Past Events

There is a well-developed theory of Sobolev spaces on metric measure spaces, stemming from the seminal works of Cheeger and Shanmugalingam in the 1990s. However, this notion does not lead to a suitable space for fractals. We develop an alternate...

Informally speaking, sampling discretization studies how well one can replace the computa- tion of integral L p norms for a given class of functions by the evaluation of these functions at a fixed small set of points. On the one hand, such problems...

Joint work with Punya Satpathy For a reductive group G, Borel and Serre introduced a compactification of a large class of arithmetic quotients of the symmetric space attached to G. After reviewing some aspects of their construction, we explain how to...

Let M be a Hermitian matrix associated to a graph X on n vertices. For any time t \geq 0, the transition matrix of the continuous quantum walk on X relative to M at time t is given by U(t)=exp(itM). For two vertices a and b of X, if there is some...

I will begin with some memories of how Jerry Marsden was as an advisor. In addition to the clarity and creativity of his mathematical thought, what has remained in my memory are his generosity with ideas, kindness as a human being, and his hands-on...

We construct a convex body $K$ in $R^n$, $n \ge 5$, with the property that there is exactly one hyperplane $H$ passing through $c(K)$, the centroid of $K$, such that the centroid of $K \cap H$ coincides with $c(K)$. This provides answers to questions...

Given two elliptic curves, the path finding problem asks to find an isogeny (i.e. a group homomorphism) between them, subject to certain degree restrictions. Path finding has uses in number theory as well as applications to cryptography. For...

We will see the definition and some examples of broken toric varieties and balloon animal maps between them. After an overview of some of the many different areas in which they appear, we look at how their geometry can be studied via complexes of...

Radial projections have been a quickly developing topic in harmonic analysis. The work of Orponen-Shmerkin-Wang connected this topic to a continuum Beck theorem for lines, finding a (lower) bound for the dimension of lines that contain at least two...

We consider the Grassmannian G r C ( k , n ) , a manifold parameterized by k -dimensional planes in complex n -dimensional space. The Schubert decomposition of the Grassmannian is perhaps the classic way to split this space into smaller pieces...