School of Mathematics

Every o-minimal structure determines a collection of "tame" or "definable" subsets of bbRn. We can then ask about the fragment of complex geometry present in the structure: Which holomorphic functions are definable, and which spaces are cut out by...

We present solutions to two problems on indefinite integral ternary quadratic forms. The first, highlighted by Margulis in 1990, concerns the distribution of the ternary Markoff spectrum associated with minima of forms. The second, initiated by...

In the theory of error-correcting codes, list decoding allows a decoder to output a list of candidates when attempting to remove noise from a corrupted input. The constructions and algorithms for such list decodable codes has had numerous...

This talk, which is based on two joint works, one with Pedro Salomão and Richard Siefring and another with Michael Hutchings and Vinicius Ramos, revolves around the role that restrictions on the knot types of periodic Reeb orbits imposed by the...

I will prove Gromov's conjecture that every 3-manifold of positive scalar curvature contains a short closed geodesic. The proof uses Min-Max theory of minimal surfaces and a combinatorial version of mean curvature flow. Time permitting, I will...

Over the past 50 years, cryptographers have constructed a number of surprising and important primitives like public-key encryption, which allows strangers to communicate privately even if eavesdroppers hear everything they say. However, there are...

The group of Hamiltonian diffeomorphisms , equipped with the Hofer metric , is a central object in symplectic topology. A landmark result by Polterovich and Shelukhin established the profound geometric complexity of this group for surfaces and their...

Kudla and Millson proved in the 80's that the generating series of special cycles in orthogonal and unitary Shimura varieties are modular forms and a well-established conjecture of Kudla asks about extensions to toroidal compactifications. In this...

I'll talk about the o-minimal structures R_LN and R_{LN,exp} where one has an effective form of the finiteness property of o-minimality. Unlike the more classical structure of Pfaffian function, R_{LN,exp} contains the period integrals for aribtrary...