School of Mathematics

We will discuss recent results towards the quantum unique ergodicity conjecture of Rudnick and Sarnak, concerning the distribution of Hecke--Maass forms on hyperbolic arithmetic manifolds. The conjecture was resolved for congruence surfaces by...

Distinct Hamiltonian isotopy classes of monotone Lagrangian tori in $\mathbb{C} P^2$ can be associated to Markov triples. With two exceptions, each of these tori are symplectomorphic to exactly three Hamiltonian isotopy classes of tori in the ball...

A d-dimensional framework is a pair (G,p⃗ ) consisting of a finite simple graph G and an embedding p⃗  of its vertices in ℝd. A framework is called rigid if every continuous motion of the vertices in ℝd that starts at p⃗ , and preserves the lengths...

New results on quantum tunneling between deep potential wells, in the presence of a strong constant magnetic field are presented. This includes a family of double well potentials containing examples for which the low-energy eigenvalue splitting...

We travel the years in order to understand the relationship between Nilpotency and Riemannian geometry: including Gromov's almost flat theorem for manifolds with bounded curvature and Fukaya-Yamaguchi's almost nilpotency of spaces with lower...

In quantum complexity theory, QMA and QCMA represent two different generalizations of NP. Both are defined as sets of languages whose Yes instances can be efficiently checked by a quantum verifier that is given a witness. With QMA the witness can be...

Kaledin established a Cartier isomorphism for cyclic homology of dg-categories over fields of characteristic p, generalizing a classical construction in algebraic geometry. In joint work with Paul Seidel, we showed that this isomorphism and related...

In this talk, I will present several a priori interior and boundary trace estimates for the 3D incompressible Navier–Stokes equation, which recover and extend the current picture of higher derivative estimates in the mixed norm. Then we discuss the...

Expander graphs are a staple of theoretical computer science. These are graphs which are both sparse and well connected. They are simple to construct and modify. Therefore they are a central gadget in numerous applications in TCS and combinatorics...

Ohta described the ordinary part of the 'etale cohomology of towers of modular curves in terms of Hida families. Ohta's approach crucially depended on the one-dimensional nature of modular curves. In this talk, I will present joint work with Chris...