# Upcoming Events

Given a spin rational homology sphere Y equipped with a cyclic group action preserving the spin structure, I will introduce equivariant refinements of Manolescu's kappa invariant, derived from the equivariant K-theory of the Seiberg--Witten Floer spectrum. These invariants give rise to…

Abstract: Of great interest is to address the final state conjecture for the dynamics of charged particles near spatially homogeneous equilibria in a plasma, where particles are transported by the self-consistent electric field generated by the meanfield Coulomb's interaction. The long-range…

In this talk, we study the behaviour of primitive rational points on expanding closed horospheres in the space of lattices. The equidistribution of these rational points is proved by Einsiedler, Mozes, Shah and Shapira (2016). Their proof uses techniques from homogeneous dynamics and relies…

The standard Hadamard's well-posedness theory has been established for linear systems, or for smooth solutions of nonlinear systems. For weak solutions of nonlinear systems, the usual calculus and functional analytic methods do not yield well-posedness theory. The difficulty is due in large part…

Characteristic classes; concluding the proof of the Index Theorem; applications.

In this talk, we'll talk about a surprising recent result about the algebraic relations between solutions of a differential equation. We will also give applications to certain recent transcendence and diophantine results.

How does the spectral theory of the Laplacian on a surface relate to its geometry? Osgood, Phillips and Sarnak provided a beautiful answer to this…

We will discuss the celebrated result of Kervaire and Milnor in the 1960s: the n-dimensional homotopy cobordism group is finite unless n=3. Further, we will investigate the interesting theorem of Gonzalez-Acuna in the 1970s: the n-dimensional homotopy and homology cobordism groups are isomorphic…

We study the Continuum Directed Random Polymer (CDRP) which arises as a universal scaling limit of discrete directed polymers. In this talk, I will present some of the recent progress in understanding the geometry of the CDRP. In particular, I will show CDRP exhibits pointwise localization and…