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Speaker: Manuel Cortés-Izurdiaga (University of Malaga) Title:  Homotopy categories of rings: some properties and consequences in module categories Abstract: Given a non-necessarily commutative ring with unit and an additive subcategory of the category of right modules, one can consider complexes of modules in the subcategory and the corresponding homotopy category. Sometimes, these homotopy categories are the […] |
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https://youtu.be/NFHUt0lnaUA Topological Quantum Matter Seminar Speaker: Shenghan Jiang, Kavli Institute for Theoretical Sciences UCAS Title: Unveiling Correlated Topological Insulators through Fermionic Tensor Network States Abstract: The study of topological band insulators has revealed fascinating phases characterized by band topology indices, harboring extraordinary boundary modes protected by anomalous symmetry actions. In strongly correlated systems, it has […]
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Probability Seminar Speaker: Youngtak Sohn (MIT) Title: Universality of max-margin classifiers Abstract: Many modern learning methods, such as deep neural networks, are so complex that they perfectly fit the training data. Despite this, they generalize well to the unseen data. Motivated by this phenomenon, we consider high-dimensional binary classification with linearly separable data. First, we […] |
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Probability Seminar Speaker: Nicola Kistler (Johann Wolfgang Goethe-Universität Frankfurt am Main) Title: Solving spin systems, the Babylonian way Abstract: The replica method, together with Parisi’s symmetry breaking mechanism, is an extremely powerful tool to compute the limiting free energy of virtually any mean field disordered system. Unfortunately, the tool is dramatically flawed from a mathematical point […]
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Joint Quantum Matter in Mathematics and Physics and Topological Quantum Matter Seminar Speaker: Liujun Zou (Perimeter Institute) Title:Â Landscape of quantum phases in quantum materials Abstract: A central goal of condensed matter physics is to understand which quantum phases of matter can emerge in a quantum material. For this purpose, one should be able to not […] |
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Member Seminar Speaker: Zi Yang Kang Title:Â Deformations of Landau-Ginzburg models and their fibers Abstract: In mirror symmetry, the dual object to a Fano variety is a Landau-Ginzburg model. Broadly, a Landau-Ginzburg model is quasi-projective variety Y with a superpotential function w, but not all such pairs correspond to Fano varieties under mirror symmetry, so a […] |
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Algebraic Geometry in String Theory Seminar Speaker: Andrew Harder, Lehigh University Title:Â Deformations of Landau-Ginzburg models and their fibers Abstract: In mirror symmetry, the dual object to a Fano variety is a Landau-Ginzburg model. Broadly, a Landau-Ginzburg model is quasi-projective variety Y with a superpotential function w, but not all such pairs correspond to Fano varieties […]
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Speaker: Matthew Foreman (UC Irvine) Title: Impossibility results in classical dynamical systems Abstract: In 1932, motivated by questions in statistical and celestial mechanics, von Neumann proposed classifying the statistical behavior of dynamical systems. In the 1960's, motivated by work of Poincaré, Smale proposed classifying the qualitative behavior of dynamical systems. These questions laid the groundwork for enormous amounts of work, but […] |
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https://youtu.be/SCIi6R_uTZM General Relativity Seminar Speaker: David Fajman (Vienna) Title: Fluid stabilization in slowly expanding cosmological spacetime Abstract: Relativistic fluids are known to form shocks during their evolution from near-homogeneous initial data. In expanding spacetimes, shock formation is suppressed, if the expansion is sufficiently strong. We refer to this effect as fluid stabilization. The occurrence of this phenomenon depends […]
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CMSA Q and A Seminar Speakers: Michael Hopkins (Harvard Math) and Minhea Popa (Harvard Math) Topics: Mike Hopkins: What are topological modular forms? Mihnea Popa: What is the abundance conjecture and why should it to be true?
