## Week of September 12, 2021

 Group Actions and Dynamics Invariant measures for horospherical actions (note: change of time!) 3:30pm - LOM 206 Around 1970, Furstenberg showed the unique ergodicity of the horocycle flow on closed hyperbolic surfaces. We will discuss a generalization of his theorem in the context of Anosov homogeneous spaces. Geometry, Symmetry and Physics Quantum difference equations, 3d mirror symmetry and wall-crossing operators 4:30pm - Zoom Zoom link: https://yale.zoom.us/j/99305994163, contact the organizers (Gurbir Dhillon and Junliang Shen) for the passcode. Abstract: The talk is based on joint work with A.Smirnov. We obtain a factorization theorem about the limit of elliptic stable envelopes to a point on a wall in H^2(X,R), which generalizes the result of M.Aganagic and A.Okounkov. This approach allows us to extend the action of quantum groups, quantum Weyl groups, R-matrices, etc., to actions on the K-theory of the symplectic dual variety. In the case of the Hilbert scheme of points in the plane, our results imply the conjectures of E.Gorsky and A.Negut. As another application of this technique, we gain a better geometric understanding of the wall crossing operators and the quantum difference equations.
 Geometry & Topology Canonical identification between scales on Ricci-flat manifolds 4:15pm - LOM 214 Uniqueness of tangent cone has been a central theme in many topics in geometric analysis. For complete Ricci-flat manifolds with Euclidean volume growth, the Green function for the Laplace equation can be used to define a functional which measures how fast the manifold converges to the tangent cone. If a tangent cone at infinity of the manifold has smooth cross section, Colding-Minicozzi proved that the tangent cone is unique, by showing a Łojasiewicz-Simon inequality for this functional. As an application of this inequality, we will describe how one can identify two arbitrarily far apart scales in the manifold in a natural way. We will also discuss a matrix Harnack inequality when there is an additional condition on sectional curvature, which is an elliptic analogue of matrix Harnack inequalities obtained by Hamilton and Li-Cao for geometric flows.
 Undergraduate Seminar Putnam Seminar 4:00pm - LOM 214 , 4:00pm - LOM 214 , 4:00pm - LOM 214 , 4:00pm - LOM 214 , 4:00pm - LOM 214 , 4:00pm - LOM 214 , 4:00pm - LOM 214 , 4:00pm - LOM 214 , 4:00pm - LOM 214 , 4:00pm - LOM 214 , 4:00pm - 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 2 4:00pm - https://yale.zoom.us/j/99019019033 (password was emailed by Ivan) This is the second lecture in the series. We will finish our discussion on the generalities of Hamiltonian reduction and start talking Frobenius constant quantizations in characteristic p.
 Geometric Analysis and Application Mean curvature flow and foliations in hyperbolic 3-manifolds 2:00pm - Abstract:  In this talk we explore some properties of the mean curvature flow with surgery and the level-set flow in negative curvature. We combine those with min-max theory to conclude that any quasi-Fuchsian and any hyperbolic 3-manifolds fibered over $S^1$ admits a foliation where every leave is minimal or has non-vanishing mean curvature. This is joint work with Marco Guaraco (Imperial College) and Vanderson Lima (Universidade Federal do Rio Grande do Sul). Seminar talk is supported in part by the Mrs. Hepsa Ely Silliman Memorial Fund.