School of Mathematics

We will discuss stochastic quantization i.e. Langevin dynamic of the Yang-Mills model on two and three dimensional torus. This is described by a Lie algebra valued stochastic PDE driven by space-time white noise. We construct (local) solution to...

We show that for any closed symplectic manifold, the number of 1-periodic orbits of any non-degenerate Hamiltonian is bounded from below by a version of total Betti number over Z, which takes account of torsions of all characteristics. The proof...

I will review some recent progress on regularity properties of vortex and SQG patches. In particular, I will present an example of a vortex patch with continuous initial curvature that immediately becomes infinite but returns to (C2) class at all...

The Chowla conjecture from 1965 predicts that all autocorrelations of the Liouville function vanish. In fact, after an adaptation, the Chowla conjecture was expected to hold for all aperiodic multiplicative functions with values in the unit disc (cf...

At Rutgers University-Camden, the student body is quite diverse, with many first-generation college students and students from underrepresented minority groups. Our students face financial challenges - a significantly large fraction of Rutgers...

Davenport’s lemma has been a crucial ingredient in recent applications of geometry of numbers to arithmetic statistics. The lemma estimates, with error-term, the number of lattice points contained in bounded semi-algebraic regions of ℝn in terms of...

We face financial choices every day. From buying a morning coffee, to an online shopping errand in the afternoon, we are asked “Cash, Credit or Debit?” and “Pay Now or Later?”  We occasionally face bigger decisions, like whether to take out a car...

In this talk, I will first discuss some instances in which orbifolds occur in geometry and dynamics, in particular, in the context of billiards and systolic inequalities. Then I will present topological conditions for an orbifold to be a manifold...

A classical theorem of Neukirch and Uchida says that number fields are completely determined by their absolute Galois groups. One might wonder about analogous results for algebraic varieties: in what situations can varieties be “reconstructed” from...

Being a scientist or mathematician can be challenging, and being a minority mathematician even more so. My path hasn’t always been easy, but it has been worthwhile and fulfilling. However, in some sense, I believe that I ended up where I am through...