Events and Activities

High dimensional expansion comes in two flavors: spectral, which relates to random walks;  and cosystolic, which relates to chains of linear maps. The later is a more mysterious notion, which turns out related to a variety of applications such as...

In the early 80s Hatcher proved the Smale Conjecture, asserting that the diffeomorphism group of the three-sphere retracts onto its isometry group.  The corresponding problem for $RP^3$ was open nearly 40 years, and resolved only in 2019 by a...

Fibered 3-manifolds are those constructed via surface homeomorphisms. Given such a manifold with pseudo-Anosov monodromy, much is already known about how topological data of the mapping class determine geometric information about the hyperbolic 3...

The Kadomtsev-Petviashvili (KP) Equation has deep connections to algebraic curves, with solutions constructed from Riemann theta functions in the style of Krichever. As a curve undergoes tropical degeneration, its theta function simplifies to a...

TBA

We will consider finite collections of squares tiles, and ask when we can tile the whole plane in an interesting way. This question is related to the algebraic structure of ‘lattices in products of trees’, which are discrete groups acting...

Suppose given a class of finite combinatorial structures, such as graphs or total orders. Nate Harman and I recently introduced a notion of measure in this context: this is a rule assigning a number to each structure such that some axioms are...

For an elliptic curve E defined over Q, the Mordell-Weil group E(Q) is a finitely generated abelian group. We prove that there are infinitely many elliptic curves E over Q for which E(Q) has rank 2. Our elliptic curves will be given by explicit...