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Quantum Matter Seminar Speaker: Cameron Krulewski (MIT) and Leon Liu (Harvard) Title: A Long Exact Sequence in Symmetry Breaking Abstract: We study defects in symmetry breaking phases, such as domain walls, vortices, and hedgehogs. In particular, we focus on the localized gapless excitations that sometimes occur at the cores of these objects. These are topologically protected by an ’t […] |
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https://youtu.be/a2S_-pl6onM New Technologies in Mathematics Seminar Speaker: Gabriel Poesia, Dept. of Computer Science, Stanford University Title: Peano: Learning Formal Mathematical Reasoning Without Human Data Abstract: Peano is a theorem proving environment in which a computational agent can start tabula rasa in a new domain, learn to solve problems through curiosity-driven exploration, and create its own higher level […]
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Probability Seminar Speaker: Antoine Maillard (ETH Zürich) Title: Fitting ellipsoids to random points Abstract: We consider the problem of exactly fitting an ellipsoid (centered at 0) to n standard Gaussian random vectors in dimension d, for very large n and d. This problem has connections to questions in statistical learning and theoretical computer science, and is […] |
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Active Matter Seminar Speaker: Alexander Grosberg (NYU) Title: Nuclear chromodynamics: non-equilibrium phase transition in the nucleus of a living cell Abstract: Nucleus of a living cell houses a cell genome - a polymer called chromatin, which is a functional form of DNA. It is very long, e.g., 2 meters long for every human cell. Nucleus is […]
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https://youtu.be/Jf8ONC2tUfc Topological Quantum Matter Seminar Speaker: Bruno Mera, Instituto Superior Tecnico Title: Uniqueness of Landau levels and their analogs with higher Chern numbers Abstract: Lowest Landau level wavefunctions are eigenstates of the Hamiltonian of a charged par- ticle in two dimensions under a uniform magnetic field. They are known to be holomorphic both in real and momentum spaces, […] |
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Algebraic Geometry in String Theory Seminar Speaker: Sheldon Katz, UIUC Title: Stacky small resolutions of determinantal octic double solids and noncommutative Gopakumar-Vafa invariants Abstract: A determinantal octic double solid is the double cover X of P^3 branched along the degree 8 determinant of a symmetric matrix of homogeneous forms on P^3. These X are nodal […]
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Speaker: Brian Williams (Boston University) Title: Koszul duality in QFT Abstract: We will describe appearances of the algebraic phenomena of Koszul duality in the context of boundary conditions and defects in quantum field theory. Primarily motivated by topological string theory, this point of view was pioneered by Costello and Li in their proposal for a […] |
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https://youtu.be/cboxkchYFUk General Relativity Seminar Speaker: Daniel Kolb (Max Planck Institute) Title: Quasi-Local Mass in a Binary Black Hole Merger Abstract: One of the major open problems in classical general relativity is how one should define the mass of a finite region of space. In this talk, we will investigate a promising definition proposed by Wang and […] |
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https://youtu.be/QGVYBN7vBT8 Topological Quantum Matter Seminar Speaker: Amanda Young, UIUC Title: A bulk gap in the presence of edge states for a truncated Haldane pseudopotential Abstract: Haldane pseudopotentials were first introduced as Hamiltonian models for the fractional quantum Hall effect, and it has been long expected that they should exhibit the characteristic properties of this exotic […]
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https://youtu.be/JYt-ldZ3DqM New Technologies in Mathematics Seminar Speaker: Abhishek Panigrahi, Dept. of Computer Science, Princeton University Title: On the Power of Forward pass through Transformer Architectures Abstract: Highly trained transformers are capable of interesting computations as they infer for an input. The exact mechanism that these models use during forward passes is an interesting area of […]
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Probability Seminar Speaker: Jinyoung Park (NYU) Title: Thresholds Abstract: For a finite set X, a family F of subsets of X is said to be increasing if any set A that contains B in F is also in F. The p-biased product measure of F increases as p increases from 0 to 1, and often […] |
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Member Seminar Speaker: Aghil Alaee Title:Â A quasi-local mass in general relativity Abstract:Â One of the fundamental open problems in geometric analysis and mathematical relativity is constructing a (universal) energy/mass quantity to compute the energy/mass of a finite region of spacetime, which can include a star, black hole, or galaxy. We define a new gauge-independent quasi-local mass […] |
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https://youtu.be/y6Gc0G_2Mf0 CMSA/Tsinghua Math-Science Literature Lecture Prof. Scott Kominers will present a lecture in the CMSA/Tsinghua Math-Science Literature Lecture Series. Date: Monday, November 20, 2023 Time: 9:00 - 10:30 am ET Location: Via Zoom Webinar Title: 60 Years of Matching: From Gale and Shapley to Trading Networks Abstract: Gale and Shapley's 1962 American Mathematical Monthly paper, "College Admissions and the […]
