Past Events

An attempt to explain Langlands' contributions to non-experts.

In this joint work with Xingzhe Li, we prove the strong Morse inequalities for the area functional in the space of embedded tori and spheres in the three sphere. As a consequence, we prove that in the three dimensional sphere with positive Ricci...

Let F(x, y) be a binary form of degree at least 3 which is irreducible over the rationals. For any fixed non-zero integer m, Thue showed that the equation F(x, y) =m has at most finitely many solutions in integers x, y. I will discuss some...

We will discuss the well-known isotopy problem in symplectic geometry in dimension four. Given a compact symplectic four manifold with a fixed symplectic class, a long standing problem is to ask whether all symplectic forms in the cohomology class...

I will describe an approach to constructing a compact moduli space of hyperplane arrangements use logarithmic and tropical geometry.

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In this talk we discuss joint work with Fatma Çiçek on establishing asymptotic formulae with power saving error term for first and second moments of Rankin-Selberg L-functions L(1/2+iμ,f⊗g) where f varies over newforms of conductor pn with p being a...

I will review some aspects of degeneration technique in curve counting problems via Gromov-Witten and Donaldson-Thomas theories. This has been one of the major tools in developments in both theories and computing the invariants. I will then talk...

Many of the words that we use to describe biological disease are often also used to describe cyber systems (e.g. virus, infected). The overall goal of my research in this area is to see how far we can push this metaphor and what we can learn about...