Video Lectures

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...

The ubiquity of substructures in protoplanetary discs has opened debate regarding the alignment of planet formation timescales with protostellar disc evolution. Under the hypothesis of the planetary interpretation, a robust conclusion is that a...

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...

For Pauli stabilizer codes—such as surface codes and color codes—transversal logical gates are strongly constrained by the Bravyi–König bound. In particular, implementing a non-Clifford gate transversally (as required for universality) demands three...

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...

Among many things, dark matter could be made of new fundamental or composite particles, which may feebly interact with nuclei or electrons (“baryons”), as well as with themselves. Cosmological observables are a promising avenue to test such...