFIED:20250506T153832Z
UID:10003649-1746792000-1746795600@cmsa.fas.harvard.edu
SUMMARY:Asset pricing with heterogeneous agents
DESCRIPTION:Member Seminar \nSpeaker: Sergiy Verstyuk\, Harvard CMSA \nTitle: Asset pricing with heterogeneous agents \nAbstract: This talk will introduce the basics of continuous-time finance\, discuss important existing theories and models\, as well as present some new asset pricing results in a setting with many heterogeneous investors. (Joint work with Puskar Mondal.) \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-5925/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-5.9.25.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250512T150000
DTEND;TZID=America/New_York:20250512T160000
DTSTAMP:20260504T090337
CREATED:20250226T174007Z
LAST-MODIFIED:20250605T134144Z
UID:10003716-1747062000-1747065600@cmsa.fas.harvard.edu
SUMMARY:An index for 2d invertible phases of quantum many-body systems
DESCRIPTION:Quantum Field Theory and Physical Mathematics Seminar \nSpeaker: Nikita Sopenko\, IAS \nTitle: An index for 2d invertible phases of quantum many-body systems
URL:https://cmsa.fas.harvard.edu/event/qft_51225/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Field Theory and Physical Mathematics
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QFT-and-Physical-Mathematics-5.12.25-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250512T163000
DTEND;TZID=America/New_York:20250512T173000
DTSTAMP:20260504T090337
CREATED:20250407T140851Z
LAST-MODIFIED:20250506T191033Z
UID:10003734-1747067400-1747071000@cmsa.fas.harvard.edu
SUMMARY:Factorizations for data analysis
DESCRIPTION:Colloquium \nSpeaker: Anna Seigal\, Harvard University \nTitle: Factorizations for data analysis \nAbstract: We can find structure in data by factoring it into building blocks\, which should be interpretable for the context at hand. A classical example is principal component analysis (PCA)\, which uses the eigendecomposition of the covariance matrix to find axes of variation in a dataset. Starting from PCA\, I will discuss matrix and tensor factorizations for data analysis\, and the linear and multilinear algebra that underpins their theoretical properties. We will see examples from causal inference\, independent component analysis\, and dimensionality reduction.
URL:https://cmsa.fas.harvard.edu/event/colloquium-51225/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-5.12.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250514T120000
DTEND;TZID=America/New_York:20250514T130000
DTSTAMP:20260504T090337
CREATED:20250501T182905Z
LAST-MODIFIED:20250502T173004Z
UID:10003746-1747224000-1747227600@cmsa.fas.harvard.edu
SUMMARY:Report on the Perimeter Institute Theory+AI Workshop
DESCRIPTION:Conference Reports  \nSpeaker: Hugo Cui\, Harvard CMSA \nTitle: Report on the Perimeter Institute Theory+AI Workshop \nAbstract: I will give a survey and brief summary of some of the talks given at the Theory+AI Workshop: Theoretical Physics for AI event organized by Perimeter Institute in April\, on approaches to machine learning theory inspired from physics. \nLink : https://events.perimeterinstitute.ca/event/993/
URL:https://cmsa.fas.harvard.edu/event/confrep_51425/
LOCATION:CMSA 20 Garden Street Cambridge\, Massachusetts 02138 United States
CATEGORIES:Conference Reports
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Conference-Reports-5.14.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250515T100000
DTEND;TZID=America/New_York:20250515T110000
DTSTAMP:20260504T090337
CREATED:20250417T165100Z
LAST-MODIFIED:20250509T175206Z
UID:10003741-1747303200-1747306800@cmsa.fas.harvard.edu
SUMMARY:Resurgence\, number theory\, and quantum mirror curves 
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Claudia Rella (IHES) \nTitle: Resurgence\, number theory\, and quantum mirror curves \nAbstract: Resurgence provides a powerful toolbox to access the non-perturbative sectors hidden within the divergent asymptotic series of quantum theories. Under some special assumptions\, the non-perturbative data extracted via resurgent methods possess intrinsic number-theoretic properties that are deeply rooted in the symmetries and arithmetic of the geometry underlying the quantum theory. The framework of modular resurgence aims to formalise this observation. In this talk\, after introducing the basics of modular resurgence\, I will consider the TS/ST correspondence for toric Calabi-Yau threefolds and focus on the fermionic spectral traces of quantum mirror curves. Here\, a complete realisation of the modular resurgence paradigm is found in the spectral theory of local P^2—where the bridge between non-perturbative physics and the arithmetic properties of the geometry takes the form of an exact strong-weak symmetry—and is now being generalised to all local weighted projective spaces. This talk is based on arXiv:2212.10606\, 2404.10695\, 2404.11550\, and work in progress. \n  \n  \n 
URL:https://cmsa.fas.harvard.edu/event/mathphys_51525/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-5.15.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250516T120000
DTEND;TZID=America/New_York:20250516T130000
DTSTAMP:20260504T090337
CREATED:20250218T161047Z
LAST-MODIFIED:20250513T152517Z
UID:10003714-1747396800-1747400400@cmsa.fas.harvard.edu
SUMMARY:Echo Chamber: RL Post-training Amplifies Behaviors Learned in Pretraining
