Seminars Sorted by Series

Abstract: Matroids are combinatorial structures that model independence, such as that of edges in a graph and vectors in a linear space. I will introduce the theory of matroids along with their surprising connection to a class of multivariate...

Abstract: Tropical geometry is a modern degeneration technique in algebraic geometry. Think of it as a very drastic degeneration in which one associates a limiting object to a family of algebraic varieties that is entirely combinatorial.  I will...

Abstract: Matroids are combinatorial structures that model independence, such as that of edges in a graph and vectors in a linear space. I will introduce the theory of matroids along with their surprising connection to a class of multivariate...

Abstract: Tropical geometry is a modern degeneration technique in algebraic geometry. Think of it as a very drastic degeneration in which one associates a limiting object to a family of algebraic varieties that is entirely combinatorial.  I will...

In this talk, we will discuss the existence problem of extremal metrics on a Kähler manifold. The best known examples of these are Kähler-Einstein and constant scalar curvature Kähler (cscK) metrics. Yau's resolution of the Calabi conjecture proves...

The goal of this talk is to present two problems related to wandering domains. I will define the participating objects, and give a historical overview of what was done and what is left to do to solve these problems. 

No basic knowledge in complex...

In this talk, we will discuss the computation of motivic stable homotopy groups and their applications in classical computations. Specifically, we will discuss an example of complex motivic applications in classical theory, the Adams spectral...

Combinatorial discrepancy asks the following question: Given a ground set U and a collection S of subsets of U, how do we color each element in U red or blue so that each subset in S has almost an equal number of each color? A straightforward idea...

We will explore some counting problems for number fields in which the conjectures formulated first by Malle and refined by Bhargava play a central role. In the process we will see some standard techniques in analytic number theory. 

For a low-dimensional manifold, one often tries to understand its intrinsic topology and geometry through its submanifolds, in particular of co-dimension 1. To be interesting and to give some information, such a submanifold should interact with the...

I’ll describe graph complexes, introduced by Kontsevich in the context of mathematical physics. I’ll survey its connections to geometry and topology, highlighting its relation to the cohomology of moduli spaces of curves. 

We give a gentle introduction to rational and Du Bois singularities in algebraic geometry. Through examples, we will see how birational geometry comes into play with the theory of differential operators. Time permitting, we discuss the sheaf...

Persistence modules offer a way to analyze how features, such as connected components or holes, evolve as a space is gradually changed. One can think of a persistence module as a sequence of vector spaces, each corresponding to a particular stage of...

In the 1970s, Viro's method paved an important path in the study of the topology of real algebraic varieties and became a precursor to tropical geometry. This method involves subdividing an integer polytope and using the information from each of its...

Open book decompositions provide a topological decomposition of a given manifold. We focus on dimension three. While the definition seems to be purely topological, it encodes information about fibered knots, surface dynamics, contact structures of...

CAT(0) cube complexes are cell complexes whose cells are cubes, whose naturally defined metric is non-positively curved in some precise sense. 

They can be equivalently defined in a variety of ways, which a priori looks very different. They naturally...

Tropical enumerative geometry is a branch of combinatorial algebraic geometry that aims to count algebraic objects (usually curves on some surface passing through a number of points) by turning them into combinatorial objects, called tropical curves...

I will give an overview of the classical study of local complex dynamics in one dimension, and the more recent study in several complex variables; with an emphasis on the `neutral’ case, that is when the local behavior is neither attracting nor...