Title: Cornering the universal shape of fluctuations and entanglement Abstract: Understanding the fluctuations of observables is one of the main goals in physics. We investigate such fluctuations when a subregion of the full system can be observed, focusing on geometries with corners. We report that the dependence on the opening angle is super-universal: up to […]
https://youtu.be/leONsS4LiV4 Speaker: JM Landsberg, Texas A&M Title: The complexity of matrix multiplication approached via algebraic geometry and representation theory Abstract: In 1968 V. Strassen discovered the way we usually multiply matrices is not the most efficient possible, and after considerable work by many authors, it is generally conjectured by computer scientists that as the size […]
Title: Quantum gravity from quantum matter Abstract: We present a model of quantum gravity in which dimension, topology and geometry of spacetime are collective dynamical variables that describe the pattern of entanglement of underlying quantum matter. As spacetimes with arbitrary dimensions can emerge, the gauge symmetry is generalized to a group that includes diffeomorphisms in […]
Title: Asymptotic localization, massive fields, and gravitational singularities Abstract: I will review three recent developments on Einstein’s field equations under low decay or low regularity conditions. First, the Seed-to-Solution Method for Einstein’s constraint equations, introduced in collaboration with T.-C. Nguyen generates asymptotically Euclidean manifolds with the weakest or strongest possible decay (infinite ADM mass, Schwarzschild […]
Member Seminar Speaker: Michael Simkin Title: Threshold phenomena in random graphs and hypergraphs Abstract: In 1959 Paul Erdos and Alfred Renyi introduced a model of random graphs that is the cornerstone of modern probabilistic combinatorics. Now known as the “Erdos-Renyi” model of random graphs it has far-reaching applications in combinatorics, computer science, and other fields. The […]
Title: More Exact Results in Gauge Theories: Confinement and Chiral Symmetry Breaking Abstract: In this follow-up to Hitoshi Murayama’s talk “Some Exact Results in QCD-like and Chiral Gauge Theories”, I present a detailed analysis of the phases of $SO(N_c)$ gauge theory. Starting with supersymmetric $SO(N_c)$ with $N_F$ flavors, we extrapolate to the non-supersymmetric limit using […]
Abstract: One can view a partial flag variety in C^n as an adjoint orbit inside the Lie algebra of n x n skew-Hermitian matrices. We use the orbit context to study the totally nonnegative part of a partial flag variety from an algebraic, geometric, and dynamical perspective. We classify gradient flows on adjoint orbits in […]
Speaker: John Stout, Harvard University Title: Decoding Divergent Distances Abstract: Motivated by a relationship between the Zamolodchikov and NLSM metrics to the so-called quantum information metric, I will discuss recent work (2106.11313) on understanding infinite distance limits within the context of information theory. I will describe how infinite distance points represent theories that are hyper-distinguishable, in […]
Abstract: Calabi–Yau manifolds of a given dimension are connected by an intricate web of birational maps. This web has deep consequences for the derived categories of coherent sheaves on such manifolds, and for the associated string theories. In particular, for 4-folds and beyond, I will highlight certain simplices appearing in the web, and identify corresponding derived […]
Speaker: Tian Yang (Texas A&M University) Title: Hyperbolic Geometry and Quantum Invariants Abstract: There are two very different approaches to 3-dimensional topology, the hyperbolic geometry following the work of Thurston and the quantum invariants following the work of Jones and Witten. These two approaches are related by a sequence of problems called the Volume Conjectures. In this talk, I […]
https://youtu.be/3Nxe7J07TQY Speaker: Francois Chollet, Google Title: Why abstraction is the key to intelligence, and what we’re still missing Abstract: This talk provides a personal perspective on the way forward towards more human-like and more intelligent artificial systems. Traditionally, symbolic and probabilistic methods have dominated the domains of concept formation, abstraction, and automated reasoning. More recently, deep […]
Title: Three-particle mechanism for pairing and superconductivity Abstract: I will present a new mechanism and an exact theory of electron pairing due to repulsive interaction in doped insulators. When the kinetic energy is small, the dynamics of adjacent electrons on the lattice is strongly correlated. By developing a controlled kinetic energy expansion, I will show […]