DESCRIPTION:Member Seminar \nSpeaker: Samy Jelassi\, CMSA \nTitle: Echo Chamber: RL Post-training Amplifies Behaviors Learned in Pretraining \nAbstract: Reinforcement Learning has become a crucial step in training state-of-the-art language models such as DeepSeek-R1 for solving mathematical problems. In this talk\, I will first review the mechanisms of Reinforcement Learning fine-tuning. Then\, I will present a systematic end-to-end study of RL fine-tuning for mathematical reasoning\, training models entirely from scratch on different mixtures of fully open datasets and fine-tuning them with RL. Doing so allows us to investigate the effects of the pretraining data mixture on the behavior of RL\, and its interaction with the model size and choices of the algorithm hyperparameters. Our study reveals that RL algorithms consistently converge towards a dominant output distribution\, amplifying patterns in the pretraining data. We also find that models of different scales trained on the same data mixture will converge to distinct output distributions\, suggesting that there are scale-dependent biases in model generalization. \nThe second part of the talk is based on a joint work with Rosie Zhao\, Alex Meterez\, Cengiz Pehlevan\, Sham Kakade and Eran Malach: https://arxiv.org/abs/2504.07912 \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-51625/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-5.16.25.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250522T100000
DTEND;TZID=America/New_York:20250522T110000
DTSTAMP:20260504T090337
CREATED:20250417T165226Z
LAST-MODIFIED:20250519T144738Z
UID:10003742-1747908000-1747911600@cmsa.fas.harvard.edu
SUMMARY:Higher Gauge Theory and Integrability
DESCRIPTION:Mathematical Physics and Algebraic Geometry Seminar \nSpeaker: Joaquin Liniado\, Instituto de Física La Plata \nTitle: Higher Gauge Theory and Integrability \nAbstract: Integrable field theories are remarkable for possessing an infinite number of conserved quantities\, which often allow for their exact solvability. In two dimensions\, this structure is elegantly captured by the existence of a Lax connection\, whose path ordered exponential allows for the systematic construction of an infinite number of conserved quantities. In 2019\, Costello\, Witten and Yamazaki introduced a four-dimensional holomorphic extension of Chern-Simons theory that provides the first attempt at explaining the appearance of the Lax connection\, whose origin had remained somewhat mysterious until then. \nIn this talk\, we present a generalization of these ideas to three-dimensional field theories\, guided by the so-called “categorical ladder = dimensional ladder” principle. The central idea is that conserved quantities arise from surface-ordered exponentials of higher-rank tensors\, defining a higher categorical notion of the Lax connection. We show that such a structure naturally emerges from a five-dimensional holomorphic extension of higher Chern-Simons theory. This work\, carried out in collaboration with Hank Chen\, provides a framework that enables the systematic construction of integrable field theories in three dimensions. \n  \n  \n 
URL:https://cmsa.fas.harvard.edu/event/mathphys_52225/
LOCATION:Virtual
CATEGORIES:Mathematical Physics and Algebraic Geometry
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Mathematical-Physics-and-Algebraic-Geometry-5.22.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250602T090000
DTEND;TZID=America/New_York:20250604T170000
DTSTAMP:20260504T090337
CREATED:20241107T214041Z
LAST-MODIFIED:20250605T193626Z
UID:10003619-1748854800-1749056400@cmsa.fas.harvard.edu
SUMMARY:Summer School in Total Positivity and Quantum Field Theory
DESCRIPTION:Summer School in Total Positivity and Quantum Field Theory \nDates: June 2–4\, 2025 \nLocation: CMSA\, 20 Garden Street\, Cambridge MA \n\n\nIn the past decade\, there has been a great deal of interest and progress in the study of algebro-combinatorial and geometric structures appearing across diverse areas of physics\, from particle physics to cosmology. As these research programs expand\, there is an ever-growing need for mathematicians and physicists to collaborate effectively and build a shared language. Join us at Harvard University’s Center of Mathematical Sciences and Applications for a week-long summer school dedicated to addressing these interdisciplinary connections. The school welcomes graduate students\, postdocs\, and early-career researchers drawn to the intersection of mathematics and physics. Whether you are an algebraic combinatorialist looking for a better grasp on the physics\, a high energy theorist trying to figure out the math\, or a newcomer to both fields\, this summer school offers an ideal opportunity for you to learn. \n\n\nCourses taught by both mathematicians and physicists will connect ideas from total positivity\, matroid theory\, discrete geometry\, and real algebraic geometry with fundamental questions in quantum field theory. Topics will include amplituhedra\, cluster algebras\, and positive geometry as they relate to scattering amplitudes and cosmological correlators in high-energy physics. Our courses are designed to be accessible to a varied audience; speakers will be mindful of the diverse backgrounds of the participants from both fields. \nAmid this exciting period of collaboration between mathematicians and physicists\, we look forward to exploring these rich\, cutting-edge topics with you. \n\nCourses: \n\nPositive Grassmannian and Cluster Algebras\, Lara Bossinger (Instituto de Matemáticas Universidad Nacional Autónoma de México)\nslides  | exercises\n\n  \n\nPositive Geometry and Canonical Forms\, Simon Telen (MPI Leipzig)\nslides\n\n  \n\nScattering Amplitudes and Amplituhedra\, Marcus Spradlin (Brown)\nexercises\n\n  \n\nCosmology and Cosmological Polytopes\, Nima Arkani-Hamed (IAS)\n\n  \n\nOrganizers:  Jonathan Boretsky (McGill University) |  Matteo Parisi (Harvard CMSA and IAS Princeton) | Lauren Williams (Harvard University) \n\nYoutube Playlist \nSchedule  \nMonday\, June 2\, 2025 \n\n\n\n8:30–9:00 am\nMorning