School of Mathematics

The topic of the talk will be Floer theories on exact symplectic orbifolds with smooth contact boundary. More precisely, I will first describe the construction, which only uses classical transversality techniques, of a symplectic cohomology group on...

In 1986, Hooley applied (what practically amounts to) the general Langlands reciprocity (modularity) conjecture and GRH in a fresh new way, over certain families of cubic 3-folds. This eventually led to conditional near-optimal bounds for the number...

Let f=∑anxn∈ℚ[x] be a power series which is also a meromorphic function in some neighborhood of the origin. The subject of the talk will be how certain conditions on f(x) as a meromorphic function actually guarantee that f(x) is an algebraic...

In these two talks, I will describe how the classification of locally homogeneous geometric structures (closely related to flat connections) leads to interesting dynamical systems.

Many interesting dynamical systems arise from the classification of...

I will present an elementary introduction to the regularity/uniqueness issues for the Navier-Stokes equations. Thanks to the convex integration technique, the h-principle is starting to take shape for the uniqueness problem. It might be possible...

The 2011 PhD thesis of Farris outlined a scheme to show that the ECH of a prequantization bundle over a Riemann surface is isomorphic as a Z/2Z-graded group to the exterior algebra of the homology of its base. In addition to providing an overview of...

How does the dimension of the first cohomology grow in a tower of covering spaces? After a tour of examples of behaviors for low-dimensional spaces, I will focus on arithmetic manifolds. Specifically, for towers of complex hyperbolic manifolds, I...

The unbounded denominators conjecture, first raised by Atkin and Swinnerton-Dyer, asserts that a modular form for a finite index subgroup of SL2(ℤ) whose Fourier coefficients have bounded denominators must be a modular form for some congruence...

Given a finite graph, the arboreal gas is the measure on forests (subgraphs without cycles) in which each edge is weighted by a parameter β>0. Equivalently this model is bond percolation conditioned to be a forest, the independent sets of the...