Abstract: The Prague dimension of graphs was introduced by Nesetril, Pultr and Rodl in the 1970s: as a combinatorial measure of complexity, it is closely related to clique edges coverings and partitions. Proving a conjecture of Furedi and Kantor, we show that the Prague dimension of the binomial random graph is typically of order n/(log […]
Speaker: Shinsei Ryu (Princeton University) Title: Multipartitioning topological phases and quantum entanglement Abstract: We discuss multipartitions of the gapped ground states of (2+1)-dimensional topological liquids into three (or more) spatial regions that are adjacent to each other and meet at points. By considering the reduced density matrix obtained by tracing over a subset of the regions, we […]
Abstract: Let X be a compact symplectic manifold, and D a normal crossings symplectic divisor in X. We give a criterion under which the quantum cohomology of X is the cohomology of a natural deformation of the symplectic cochain complex of X \ D. The criterion can be thought of in terms of the Kodaira dimension of X […]
Abstract: In this talk I will review massive type IIA flux compactifications that seem to give rise to infinite families of supersymmetric 4d AdS vacua. These vacua provide an interesting testing ground for the swampland program. After reviewing potential shortcomings of this setup, I will discuss recent progress on overcoming them and getting a better understanding of these […]
Abstract: The last few decades have seen a surge of interest in building towards a theory of discrete curvature that attempts to translate the key properties of curvature in differential geometry to the setting of discrete objects and spaces. In the case of graphs there have been several successful proposals, for instance by Lin-Lu-Yau, Forman […]
Speaker: Richard Wentworth, University of Maryland Title: The Hitchin connection for parabolic G-bundles Abstract: For a simple and simply connected complex group G, I will discuss some elements of the proof of the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli space of semistable parabolic G-bundles over families of […]
https://youtu.be/wXZKoHEzASg Speaker: Dan Roberts, MIT & Salesforce Title: The Principles of Deep Learning Theory Abstract: Deep learning is an exciting approach to modern artificial intelligence based on artificial neural networks. The goal of this talk is to provide a blueprint — using tools from physics — for theoretically analyzing deep neural networks of practical relevance. This […]
Abstract: The talk concerns recent work with Tamas Hausel in asking how SYZ mirror symmetry works for the moduli space of Higgs bundles. Focusing on C^*-invariant Lagrangian submanifolds, we use the notion of virtual multiplicity as a tool firstly to examine if the Lagrangian is closed, but also to open up new features involving finite-dimensional algebras […]