Reception\n\n\n9:00–10:00 am\nLara Bossinger: Positive Grassmannian and Cluster Algebras I\n\n\n10:00–10:30 am\nCoffee Break\n\n\n10:30–11:10 am\nExercises\n\n\n11:10 am–12:10 pm\nNima Arkani-Hamed: Cosmology and Cosmological Polytopes I\n\n\n12:10–2:00 pm\nLunch Break\n\n\n2:00–3:00 pm\nNima Arkani-Hamed: Cosmology and Cosmological Polytopes II\n\n\n3:00–3:30 pm\nCoffee Break\n\n\n3:30–4:10 pm\nExercises\n\n\n4:10–5:10 pm\nNima Arkani-Hamed: Cosmology and Cosmological Polytopes III\n\n\n\n  \nTuesday\, June 3\, 2025 \n\n\n\n8:30–9:00 am\nMorning Reception\n\n\n9:00–10:00 am\nLara Bossinger: Positive Grassmannian and Cluster Algebras II\n\n\n10:00–10:30 am\nCoffee Break\n\n\n10:30–11:30 am\nMarcus Spradlin: Scattering Amplitudes and Amplituhedra I\n\n\n11:30 am–12:10 pm\nExercises\n\n\n12:10–2:00 pm\nLunch Break\n\n\n2:00–3:00 pm\nSimon Telen: Definitions and first examples of positive geometries\n\n\n3:00–3:30 pm\nCoffee Break\n\n\n3:30–4:30 pm\nLightning Talks\n\n\n4:30–5:30 pm\nSimon Telen: Positive geometry of polytopes\n\n\n\n  \nWednesday\, June 4\, 2025 \n\n\n\n8:30–9:00 am\nMorning Reception\n\n\n9:00–10:00 am\nLara Bossinger: Positive Grassmannian and Cluster Algebras III\n\n\n10:00–10:30 am\nCoffee Break\n\n\n10:30–11:10 am\nExercises\n\n\n11:10 am–12:10 pm\nMarcus Spradlin: Scattering Amplitudes and Amplituhedra II\n\n\n12:10–2:00 pm\nLunch Break\n\n\n2:00–3:00 pm\nMarcus Spradlin: Scattering Amplitudes and Amplituhedra III\n\n\n3:00–3:30 pm\nCoffee Break\n\n\n3:30–4:30 pm\nSimon Telen: Positive geometry of polypols\n\n\n4:30–5:10 pm\nExercises\n\n\n\n  \n\nImage credit: Annabel Ma (Harvard College)
URL:https://cmsa.fas.harvard.edu/event/positivityqft/
LOCATION:CMSA 20 Garden Street Cambridge\, Massachusetts 02138 United States
CATEGORIES:Event,Workshop
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/SummerSchool_poster_11x17_v2-scaled.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250630T090000
DTEND;TZID=America/New_York:20250711T170000
DTSTAMP:20260504T090337
CREATED:20240219T200745Z
LAST-MODIFIED:20250714T144712Z
UID:10002770-1751274000-1752253200@cmsa.fas.harvard.edu
SUMMARY:Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras
DESCRIPTION:Workshop on Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras \nDates: June 30 – July 11\, 2025 \nLocation: CMSA\, 20 Garden Street\, Cambridge MA and Max Planck Institute for Mathematics\, Bonn\, Germany \nThis event is a twinned workshop at the CMSA (Harvard) and the Max Planck Institute for Mathematics (Bonn). Lectures will alternate between the two sites\, watched simultaneously on both sides\, and there will be opportunities for dialogue between the locations. The first week will contain four pedagogical lecture series; lecturers and locations are \nMichael Hopkins\, Harvard  (CMSA)Alexei Kitaev\, Caltech (CMSA)Pieter Naaijkens\, Cardiff (MPIM)Bruno Nachtergaele\, UC Davis (MPIM) \nThe second week will consist of research talks. \nParticipants are strongly encouraged to attend at the location that minimizes travel and hence the ecological impact of the conference. \nThe application deadline was March 16\, 2025. \nDirections to CMSA \nMPIM-Bonn location: https://www.mpim-bonn.mpg.de/qft25  \n  \nRegister for Zoom Webinar \n  \nQuantum Field Theory (QFT) and Quantum Statistical Mechanics are central to high energy physics and condensed matter physics; they also raise deep questions in mathematics. The application of operator algebras to these areas of physics is well-known. Recent developments indicate that to understand some aspects QFT properly a further ingredient is needed: homotopy theory and infinity-categories. One such development is the recognition that symmetry in a QFT is better described by a homotopy type rather than a group (so-called generalized symmetries). Another one is the work of Lurie and others on extended Topological Field Theory (TFT) and the Baez-Dolan cobordism hypothesis. Finally\, there is a conjecture of Kitaev that invertible phases of matter are classified by homotopy groups of an Omega-spectrum. This workshop will bring together researchers and students approaching this physics using different mathematical techniques: operator algebras\, homotopy theory\, higher category theory\, etc. The goal is to catalyze new interactions between different communities. At the workshop recent developments will be reviewed and hopefully progress can be made on two outstanding problems: the Kitaev conjecture as well as the long-standing goal of finding a proper mathematical formulation for QFT. \nOrganizers: \n\nDan Freed\, Harvard University CMSA & Math\nDennis Gaitsgory\, MPIM Bonn\nOwen Gwilliam\, UMass Amherst\nAnton Kapustin\, Caltech\nCatherine Meusburger\, University of Erlangen-Nürnberg\n\n  \nTalks are recorded and available on the CMSA Youtube Playlist. \n\nBACKGROUND READING \nParticipants are encouraged to have some basic familiarity with the definition of a C*-algebra and quantum spin system. Some knowledge of quantum channels (completely positive trace-preserving maps) and quantum circuits will be useful. Some knowledge of Clifford algebras will also be helpful. \nPossible references include: \n 1) arXiv:1311.2717 (Sections 2.1\, 2.2\, 2.4\, and 2.5 up to Theorem 2.5.3) \n 2) Lectures by Daniel Spiegel on “C*-Algebraic Foundations of Quantum Spin Systems”\, at the Summer School on C*-Algebraic Quantum Mechanics and Topological Phases of Matter\, University of Colorado Boulder\, July 29 to August 2\, 2024. (lecture notes and video recordings: https://sites.google.com/colorado.edu/caqm). \n3) https://nextcloud.tfk.ph.tum.de/etn/wp-content/uploads/2022/09/JvN_lecture_notes_S2016_abcde-1.pdf \n4) https://en.wikipedia.org/wiki/Classification_of_Clifford_algebras \n5) Karoubi\, K-theory\, section III.3 \n6.) Alexei Kitaev: A norm bound for 1D local matrices (pdf) \n  \nSchedule Times are Eastern Time  \ndownload schedule pdf \nWorkshop on Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras \nJune 30 – July 11\, 2025 \n  \n\n\n\n\nMonday\, June 30 \n\n\n\n\n8:00–9:00 am \n\n\nMPIM \n\n\nBruno Nachtergaele\, UC Davis \nTitle: Ground states of quantum lattice systems: Quantum Lattice Systems: observables\, dynamics\, ground states\, GNS representation\, ground state gap\, examples \n\n\n\n\n9:00–9:30 am \n\n\n  \n\n\nBreakfast break \n\n\n\n\n9:30–10:30 am \n\n\nCMSA \n\n\nMichael Hopkins\, Harvard \nTitle: Lattice models and topological quantum field theories I \nAbstract: This series will cover the relationship between gapped Hamiltonian lattice models and topological quantum field theories\, with an emphasis on a conjecture of Kitaev. \n\n\n\n\n10:30–10:45 am \n\n\n  \n\n\nbreak \n\n\n\n\n10:45–11:45 am \n\n\nMPIM \n\n\nPieter Naajkens\, Cardiff \nTitle: Introduction to superselection sector theory: Motivation and introduction of basic setting \nAbstract: (week 1 lectures) In this series of lectures\, I will give an introduction to the operator-algebraic (Doplicher-Haag-Roberts) approach to study the superselection sectors of a (2D) gapped quantum spin system. The sectors have a rich mathematical structure of a braided monoidal category. This category describes all the algebraic properties of the ‘anyons’ or ‘charges’ such quantum spin systems can have. The aim of these lectures is to build up this theory from first principles\, using simple examples of topologically ordered models to illustrate the main ideas. If time permits\, I will elaborate on how this fits into the larger programme of the classification of gapped phases of matter\, and long-range entangled states in particular. No prior knowledge of operator algebras or tensor categories is assumed. \nSLIDES (pdf) \n\n\n\n\n11:45 am –12:00 pm \n\n\n  \n\n\nbreak \n\n\n\n\n12:00–1:00 pm \n\n\nCMSA \n\n\nAlexei Kitaev\, Caltech \nTitle: Local definitions of gapped Hamiltonians and topological and invertible states I \n\n\n\n\nTuesday\, July 1 \n\n\n\n\n8:00–9:00 am \n\n\nMPIM \n\n\nBruno Nachtergaele\, UC Davis \nTitle: Ground states of quantum lattice systems: Quasilocality: almost local observables and interactions\, Lieb-Robinson bounds\, quasi-adiabatic evolution\, stability I \n\n\n\n\n9:00–9:30 am \n\n\n  \n\n\nBreakfast break \n\n\n\n\n9:30–10:30 am \n\n\nCMSA \n\n\nMichael Hopkins\, Harvard \nTitle: Lattice models and topological quantum field theories II \n\n\n\n\n10:30–10:45 am \n\n\n  \n\n\nbreak \n\n\n\n\n10:45–11:45 am \n\n\nMPIM \n\n\nPieter Naajkens\, Cardiff \nTitle: Introduction to superselection sector theory: Building the braided (fusion) category of superselection sectors I \nSLIDES (pdf) \n\n\n\n\n11:45 am –12:00 pm \n\n\n  \n\n\nbreak \n\n\n\n\n12:00–1:00 pm \n\n\nCMSA \n\n\nAlexei Kitaev\, Caltech \nTitle: Local definitions of gapped Hamiltonians and topological and invertible states II \n\n\n\n\nWednesday\, July 2 \n\n\n\n\n8:00–9:00 am \n\n\nMPIM \n\n\nBruno Nachtergaele\, UC Davis \nTitle: Ground states of quantum lattice systems: Quantum Entanglement in many-body systems: short-range entangled states\, topological entanglement\, stability II \n\n\n\n\n9:00–9:30 am \n\n\n  \n\n\nBreakfast break \n\n\n\n\n9:30–10:30 am \n\n\nCMSA \n\n\nMichael Hopkins\, Harvard \nTitle: Lattice models and topological quantum field theories III \n\n\n\n\n10:30–10:45 am \n\n\n  \n\n\nbreak \n\n\n\n\n10:45–11:45 am \n\n\nMPIM \n\n\nPieter Naajkens\, Cardiff \nTitle: Introduction to superselection sector theory: Building the braided (fusion) category of superselection sectors II \nSLIDES (pdf) \n\n\n\n\n11:45 am –12:00 pm \n\n\n  \n\n\nbreak \n\n\n\n\n12:00–1:00 pm \n\n\nCMSA \n\n\nAlexei Kitaev\, Caltech \nTitle: Local definitions of gapped Hamiltonians and topological and invertible states III \n\n\n\n\nThursday\, July 3 \n\n\n\n\n8:00–9:00 am \n\n\nMPIM \n\n\nBruno Nachtergaele\, UC Davis \nTitle: Ground states of quantum lattice systems: Quantum Phase Diagrams: order parameters\, topological invariants\, examples \n\n\n\n\n9:00–9:30 am \n\n\n  \n\n\nBreakfast break \n\n\n\n\n9:30–10:30 am \n\n\nCMSA \n\n\nMichael Hopkins\, Harvard \nTitle: Lattice models and topological quantum field theories IV \n\n\n\n\n10:30–10:45 am \n\n\n  \n\n\nbreak \n\n\n\n\n10:45–11:45 am \n\n\nMPIM \n\n\nPieter Naajkens\, Cardiff \nTitle: Introduction to superselection sector theory: Classification of phases and long-range entanglement \nSLIDES (pdf) \n\n\n\n\n11:45 am –12:00 pm \n\n\n  \n\n\nbreak \n\n\n\n\n12:00–1:00 pm \n\n\nCMSA \n\n\nAlexei Kitaev\, Caltech \nTitle: Local definitions of gapped Hamiltonians and topological and invertible states IV \n\n\n\n\nNo talks Friday July 4  \n\n\n\n\n  \n\n\n\n\nMonday July 7 \n\n\n\n\n8:00–9:00 am \n\n\nMPIM \n\n\nJackson van Dyke\, TU Munich \nTitle: Moduli spaces of projective 3d TQFTs \nAbstract: A gapped quantum system is well-approximated at low energy by a projective topological field theory. Therefore questions concerning the classification\, symmetries\, and anomalies of gapped quantum systems can be reinterpreted via the homotopy theory of the moduli space of such theories. I will describe a moduli space of 3-dimensional TQFTs\, and the sense in which its homotopy theory informs us about the low energy behavior of gapped systems in 2+1 dimensions. This moduli space depends on the fixed target category: Explicitly\, it is built from the classifying spaces of higher groups of automorphisms of ribbon categories. The emphasis will be on target categories which have convenient algebraic features\, yet are analytically robust enough to