Colloquium Speaker: Wenbin Yan (Tsinghua University) Title: Tetrahedron instantons and M-theory indices Abstract: We introduce and study tetrahedron instantons. Physically they capture instantons on $\mathbb{C}^{3}$ in the presence of the most general intersecting codimension-two supersymmetric defects. In this talk, we will review instanton moduli spaces, explain the construction, moduli space and partition functions of tetrahedron instantons. We […]
https://youtu.be/MSw8HV0eHo8 Speaker: Ben Edelman, Harvard Computer Science Title: Toward Demystifying Transformers and Attention Abstract: Over the past several years, attention mechanisms (primarily in the form of the Transformer architecture) have revolutionized deep learning, leading to advances in natural language processing, computer vision, code synthesis, protein structure prediction, and beyond. Attention has a remarkable ability to enable the […]
Member Seminar Speaker: Matteo Parisi Title: Amplituhedra, Scattering Amplitudes and Triangulations Abstract: In this talk I will discuss about Amplituhedra – generalizations of polytopes inside the Grassmannian – recently introduced by physicists as new geometric constructions encoding interactions of elementary particles in certain Quantum Field Theories. In particular, I will explain how the problem of finding […]
Speaker: Takuro Mochizuki (Kyoto University) Title: Kobayashi-Hitchin correspondences for harmonic bundles and monopoles Abstract: In 1960's, Narasimhan and Seshadri discovered the equivalence between irreducible unitary flat bundles and stable bundles of degree $0$ on compact Riemann surfaces. In 1980's, Donaldson, Uhlenbeck and Yau generalized it to the equivalence between irreducible Hermitian-Einstein bundles and stable bundles on smooth […]
https://youtu.be/updzX0XPYU4 Speaker: James Bonifacio, Cambridge DAMTP Title: Bootstrapping hyperbolic manifolds Abstract: Hyperbolic manifolds are a class of Riemannian manifolds that are important in mathematics and physics, playing a prominent role in topology, number theory, and string theory. Associated with a given hyperbolic metric is a sequence of numbers corresponding to the discrete eigenvalues of the […]
Member Seminar Speaker:An Huang Title: Quadratic reciprocity from a family of adelic conformal field theories Abstract: This talk aims to provide a physics framework to understand quadratic reciprocity. Specifically, we consider a deformation of the two-dimensional free scalar field theory by raising the Laplacian to a positive real power. It turns out that the resulting non-local […]
Speaker: Bartek Czech, Tsinghua University Title: Holographic Cone of Average Entropies and Universality of Black Holes Abstract: In the AdS/CFT correspondence, the holographic entropy cone, which identifies von Neumann entropies of CFT regions that are consistent with a semiclassical bulk dual, is currently known only up to n=5 regions. I explain that average entropies of p-partite subsystems can […]
Speaker: Richard Kenyon (Yale) Title: Dimers and webs Abstract: We consider SL_n-local systems on graphs on surfaces and show how the associated Kasteleyn matrix can be used to compute probabilities of various topological events involving the overlay of n independent dimer covers (or “n-webs”). This is joint work with Dan Douglas and Haolin Shi.
https://youtu.be/Suhp3OLASSo Speaker: Jared Kaplan, Johns Hopkins Dept. of Physics & Astronomy Title: Scaling Laws and Their Implications for Coding AI Abstract: Scaling laws and associated downstream trends can be used as an organizing principle when thinking about current and future ML progress. I will briefly review scaling laws for generative models in a number of […]
Member Seminar Speaker: Martin Lesourd Title: Positive Mass, Density, and Scalar Curvature on Noncompact Manifolds Abstract: I’ll describe some recent work spanning a couple of different papers on the topics mentioned in the title: Positive Mass, Density, and Scalar Curvature on Noncompact Manifolds. Two of these are with R. Unger, Prof. S-T. Yau, and two others are with R. Unger, […]
Abstract: The low dimensional manifold hypothesis posits that the data found in many applications, such as those involving natural images, lie (approximately) on low dimensional manifolds embedded in a high dimensional Euclidean space. In this setting, a typical neural network defines a function that takes a finite number of vectors in the embedding space as input. However, one often […]
https://youtu.be/QaOZCa8SFvA Speaker: Iddo Drori, MIT EE&CS and Columbia School of Engineering Title: Machine Learning 30 STEM Courses in 12 Departments Abstract: We automatically solve, explain, and generate university-level course problems from thirty STEM courses (at MIT, Harvard, and Columbia) for the first time. We curate a new dataset of course questions and answers across a dozen […]