Member Seminar Speaker: Bowen Yang Title: Classification of 2D Stabilizer States Abstract: I will explain how translation-invariant two-dimensional stabilizer states are completely classified by finite abelian groups with nondegenerate quadratic forms—that is, by abelian anyon theories. The proof uses the algebraic structure of stabilizer codes as modules over Laurent polynomial rings, revealing how their physical […]
Member Seminar Speaker: Francesco Mori, CMSA Title: Optimal learning protocols via statistical physics and control theory Abstract: Behind the impressive performance of modern machine learning lies a toolkit of training tricks, from tuning learning rates to curating training data. These heuristics are powerful but hard to interpret and possibly suboptimal, leaving open the challenge of finding general […]
Member Seminar Speaker: Houcine Ben Dali, Harvard CMSA Title: A combinatorial formula for interpolation Macdonald polynomials Abstract: In 1996, Knop and Sahi introduced a remarkable family of inhomogeneous symmetric polynomials, defined via vanishing conditions, whose top homogeneous parts are exactly the Macdonald polynomials. Like the Macdonald polynomials, these interpolation Macdonald polynomials are closely connected to […]
Member Seminar Speaker: Stephen Landsittel Title: Some results about saturation Abstract: Given a local ring R we can ask when saturation of ideals in R commutes with other operations on ideals (such as extension to a ring containing R). We show that the condition that extension of ideals along a ring map R \to S […]
Member Seminar Speaker: Ahsan Khan, Harvard CMSA Title: Lie algebra cohomology and Seiberg-Witten theory Abstract: I will discuss how a certain (relative) Lie algebra cochain complex categorifies the Schur index of N=2 supersymmetric gauge theory. For the special case of Seiberg-Witten theory I will provide a conjectured description of this cohomology.
Member Seminar Speaker: Lorenzo Riva, Harvard CMSA Title: A leisurely stroll through the theory of adjunctions Abstract: Adjoint functors (and, more generally, adjunctions in a 2-category) are ubiquitous in algebra and topology. In this talk I will give an overview of the basics of adjunctions, with the ultimate goal being understanding the statement of the […]
Member Seminar Speaker: Blake Bordelon, CMSA Title: Theory of Task-Adapted Dynamics in Large Recurrent Neural Networks Abstract: Recurrent neural networks (RNNs) encode expressive and flexible dynamical systems which can adapt to perform tasks by modifying the internal connections between neurons. In this work we analyze the structure of the dynamical systems encoded in RNNs after […]
Member Seminar Speaker: Saman Habibi Esfahani, CMSA Title: Gauge theory, from low dimensions to higher dimensions and back Abstract: Almost thirty years ago, Donaldson and Thomas proposed extending powerful ideas from gauge theory, which had transformed the study of three- and four-dimensional manifolds, to higher dimensions, with the goal of defining new invariants of special […]
Member Seminar Speaker: Elliott Gesteau, CMSA Title: Failures of Holographic Emergence Abstract: Recent developments have taught us that some semiclassical spacetimes, in particular those containing closed universe components, cannot emerge from a holographic correspondence. In this talk, I will explain how one can get to this conclusion by using either quantum information theory or properties of the large N limit of […]
Member Seminar Speaker: Sunghyuk Park, CMSA Title: Quantum topology from dynamics Abstract: Dynamics studies the long-term behavior of systems that evolve over time, such as the famous Lorenz system. Quantum topology, by contrast, studies knots and low-dimensional manifolds through invariants that are usually constructed using representation-theoretic tools. In this talk, I will explain how quantum invariants of […]
Member Seminar Speaker: Vasily Krylov Title: Higgs and Coulomb branches: Geometry and Representation Theory Abstract: Higgs and Coulomb branches of quiver gauge theories form two important families of Poisson varieties that are expected to be exchanged under so-called 3D mirror symmetry. Quantized Coulomb branches are associative algebras deforming the algebras of functions on Coulomb branches. They are […]
Member Seminar Speaker: Daniel Spiegel Title: The Intermingling of Symmetry and Parametrization in Matrix Product States Abstract: In the study of quantum spin systems, it is by now well-known that interesting phases of quantum matter can arise from gapped ground states when the system is invariant under a symmetry group G or when the system varies continuously […]