allow for boundary/relative theories defined in terms of unitary representations on topological vector spaces. \n\n\n\n\n9:00–9:30 am \n\n\n  \n\n\nBreakfast break \n\n\n\n\n9:30–10:30 am \n\n\nCMSA \n\n\nConstantin Teleman\, UC Berkeley \nTitle: Quantizing homotopy types \nAbstract: Kontsevich (90’s) proposed a topological quantization of (sigma-models into) finite homotopy types to top dimensions (d\, d+1). Its enhancement to a `fully extended’ TQFT was described later (Freed\, Hopkins\, Lurie and the speaker) in the target category of iterated algebras. Independently\, Chas and Sullivan constructed a (partially defined) 2-dimensional TQFT (d=1) with target compact oriented manifolds. I will briefly review the features of the finite homotopy theory and its boundary conditions\, with particular interest in Dirichlet conditions; their analogue in Chas-Sullivan theory (older work by Blumberg\, Cohen and the speaker). Finally\, I propose a generalization combining these to a higher-dimensional Chas-Sullivan theory. \nSlides (link) \n\n\n\n\n10:30–10:45 am \n\n\n  \n\n\nbreak \n\n\n\n\n10:45–11:45 am \n\n\nMPIM \n\n\nMatthias Ludewig\, University of Greifswald \nTitle: Generalized Kitaev Pairings and Higher Berry curvature in coarse geometry \nAbstract: In Appendix C of his “Anyons” paper\, Kitaev introduced the notion of a “generalized Chern number” for a 2-dimensional system by diving the system in three ordered parts and measuring a signed rotational flux. This construction has since been used by several authors to measure topological non-triviality of a physical system. In recent work with Guo Chuan Thiang\, we observe that the recipe provided by Kitaev can be interpreted in coarse geometry as the pairing of a K-theory class with a coarse cohomology class. A corresponding index theorem then provides a proof that the set of values of this “Kitaev pairing” is always quantized\, as already argued by Kitaev. In our work\, we generalize Kitaev’s definition and the corresponding quantization result to arbitrary dimensions. By replacing a single Hamiltonian with a whole family of Hamiltonians (parametrized by a space X)\, we recover and extend the construction of “Higher Berry curvatures” by Kapustin and Spodyneiko. Given a coarse cohomology class\, we obtain a characteristic class on the parameter space X\, which is integral whenever integrated against a cycle in X that lies in the image of the homological Chern character (so\, in particular\, spheres in X). \n\n\n\n\n11:45 am –12:00 pm \n\n\n  \n\n\nbreak \n\n\n\n\n12:00–1:00 pm \n\n\nCMSA \n\n\nTheo Johnson-Freyd\, Perimeter Institute \nTitle: Some thoughts about the Kapustin–Kitaev cobordism conjecture \nAbstract: In 2013\, Kitaev explained that\, under some reasonable locality hypotheses\, gapped invertible phases of bosonic lattice models in different dimensions are naturally organized into an \Omega-spectrum. The following year\, Kapustin conjectured that this spectrum is dual to a Thom spectrum\, specifically (smooth) oriented bordism MSO\, and that for fermionic lattice models one sees instead the dual to spin bordism. In 2016\, Freed and Hopkins proved Kapustin’s conjecture for invertible phases of continuous unitary QFTs valued in an at-the-time conjectural universal target category. Freed and Hopkins put bordism categories into the statement of the problem\, by working from the beginning with continuous QFTs. Kapustin’s conjecture for lattice models remains open.David Reutter and I\, in ongoing work in progress\, have investigating Kapustin’s conjecture from the perspective of deeper category theory. We have built the universal target category for phases satisfying a finite semisimplicity hypothesis\, and we are working on relaxing finite semisimplicity. We can show that any spectrum of invertible finite-semisimple phases will indeed be dual to a Thom spectrum for some topological group G acting on the spectrum of spheres. For example\, if one looks just at those bosonic phases which can be topologically condensed from the vacuum\, G is almost the (oriented) piecewise linear group\, whose Thom spectrum is the bordism spectrum MSPL is the (oriented) *piecewise* smooth manifolds; the difference between MSPL and MSO is only visible in dimensions 7 and above. I say almost because in fact our G is what you would get if you tried to build MSPL\, but could only make finitary measurements\, which surely is explained by our restriction to condensable semisimple TQFTs. We conjecture that MSPL\, rather than MSO\, classifies invertible gapped phases of bosonic lattice models.The general relation between MSPL and topological phases is explained by a certain “surgery exact sequence” for topological phases that mirrors the surgery sequence for MSPL. By studying this sequence\, we can also answer the question of which invertible phases admit a gapped boundary condition. In particular that only (the trivial phase and) the Arf–Kervaire invariants admit finite-semisimple gapped boundary conditions. \nSLIDES (pdf) \n\n\n\n\nTuesday\, July 8 \n\n\n\n\n8:00–9:00 am \n\n\nMPIM \n\n\nDavid Reutter\, University of Hamburg \nTitle: On the categorical spectrum of topological quantum field theories \nAbstract: As originally suggested by Kitaev\, invertible topological quantum field theories of varying dimensions should assemble into a spectrum/generalized homology theory. A candidate for such a spectrum of invertible TQFTs was proposed by Freed and Hopkins\, with the defining property that (isomorphism classes of) n-dimensional invertible TQFTs are completely determined by their partition functions on closed n-manifolds. More generally\, not-necessarily-invertible TQFTs should assemble into a ‘categorical spectrum’\, an analogue of