Monday, September 21, 2020
Time  Items 

All day 

2pm 
09/21/2020  2:30pm Abstract: Deep learning has revolutionized our ability to generate novel images and 3D shapes. Neural networks are typically trained to map a highdimensional latent code to full realistic samples. In this talk, I will present two recent works focusing on generation of handwritten text and 3D shapes. In these works, we take a different approach and generate image and shape samples using a more granular partbased decomposition, demonstrating that the whole is not necessarily “greater than the sum of its parts”. I will also discuss how our generation by decomposition approach allows for a semantic manipulation of 3D shapes and improved handwritten text recognition performance. Location:
https://us02web.zoom.us/j/89627764901

4pm 
09/21/2020  4:00pm Let $\mathbb{H}^n$ be the hyperbolic $n$space and $\Gamma$ be a geometrically finite discrete subgroup in $\operatorname{Isom}_{+}(\mathbb{H}^n)$ with parabolic elements. We establish exponential mixing of the geodesic flow over the unit tangent bundle $T^1(\Gamma\backslash \mathbb{H}^n)$ with respect to the BowenMargulisSullivan measure. Previously, such results were proved by Naud, Stoyanov and SarkarWinter for convex cocompact discrete subgroups and MohammadiOh and EdwardsOh for $\Gamma$ with large critical exponent. Our approach is to construct a coding for the geodesic flow and then prove a Dolgopyattype spectral estimate for the corresponding transfer operator. In the talk, I am planning to explain the construction of the coding. I will also discuss the application of obtaining a resonancefree region for the resolvent on $\Gamma\backslash \mathbb{H}^n$. This is a joint work with Jialun Li. Location:
Zoom
09/21/2020  4:30pm I will briefly review a conjectural picture of the hyperkahler metrics on moduli spaces of Higgs bundles which arose from quantum field theory, and then describe some recent progress toward proving these conjectures; this is work of various people including MazzeoSwobodaWeissWitt, Fredrickson, DumasN, FredricksonN. A recent surprise is that for Higgs bundles of rank > 2, one needs to use “higher symmetries” which generalize the covariance of Higgs bundles under holomorphic vector fields. Location:
https://yale.zoom.us/j/99433355937 (password was emailed by Ivan on 9/11, also available from Andy by email)
