School of Mathematics

Edit distance is a similarity measure for strings that counts how many characters have to be deleted, inserted or substituted in one string to get another one. It has many applications from comparing DNA sequences to text processing. We are still in...

In this talk I want to explain some surprising features of the pro-etale cohomology of rigid-analytic varieties, and how they can be explained by a six functor formalism with values in solid quasi-coherent sheaves on the Fargues-Fontaine curve.

This...

In 2014, Fargues realized that one can formulate the local Langlands correspondence over p-adic fields as a geometric Langlands correspondence on the Fargues-Fontaine curve. This raises the question of a similar realization of the local Langlands...

In joint work with Bulent Tosun, it was shown that Heegaard Floer theory provides an obstruction for a contact 3-manifold to embed as a contact type hypersurface in standard symplectic 4-space. As one consequence, no Brieskorn homology sphere admits...

Where are the hard problems? In the absence of a proof of P ≠ NP, researchers have spent years proving unconditional lower bounds for constrained models of computation. In time, a distinct theme arose: random problems (in particular random...

Interaction models discussed here are the (asymmetric) quantum Rabi model (QRM), which describes the interaction between a photon and two-level atoms, and the non-commutative harmonic oscillator (NCHO). The latter can be considered as a covering...

Given two univariate polynomials, how does one compute their greatest common divisor (GCD)? This problem can be solved in polynomial time using the Euclidean algorithm, and even in quasi-linear time using a fast variant of the Euclidean algorithm...

In their 2001 paper, Hofer, Wysocki and Zehnder conjectured that every autonomous Hamiltonian flow has either two or infinitely many simple periodic orbits on any compact star-shaped energy level; in the same paper, the authors prove this assuming...

Over the last two decades we have developed good understanding how to quantify the impact of strategic user behavior on outcomes in many games (including traffic routing and online auctions) and showed that the resulting bounds extend to repeated...