Abstract: I will first review the construction of the moduli space of tropical curves (or metric graphs), and its relation to graph complexes. The graph Laplacian may be interpreted as a tropical version of the classical Torelli map and its determinant is the Kirchhoff graph polynomial (also called 1st Symanzik), which is one of the two […]
Abstract: It is by now well-known that mirror symmetry may be expressed as an equivalence between categories associated to dual Kahler manifolds. Following a proposal of Teleman, we inaugurate a program to understand 3d mirror symmetry as an equivalence between 2-categories associated to dual holomorphic symplectic stacks. We consider here the abelian case, where our theorem […]
Abstract: Billiards on an elliptical billiard table are completely integrable: phase space is foliated by invariant submanifolds for the billiard flow. Birkhoff conjectured that ellipses are the only plane domains with integrable billiards. Avila-deSimoi- Kaloshin proved the conjecture for ellipses of sufficiently small eccentricity. Kaloshin-Sorrentino proved local results for all eccentricities. On the quantum level, the analogous […]
Abstract: Some recent work in the quantum gravity literature has considered what happens when the amplitudes of a TQFT are summed over the bordisms between fixed in-going and out-going boundaries. We will comment on these constructions. The total amplitude, that takes into account all in-going and out-going boundaries can be presented in a curious factorized form. […]
https://youtu.be/9Mq9Jvmo3ic Abstract: The Swampland program aims at uncovering the universal implications of quantum gravity at low-energy physics. I will review the basic ideas of the Swampland program, formal and phenomenological implications, and provide a survey of the techniques commonly used in Swampland research including tools from quantum information, holography, supersymmetry, and string theory.
Abstract: Deep neural networks have achieved significant empirical success in many fields, including the fields of computer vision and natural language processing. Along with its empirical success, deep learning has been theoretically shown to be attractive in terms of its expressive power. However, the theory of expressive power does not ensure that we can efficiently find an optimal solution in […]
Member Seminar Speaker: Yingying Wu Title: Moduli Space of Metric SUSY Graphs Abstract: SUSY curves are algebraic curves with additional supersymmetric or supergeometric structures. In this talk, I will present the construction of dual graphs of SUSY curves with Neveu–Schwarz and Ramond punctures. Then, I will introduce the concept of the metrized SUSY graph and […]
Open Mic Discussion Topic: Entropy bounds (species bound, Bekenstein bound, CKN bound, and the like)
Abstract: The AdS/CFT conjecture in physics posits the existence of a correspondence between gravitational theories in asymptotically Anti-de Sitter (aAdS) spacetimes and field theories on their conformal boundary. In this presentation, we prove rigorous mathematical statements toward this conjecture. In particular, we show there is a one-to-one correspondence between aAdS solutions of the Einstein-vacuum equations and a suitable space of data on […]
Abstract: We introduce a class of random graph processes, which we call \emph{flip processes}. Each such process is given by a \emph{rule} which is just a function $\mathcal{R}:\mathcal{H}_k\rightarrow \mathcal{H}_k$ from all labelled $k$-vertex graphs into itself ($k$ is fixed). The process starts with a given $n$-vertex graph $G_0$. In each step, the graph $G_i$ is obtained […]
Speaker: Joel E. Cohen (Rockefeller University and Columbia University) Title: Fluctuation scaling or Taylor’s law of heavy-tailed data, illustrated by U.S. COVID-19 cases and deaths Abstract: Over the last century, ecologists, statisticians, physicists, financial quants, and other scientists discovered that, in many examples, the sample variance approximates a power of the sample mean of each of a set […]
Youtube Video Abstract: I will show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum, i.e. if it is an eigenstate of the translation symmetry with eigenvalue not equal to 1. Equivalently, any state that can be connected with a non-zero momentum state through […]