School of Mathematics

Emmy Noether was a central figure in the development of abstract algebra in the early 20th century. Her ideas were profoundly influential, touching nearly every corner of mathematics. In this talk, I'll discuss how those ideas have taken new shape...

The Deligne--Simpson problem asks for a criterion of the existence of connections on an algebraic curve with prescribed singularities at punctures. We give a solution to a generalization of this problem to $G$-connections on $\mathbb{P}^1$ with a...

It is well-known that for any finite group $G$, there exists a closed $3$-manifold $M$ with $G$ as a quotient of the fundamental group of $M$. However, we can ask more detailed questions about the possible finite quotients of $3$-manifold groups, e...

The aim of this talk is to present some results on isometries of even, unimodular lattices and automorphisms of K3 surfaces.

The talk is based on joint work with Michael Groechenig and Johan de Jong.
We single out integrality properties of the topological fundamental group of smooth quasi-projective complex varieties which rely on the Langlands program (both arithmetic...

Vanishing theorems in complex algebraic geometry, such as the Kodaira vanishing theorem, play an important role in understanding the structure of complex algebraic varieties. Ultimately, they rely on critical input from Hodge theory. After recalling...

(joint work with Martin Kalck) Periods are complex numbers obtained by integrating algebraic differential forms over $\mathbf{Q}$ over a domain of algebraic nature. This includes numbers like $\pi$, $\log(2)$ or the values of the Riemann zeta...

Report on a paper written during the pandemic joint with Minseon Shin and Max Lieblich. Some key words: Brauer groups, nontorsion elements of $\mathrm{H}^2(X, \mathbf{G}_m)$, resolution property, Jouanolou devices, and derived categories. I will try...

Let SO(3,R) be the 3D-rotation group equipped with the real-manifold topology and the normalized Haar measure \mu. Confirming a conjecture by Breuillard and Green, we show that if A is an open subset of SO(3,R) with sufficiently small measure, then...