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https://youtu.be/3i_DtaeQ0nE Topological Quantum Matter Seminar Speaker: Prashant Kumar, University of Chicago Title:Â Emergent composite-fermion Luttinger liquid at the half-filled Landau level Abstract:Â The half-filled Landau level is a fascinating point in the phase diagram of quantum Hall effect that has been hypothesized to be a non-Fermi liquid where composite-fermions (CFs) emerge at low energies. In this talk, […]
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Speaker: Jeff W. Lichtman (Harvard University) Title:Â The analytical challenges of connectomics Abstract:Â Recent progress in generating synapse-level maps of brains, a field known as connectomics, brings both opportunities and challenges. The upside is that the biophysical instantiation of memories, behaviors, and knowledge will soon be before us. The downside is that no one knows exactly how […] |
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Quantum Matter Seminar Speaker: Guilherme Delfino Silva (Boston University) Title: Modulated Gauge Theories and Fracton Behavior in 2D Abstract: In this talk we investigate deconfined phases of two-dimensional ZN lattice gauge theories associated to spatially modulated symmetries. In order to study the low-energy physics of such modulated gauge theories we propose and explore exactly solvable […] |
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Algebraic Geometry in String Theory Seminar Speaker: An Huang (Brandeis) Pre-talk Speaker: TBA: 10:00-10:30 am Title: A p-adic Laplacian on the Tate curve Abstract: We shall first explain the relation between a family of deformations of genus zero p-adic string worldsheet action and Tate's thesis. We then propose a genus one p-adic string worldsheet action. […]
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Speaker: Dana Bartosova (University of Florida) Title:Â What do topological dynamics, combinatorics, and model theory have in common? Abstract:Â A striking correspondence between dynamics of automorphism groups of countable first order structures and Ramsey theory of finitary approximation of the structures was established in 2005 by Kechris, Pestov, and Todocevic. Since then, their work has been generalized […] |
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https://youtu.be/cSgyLwg0v00 General Relativity Seminar Speaker: David Kubiznak (Charles University) Title: Remarkable symmetries of rotating black holes Abstract: It is well known that the Kerr geometry admits a non-trivial Killing tensor and its 'square root' known as the Killing-Yano tensor. These two objects stand behind Carter's constant of geodesic motion as well as allow for separability of test […]
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Probability Seminar Speaker: Jun Yin (UCLA) Title: A random matrix model towards the quantum chaos transition conjecture Abstract: The Quantum Chaos Conjecture has long fascinated researchers, postulating a critical spectrum phase transition that separates integrable systems from chaotic systems in quantum mechanics. In the realm of integrable systems, eigenvectors remain localized, and local eigenvalue statistics […] |
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https://youtu.be/fB9xJyJj8zU Topological Quantum Matter Seminar Speaker: Valentin Crepel, Flatiron Institute Title: Anomalous Landau level analog in solids: search and implications for 2d heterostructures Abstract: The recent experimental observation of fractional Chen insulators — the analog of fractional quantum Hall states realized in absence of any applied magnetic field — calls for more detailed theoretical investigations […] |
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Probability Seminar Speaker: Wei-Kuo Chen (University of Minnesota) Title: A Gaussian convexity for logarithmic moment generating function Abstract: Convex functions of Gaussian vectors are prominent objectives in many fields of mathematical studies. In this talk, I will establish a new convexity for the logarithmic moment generating function for this object and draw two consequences. The first leads to […] |
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Member Seminar Speaker: Samy Jelassi Title: An introduction to mixture of experts in deep learning Abstract: Scale has opened new frontiers in natural language processing – but at a high cost. Mixture-of-Experts (MoE) have been proposed as a path to even larger and more capable language models. They select different parameters for each incoming example. By […]
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Quantum Matter Seminar Speaker: Abijith Krishnan (MIT) Title: A Plane Defect in the 3d O(N) Model Abstract:Â It was recently found that the classical 3d O(N) model in the semi-infinite geometry can exhibit an "extraordinary-log" boundary universality class, where the spin-spin correlation function on the boundary falls off as (log x)^(-q). This universality class exists for […]
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Topological Quantum Matter Seminar Speaker: Kaifeng Bu (Harvard University) Title:Â Quantum information: the interplay of mathematics and physics Abstract:Â I will provide an introduction to quantum information, which points to a new connection with experiment on the one hand, and a potential new area of mathematical analysis on the other. I will introduce two recent results about […] |
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