Monday, February 12, 2024
Time  Items 

All day 

4:00pm 
02/12/2024  4:00pm On Riemann surfaces, pseudoAnosov maps constitute the majority of the mapping class group and these maps display many interesting dynamical properties. One way to generate pseudoAnosov maps is by compositions of Dehn twists. In this talk, I’ll show that on symplectic manifolds, we can also compose symplectic Dehn twists to obtain maps that display hyperbolic properties including positive topological entropy, stable and unstable laminations, and exponential growth of the Floer homology group. This represents joint work with Wenmin Gong and Jinxin Xue.
Location:
KT 205
02/12/2024  4:30pm The main theorem of this talk will be that the affine closure of the cotangent bundle of the basic affine space (also known as the universal hyperkahler implosion) has symplectic singularities for any reductive group, where essentially all of these terms will be defined in the course of the talk. After discussing some motivation for the theory of symplectic singularities, we will survey some of the basic facts that are known about the universal hyperkahler implosion and discuss how they are used to prove the main theorem. Time permitting, we will also discuss a recent result, joint with Harold Williams, which identifies the universal hyperkahler implosion in type A with a Coulomb branch in the sense of Braverman, Finkelberg, and Nakajima, confirming a conjectural description of Dancer, Hanany, and Kirwan. Location:
KT217
