Abstracts
Week of September 26, 2021
Group Actions and Dynamics  Distribution of orbits of geometrically finite groups 
4:00pm 
Zoom

We often seek to understand a group through the distribution of its orbits on a given space. In particular, the distribution of lattice orbits has been studied intensively in a variety of groups. In this talk we will discuss the distribution of orbits of geometrically finite groups acting on the light cone. We will see what can be said about the distribution, and how it relates to the distribution of the horospherical orbits in the frame bundle of certain infinite volume hyperbolic manifolds. This is a joint work with Jacqueline Warren. 
Geometry, Symmetry and Physics  Exceptional Lie algebras from twisted supergravity 
4:30pm 
Zoom

Abstract: Nontopological twists of supersymmetric gauge theories have played an increasingly important role in mathematics in part due to relationships to vertex algebras and quantum groups. On the other hand, motivated by the higher genus Bmodel, twists of 10dimensional theories of supergravity have also been introduced. In this talk, we give a complete description of the maximally nontopological twist of 11dimensional supergravity, the low energy limit of Mtheory. I will explain the unexpected result that the global symmetry algebra of the model is equivalent to an infinitedimensional exceptional super Lie algebra known as E(5,10). I will also explain the relationship between other exceptional algebras and extended objects such as M2 and M5 branes in the twisted setting. Zoom link: https://yale.zoom.us/j/99305994163, contact the organizers (Gurbir Dhillon and Junliang Shen) for the passcode. 
Algebra and Number Theory Seminar  padic unlikely intersection results and consequences 
10:30am 
Zoom

The MordellLang conjecture (a theorem) is an "unlikely intersection" result stating that an irred. subvariety of a semiabelian variety G that has dense intersection with the divisible hull of a finitely generated subgroup of G must in fact be the translate of a subgroup variety of G. We present certain padic incarnations of this result, chiefly in the context of formal groups Gˆ. Moreover, we outline some consequences to density questions arising via padic variational techniques within the Langlands programme. 
Geometry & Topology  Closed hypersurfaces of low entropy are isotopically trivial 
4:15pm 
LOM 214

We show that any closed connected hypersurface in 4dimensional Euclidean space with entropy less than or equal to that of the round cylinder is smoothly isotopic to the standard threesphere. This is joint work with Jacob Bernstein. 
Undergraduate Seminar  Putnam Seminar 
4:00pm 
LOM 214
LOM 214
LOM 214
LOM 214
LOM 214
LOM 214
LOM 214
LOM 214
LOM 214
LOM 214
LOM 214

The Putnam seminar meets every Wednesday from 4 to 5:30 in LOM 214. As always, everyone is warmly welcomed to come to hang out, learn more cool math, and meet folks. The seminar is casual, and folks can come and go as they like. See Pat Devlin’s webpage (and/or contact him) for more information. Folks can sign up for the mailing list here: https://forms.gle/nYPx72KVJxJcgLha8 
Algebra and Geometry lecture series  Quantizations in charateristic p. Lecture 4 
4:00pm 
https://yale.zoom.us/j/99019019033 (password was emailed by Ivan)

This is the fourth lecture in the series. Details can be found here: Algebra and Geometry lecture series (yale.edu) 
Geometric Analysis and Application  Boundary unique continuation of Dini domains  2:00pm  
Abstract: Let u be a harmonic function in a domain \Omega \subset \mathbb{R}^d. It is known that in the interior, the singular set \mathcal{S}(u) = \{u=\nabla u=0 \} is (d2)dimensional, and moreover \mathcal{S}(u) is (d2)rectifiable and its Minkowski content is bounded (depending on the frequency of u). We prove the analogue near the boundary for C^1Dini domains: If the harmonic function u vanishes on an open subset E of the boundary, then near E the singular set \mathcal{S}(u) \cap \overline{\Omega} is (d2)rectifiable and has bounded Minkowski content. Dini domain is the optimal domain for which \nabla u is continuous towards the boundary, and in particular every C^{1,\alpha} domain is Dini. The main difficulty is the lack of the monotonicity formula for the frequency function near the boundary of a Dini domain. This is joint work with Carlos Kenig 