Upcoming Events

In this talk we will introduce the modular method, the approach followed by Wiles to prove Fermat’s Last Theorem. We will explain the role of elliptic curves, modular forms, and Galois representations in this framework, and discuss how the method has...

Fix a positive integer n and a graph F . A graph G with n vertices is called F -saturated if G contains no subgraph isomorphic to F but each graph obtained from G by joining a pair of nonadjacent vertices contains at least one copy of F as a subgraph...

‘Reef halos’ are rings of sand, barren of vegetation, encircling reefs. However, the extent to which various biotic (e.g., herbivory) and abiotic (e.g., temperature, nutrients) factors drive changes in halo prevalence and size remains unclear. The...

The Turan density of a forbidden hypergraph F is the largest edge density a large hypergraph H can have without containing any copy of F, and determining this number for various F is a notoriously difficult problem. One on-ramp to this question (from...

12:30 - 1:30 PM: Lunch/Coffee/Tea/Snacks 1:30 - 1:35: Opening Remarks 1:35 - 1:50: Jonathan Hermon A simple characterization of the effective resistance metric on vertex transitive graphs The effective resistance satisfies the triangle inequality and...

For a complex projective variety, the Lefschetz standard conjectures predict the existence of algebraic self-correspondences that are inverse to the hard Lefschetz isomorphisms. They have broad implications for Hodge theory and the theory of motives...

A ring spectrum (a.k.a. a multiplicative cohomology theory) E is complex-orientable if every complex vector bundle admits a Thom class in E . While many familiar spectra are complex-orientable, notable examples fail to be so — such as real K-theory...

An n-by-n matrix A=[a_{ij}] is said to be a pairwise comparison matrix (PC matrix) or a reciprocal matrix if it is positive and a_ij=1/a_ji, for all i,j=1,...,n. If, in addition, a_ika_kj=a_ij for all i,j,k, the matrix is said to be consistent. There...

The first regularity results for maps optimizing an open class of cost were proved by Ma-Trudinger-Wang (2005) using a key inequality which they introduced (based on a classical strategy of Pogorelov). Away from the boundary, this inequality controls...

Random walks or diffusions with Dirichlet boundary condition (killing at the boundary) admit a Perron-Frobenius eigenfunction (the unique positive normalized eigenfunction when the domain is bounded). Starting with gambler's ruin problems, we discuss...