a spectrum with non-invertible cells at each level. In this talk\, I will explain that there exists a unique such categorical spectrum satisfying a list of reasonable assumptions on the collection of (compact/very finite & discrete) TQFTs; one of these assumptions being that its invertibles agree with Freed and Hopkins’ suggestion. I will explain these assumptions\, sketch how this categorical spectrum looks like in low-dimensions\, outline its construction\, and how it may be used to learn about gapped boundaries of anomaly theories in high dimensions. This is based on work in progress with Theo Johnson-Freyd. \n\n\n\n\n9:00–9:30 am \n\n\n  \n\n\nBreakfast break \n\n\n\n\n9:30–10:30 am \n\n\nCMSA \n\n\nAgnes Beaudry\, UC Boulder \nTitle: An algebraic theory of planon-only fracton orders \nAbstract: In this talk\, I will describe an algebraic theory for planon-only abelian fracton orders. These are three-dimensional gapped phases with the property that fractional excitations are abelian particles restricted to move in parallel planes. The fusion and statistics data can be identified with a finitely generated module over a Laurent polynomial ring together with a U(1)-valued quadratic form. These systems thus lend themselves to an elegant algebraic theory which we expect will lead to easily computable phase invariants and a classification. As a starting point\, we establish a necessary condition for physical realizability\, the excitation-detector principle\, which I will explain. We conjecture that this criterion is also sufficient for realizability. I will also discuss preliminary classification results.This talk is based on joint with Michael Hermele\, Wilbur Shirley and Evan Wickenden. \n\n\n\n\n10:30–10:45 am \n\n\n  \n\n\nbreak \n\n\n\n\n10:45–11:45 am \n\n\nMPIM \n\n\nJoão Faria Martins\, University of Leeds \nTitle: A categorification of Quinn’s finite total homotopy TQFT with application to TQFTs and once-extended TQFTs derived from discrete higher gauge theory \nAbstract: Quinn’s Finite Total Homotopy TQFT is a topological quantum field theory defined for any dimension n of space\, depending on the choice of a homotopy finite space B. For instance\, B can be the classifying space of a finite group or a finite 2-group.In this talk\, I will report on recent joint work with Tim Porter on once-extended versions of Quinn’s Finite Total Homotopy TQFT\, taking values in the symmetric monoidal bicategory of groupoids\, linear profunctors\, and natural transformations between linear profunctors. The construction works in all dimensions\, yielding (0\,1\,2)-\, (1\,2\,3)-\, and (2\,3\,4)-extended TQFTs\, given a homotopy finite space B. I will  show how to compute these once-extended TQFTs when B is the classifying space of a homotopy 2-type\, represented by a crossed module of groups.Reference: Faria Martins J\, Porter T: “A categorification of Quinn’s finite total homotopy TQFT with application to TQFTs and once-extended TQFTs derived from strict omega-groupoids.” arXiv:2301.02491 [math.CT] \n\n\n\n\n11:45 am –12:00 pm \n\n\n  \n\n\nbreak \n\n\n\n\n12:00–1:00 pm \n\n\nCMSA \n\n\nEmil Prodan\, Yeshiva University \nTitle: Mapping the landscape of frustration-free models \nAbstract: Frustration-free models are of great interest because they are amenable to specialized techniques and their understanding is more complete among the general quantum spin models. In this talk\, I will establish an almost bijective relation between frustration-free families of projections and a subclass of hereditary subalgebras defined by an intrinsic property. This relation sets further synergies between frustration-free models and open projections in double duals\, and subsets of pure states spaces. These connections enable a better understanding of the class of frustration-free models. For example\, the open projections in the double dual derived from frustration-free models is dense in the norm-topology in the space of generic open projections\, thus assuring us that\, for many purposes\, we can choose to work with frustration-free models without losing generality. Furthermore\, the Cuntz semigroup\, originally designed to classify the positive elements of C*-algebra\, has been proven to also classify the open projections. Given the mentioned connections\, we now have a new device to investigate the ground states of quantum spin models. \nSLIDES (pdf) \n\n\n\n\nWednesday\, July 9 \n\n\n\n\n8:00–9:00 am \n\n\nMPIM \n\n\nAlexander Schenkel\, University of Nottingham \nTitle: C*-categorical prefactorization algebras for superselection sectors and topological order \nAbstract: I will present a geometric framework to encode the algebraic structures on the category of superselection sectors of an algebraic quantum field theory on the n-dimensional lattice Z^n. I will show that\, under certain assumptions which are implied by Haag duality\, the monoidal C*-categories of localized superselection sectors carry the structure of a locally constant prefactorization algebra over the category of cone-shaped subsets of Z^n. Employing techniques from higher algebra\, one extracts from this datum an underlying locally constant prefactorization algebra defined on open disks in the cylinder R^1 x S^{n-1}. While the sphere S^{n-1} arises geometrically as the angular coordinates of cones\, the origin of the line R^1 is analytic and rooted in Haag duality. The usual braided (for n=2) or symmetric (for n>2) monoidal C*-categories of superselection sectors are recovered by removing a point of the sphere and using the equivalence between E_n-algebras and locally constant prefactorization algebras defined on open disks in R^n. The non-trivial homotopy groups of spheres induce additional algebraic structures on these E_n-monoidal C*-categories\, which in the simplest case of Z^2 is given by a braided monoidal self-equivalence arising geometrically as a kind of ‘holonomy’ around the circle S^1.This talk is based on joint work with Marco Benini\, Victor Carmona and Pieter Naaijkens. \n\n\n\n\n9:00–9:30 am \n\n\n  \n\n\nBreakfast break \n\n\n\n\n9:30–10:30 am \n\n\nCMSA \n\n\nLukasz Fidkowski\, University of Washington \nTitle: Non-invertible bosonic chiral symmetry on the lattice \nAbstract: We construct a Hamiltonian lattice realization of the non-invertible chiral symmetry that mimics an axial rotation at a rational angle in a U(1) gauge theory with bosonic charged matter.  