Ákos Nagy, University of California Santa Barbara
"The asymptotic geometry of G_2-monopoles"
Gigliola Staffilani, MIT
"The many faces of dispersive equations"
Yifeng Huang, University of Michigan - Ann Arbor
"A generating function for counting mutually annihilating matrices over a finite field"
Lei Alice Chen, California Institute of Technology
"Actions of Homeo and Diffeo groups on manifolds"
In this talk, I discuss the general question of how to obstruct and construct group actions on manifolds. I will focus on large groups like Homeo(M) and Diff(M) about how they can act on another manifold N. The main result is an orbit classification theorem, which fully classifies possible orbits. I will also talk about some low dimensional applications and open questions. This is a joint work with Kathryn Mann.
Caleb Suan, Department of Pure Mathematics, University of Waterloo
"Intro to Knots and Knot Invariants"
Michael Brannan, Texas A&M University
"Quantum symmetries of graphs"
Brady Ali Medina, Department of Pure Mathematics, University of Waterloo
"A different way to generalize the Weierstrass semigroup"
Jonathan Zhu, Princeton
"Mean curvature flow and explicit Łojasiewicz inequalities"
Junliang Shen, MIT
"The P=W conjecture and hyper-Kähler geometry"
The P=W conjecture by de Cataldo, Hausel, and Migliorini suggests a surprising connection between the topology of Hitchin systems and Hodge theory of character varieties. In this talk, we will focus on interactions between topology of Lagrangian fibrations and Hodge theory in general hyper-Kaehler geometries. Such connections shed new light on both the P=W conjecture for Hitchin systems and the Lagrangian base conjecture for compact hyper-Kähler manifolds.
Sherry Gong, Stanford University
"Invariants of knots and links"
We give an overview of some invariants to distinguish knots and links, and discuss some particular algebraic and geometric invariants. We discuss how these invariants relate to the smooth 4-dimensional Poincare conjecture, one of the most important questions in 4-manifold topology.
A post-colloquium meet and greet will be held at 2:00 pm using the same Zoom meeting link.