Abstract: There is a close connection between the scattering amplitudes in planar N=4 SYM theory and the cells in the positive Grassmannian. In the context of BCFW recursion relations the tree-level S-matrix is represented as a sum of planar on-shell diagrams (aka plabic graphs) and associated with logarithmic forms on the Grassmannian cells of certain dimensionality. […]
Abstract: In this talk I will explain the construction of a determinant map for Tate objects and two applications: (i) to construct central extensions of iterated loop groups and (ii) to produce a determinant theory on certain ind-schemes. For that I will introduce some aspects of the theory of Tate objects in a couple of contexts.
Abstract: The standard definition of symmetries of a structure given on a set S (in the sense of Bourbaki) is the group of bijective maps S to S, compatible with this structure. But in fact, symmetries of various structures related to storing and transmitting information (such as information spaces) are naturally embodied in various classes of loops […]
Youtube Video Abstract: It has been known that the four-dimensional abelian chiral gauge theories of an anomaly-free set of Wely fermions can be formulated on the lattice preserving the exact gauge invariance and the required locality property in the framework of the Ginsparg- Wilson relation. This holds true in two dimensions. However, in the related formulation […]
Abstract: A main challenge in analyzing single-cell RNA sequencing (scRNA-seq) data is to reduce technical variations yet retain cell heterogeneity. Due to low mRNAs content per cell and molecule losses during the experiment (called ‘dropout’), the gene expression matrix has a substantial amount of zero read counts. Existing imputation methods treat either each cell or each […]
Abstract: In this talk, we briefly introduce our recent work on establishing the global existence and stability to the future of non-linear perturbation of de Sitter-like solutions to the Einstein-Yang-Mills system in n≥4 spacetime dimension. This generalizes Friedrich’s (1991) Einstein-Yang-Mills stability results in dimension n=4 to all higher dimensions. This is a joint work with […]
Youtube video Abstract: I will explain a mechanism to cancel the vacuum energy and both terms in the Weyl anomaly in the standard model of particle physics, using conformally-coupled dimension-zero scalar fields. Remarkably, given the standard model gauge group SU(3)xSU(2)xU(1), the cancellation requires precisely 48 Weyl spinors — i.e. three generations of standard model fermions, […]
On April 15, 2022, the CMSA will hold a one-day workshop, Machine Learning and Mathematical Conjecture, related to the New Technologies in Mathematics Seminar Series. Location: Room G10, 20 Garden Street, Cambridge, MA 02138. Organizers: Michael R. Douglas (CMSA/Stony Brook/IAIFI) and Peter Chin (CMSA/BU). Machine learning has driven many exciting recent scientific advances. It has enabled […]
Eric Maskin (Harvard University) Three Introductory Lectures on Game Theory for Mathematicians April 18, 2022 | 9:30 – 11:00 am ET Title: Game Theory Basics and Classical Existence Theorems Abstract: Games in extensive and normal form. Equilibrium existence theorems by Nash, von Neumann, and Zermelo Talk chairs: Scott Kominers, Sergiy Verstyuk SLIDES | VIDEO
Open mic Swampland Discussion Topic: Cobordism
Abstract: In studying complex Chern-Simons theory on a Seifert manifold, Gukov-Pei proposed an equivariant Verlinde formula, a one-parameter deformation of the celebrated Verlinde formula. It computes, among many things, the graded dimension of the space of holomorphic sections of (powers of) a natural determinant line bundle over the Hitchin moduli space. Gukov-Pei conjectured that the equivariant Verlinde numbers are equal to the equivariant quantum K-invariants […]
Abstract: Wilson loop diagrams can be used to study amplitudes in N=4 SYM. I will set them up and talk about some of their combinatorial aspects, such as how many Wilson loop diagrams give the same positroid and how to combinatorially read off the dimension and the denominators for the integrands. **This talk will be […]