We provide a heuristic argument that this setup allows a symmetric Hamiltonian which flows\, at low energies\, to a known field theory with this symmetry. \n\n\n\n\n10:30–10:45 am \n\n\n  \n\n\nbreak \n\n\n\n\n10:45–11:45 am \n\n\nMPIM \n\n\nNils Carqueville\, University of Vienna \nTitle: Gauging categorical symmetries \nAbstract: Orbifold data are categorical symmetries that can be gauged in oriented defect topological quantum field theories. We review the general construction and apply it to 2-group symmetries of 3-dimensional TQFTs; upon further specialisation this leads to equivariantisation of G-crossed braided fusion categories. We also describe a proposal\, via higher dagger categories\, to gauging categorical symmetries in the context of other tangential structures. This is based on separate projects with Benjamin Haake and Tim Lüders. \n\n\n\n\n11:45 am –12:00 pm \n\n\n  \n\n\nbreak \n\n\n\n\n12:00–1:00 pm \n\n\nCMSA \n\n\nNikita Sopenko\, IAS \nTitle: Reflection positivity and invertible phases of 2d quantum many-body systems \nAbstract: Reflection positivity is a property that is usually taken as an assumption in the classification of topological phases of matter via continuous quantum field theories. For general quantum many-body systems\, this property does not hold. This raises the question of whether it somehow emerges in the effective theory from the microscopic description\, thereby justifying the field-theoretic approach.In this talk\, I will discuss reflection positivity in the context of invertible phases of two-dimensional lattice systems. I will explain why every such phase admits a reflection-positive representative\, and why inverse phases are represented by complex conjugate states. I will also introduce an index that distinguishes these phases and is conjecturally related to the chiral central charge. \n\n\n\n\nThursday\, July 10 \n\n\n\n\n8:00–9:00 am \n\n\nMPIM \n\n\nIlka Brunner\, Ludwig-Maximilians University of Munich \nTitle: Defects as functors between phases of Abelian gauged linear sigma models \nAbstract: Defects act naturally on boundary conditions\, providing functors between D-brane categories. In the context of gauged linear sigma models\, one can use defects to transport branes from one phase to another. In this talk\, I will show how to construct such defects explicitly. \n\n\n\n\n9:00–9:30 am \n\n\n  \n\n\nBreakfast break \n\n\n\n\n9:30–10:30 am \n\n\nCMSA \n\n\nDavid Penneys\, Ohio State \nTitle: Holography for bulk-boundary local topological order \nAbstract: In previous joint work [arXiv:2307.12552] with C. Jones\, Naaijkins and Wallick\, we introduced local topological order (LTO) axioms for quantum spin systems which allowed us to define a physical boundary manifested by a net of boundary algebras in one dimension lower. This gives a formal setting for topological holography\, where the braided tensor category of DHR bimodules of the physical boundary algebra captures the bulk topological order.In joint work with C. Jones and Naaijkens\, we extend the LTO axioms to quantum spin systems equipped with a topological boundary\, again producing a physical boundary algebra for the bulk-boundary system\, whose category of (topological) boundary DHR bimodules recovers the topological boundary order. We perform this analysis in explicit detail for Levin-Wen and Walker-Wang bulk-boundary systems.Along the way\, we introduce a 2D braided categorical net of algebras built from a unitary braided fusion category (UBFC)\, which arise as boundary algebras of Walker-Wang models. We consider the canonical state on this braided categorical net corresponding to the standard topological boundary for the Walker-Wang model. Interestingly\, in this state\, the cone von Neumann algebras are type I with finite dimensional centers\, in contrast with the type II and III cone von Neumann algebras from the Levin-Wen models studied in [arXiv:2307.12552]. Their superselection sectors recover the underlying unitary category of our UBFC\, and we conjecture the superselection category also captures the fusion and braiding. \n\n\n\n\n10:30–10:45 am \n\n\n  \n\n\nbreak \n\n\n\n\n10:45–11:45 am \n\n\nMPIM \n\n\nChristoph Schweigert\, University of Hamburg \nTitle: Tensor network states: a topological field theory perspective. \nAbstract: Projected entangled pair states (PEPS) and matrix product operators (MPO) are standard tools in quantum information theory and quantum many-body physics. We explain how to understand them in terms of Turaev-Viro models on manifolds with boundary. We then sketch how a recently developed categorical Morita theory for spherical module categories can be used to find generalizations of the standard PEPS tensors. \n\n\n\n\n11:45 am –12:00 pm \n\n\n  \n\n\nbreak \n\n\n\n\n12:00–1:00 pm \n\n\nCMSA \n\n\nGreg Moore\, Rutgers \nTitle: p-form puzzles \nAbstract: It is commonly stated that level k BF theory for a p-form (and a form of complementary dimension) is equivalent to a homotopy sigma model with target space K(A\,p) where A is a cyclic group of order k.  