Past Events
Abstract: Consider a Liouville domain D embedded in a closed symplectic manifold M. To D one can associate two types of Floer theoretic invariants: intrinsic ones like the wrapped Fukaya category which depend on D only, and relative ones which involve both D and M. It is often the case…
The general goal of Higher Hida theory is to define and understand the ordinary part of integral coherent cohomology of Shimura varieties. In this talk we will focus on the simplest example of a Shimura variety for a non-split reductive group. We describe the results, notably vanishing…
The Ramsey number r(s,t) denotes the minimum N such that in any red-blue coloring of the edges of the complete graph on N vertices, there exists a red complete graph on s vertices or a blue complete graph on t vertices. While the study of these quantities goes back almost one hundred…
I'll describe joint work with Karpukhin, Kusner, and McGrath, in which we produce many new families of closed minimal surfaces in S^3 and free boundary minimal surfaces in B^3 via constrained optimization problems for Laplace and Steklov eigenvalues on surfaces. Along the way, I'll highlight…
The study of exponential sums with multiplicative coefficients is classical in analytic number theory, yet our understanding of them is far from complete. This is unsurprising, seeing as multiplicative functions alone are often difficult objects to grasp. However, in recent years, our…
We will derive the transport equation as the second term in our approach to solving hyperbolic PDEs, describe the meaning of this equation from our symplectic perspective, and, if time permits, outline a solution strategy.
Steady Kahler-Ricci solitons are eternal solutions of the Kahler-Ricci flow. I will present new examples of such solitons with strictly positive sectional curvature that live on C^n and provide an answer to an open question of H.-D. Cao in complex dimension n>2. This is joint work with Pak-…
I will talk about a new algebra of operations on polynomials which has the property
$T_iT_j=T_jT_{i+1}$ for $i>j$ and a family of polynomials dual to them called forest polynomials. This family of operations plays the exact role for quasisymmetric polynomials and forest polynomials as…
We survey some extensions of the classical notions of Du Bois and rational singularities, known as the k-Du Bois and k-rational singularities. By now, these notions are well-understood for local complete intersections (lci). We explain the difficulties beyond the lci case, and propose new…
We will give an accessible introduction to the Hasse-Weil conjecture for curves and related problems in the Langlands program. We will discuss some recent work with G. Boxer, F. Calegari and T. Gee in which we prove the modularity of a positive proportion of genus two curves. We will explain…