Some aspects of this standard statement are puzzling me. I’ll explain what they are. (Perhaps someone in the audience can resolve my puzzles.) Then I’ll revisit the (again standard) electromagnetic duality of p-form electrodynamics. The conclusion will be that a slightly modified version of Ray-Singer torsion is the partition function of an invertible topological field theory. \n\n\n\n\nFriday\, July 11Note: On Friday\, there will be separate schedules for Bonn and CMSA. \nTo view the Bonn schedule\, please visit the program page at: https://www.mpim-bonn.mpg.de/qft25 \n\n\n\n\n8:00–9:00 am \n\n\nCMSA \n\n\nMarkus Pflaum\, UC Boulder \nTitle: A tour d’horizon through homotopical aspects of C*-algebraic quantum spin systems \nAbstract: In the talk I report on joint work with Beaudry\, Hermele\, Moreno\, Qi and Spiegel\, where a homotopy theoretic framework for studying state spaces of quantum lattice spin systems has been introduced using the language of C*-algebraic quantum mechanics. First some old and new results about the state space of the quasi-local algebra of a quantum lattice spin system when endowed with either the natural metric topology or the weak* topology will be presented. Switching to the algebraic topological side\, the homotopy groups of the unitary group of a UHF algebra will then be determined and it will be indicated that the pure state space of any UHF algebra in the weak* topology is weakly contractible. In addition\, I will show at the example of non-commutative tori that also in the case of a not commutative C*-algebra\, the homotopy type of the state space endowed with the weak* topology can be non-trivial and is neither deformation nor Morita invariant. Finally\, I indicate how such tools together with methods from higher homotopy theory such as E_infinity spaces may lead to a framework for constructing Kitaev’s loop-spectrum of bosonic invertible gapped phases of matter. \n\n\n\n\n9:00–9:30 am \n\n\n  \n\n\nBreakfast break \n\n\n\n\n9:30–11:00 am \n\n\nCMSA \n\n\nSpeed Talks \nBen Gripaios\, University of CambridgeTitle: Locality and smoothness of QFTs \nCarolyn Zhang\, Harvard UniversityTitle: SymTFT approach for (non-)invertible symmetries of mixed states \nRoman Geiko\, UCLATitle: Omega-spectrum of stabilizer invertible phases \n\n\n\n\n11:00–11:15 am \n\n\n  \n\n\nbreak \n\n\n\n\n11:15–12:45 pm \n\n\nCMSA \n\n\nSpeed Talks continued \nEric Roon\, Michigan State UniversityTitle: Finitely Correlated States Driven by Topological Dynamics \nDmitri Pavlov\, Texas Tech UniversityTitle: The classification of two-dimensional extended conformal field theories \nBowen Shi\, University of Illinois Urbana-ChampaignTitle: Mathematical Puzzles from the Entanglement Bootstrap: On Immersions and regular homotopySLIDES (pdf) \n\n\n\n\n  \n 
URL:https://cmsa.fas.harvard.edu/event/mpqft25/
LOCATION:Hybrid
CATEGORIES:Event,Workshop
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250731T110000
DTEND;TZID=America/New_York:20250731T120000
DTSTAMP:20260504T090337
CREATED:20250730T163542Z
LAST-MODIFIED:20250730T182012Z
UID:10003759-1753959600-1753963200@cmsa.fas.harvard.edu
SUMMARY:Joint BHI/CMSA Foundation Seminar: The semiclassical energy outflux emerging from a collapsing shell
DESCRIPTION:Joint BHI/CMSA Foundation Seminar \nLocation: BHI seminar room \nSpeaker: Noa Zilberman (Princeton University) \nTitle: The semiclassical energy outflux emerging from a collapsing shell \nAbstract: When a compact object collapses to form a black hole\, quantum field theory predicts the emission of an energy outflux to future null infinity\, which later relaxes to Hawking radiation. Within the semiclassical framework\, we derive a simple\, closed form\, analytical expression for the energy outflux emitted from a spherical thin null shell collapsing to form a black hole. In particular\, this energy outflux vanishes (quadratically in r-2M) as the shell approaches the horizon. This result refutes claims that the Hawking energy outflux originates from the collapsing body\, showing instead that it develops in a broad strong-field region. Additionally\, this vanishing implies that semiclassical backreaction cannot prevent or significantly affect the classical process of gravitational collapse and horizon formation (as sometimes claimed). \n 
URL:https://cmsa.fas.harvard.edu/event/joint-bhi-cmsa-foundation-seminar-the-semiclassical-energy-outflux-emerging-from-a-collapsing-shell/
LOCATION:Black Hole Initiative\, 20 Garden Street\, Cambridge MA\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Foundation Seminar
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END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250902T161500
DTEND;TZID=America/New_York:20250902T183000
DTSTAMP:20260504T090337
CREATED:20250829T204330Z
LAST-MODIFIED:20250902T170240Z
UID:10003773-1756829700-1756837800@cmsa.fas.harvard.edu
SUMMARY:Fukaya category and gauge theory
DESCRIPTION:Geometry and Quantum Theory Seminar \nSpeaker: Saman Habibi Esfahani\, Harvard CMSA \nTitle: Fukaya category and gauge theory \nAbstract: After setting up some background\, I will discuss the Fukaya $A_\ infty$-category and several instances where it appears in gauge theory\, such as in the study of flat connections on Riemann surfaces\, holomorphic sections of some hyperkähler bundles\, and instantons and holomorphic curves in K3 surfaces. If time permits\, I will also outline potential applications of these ideas to the study of 3-manifolds and manifolds with special holonomy. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/quantumgeo_9225/
LOCATION:Science Center 507\, 1 Oxford Street\, Cambridge\, 02138
CATEGORIES:Geometry and Quantum Theory Seminar
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