Video Lectures

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...

The entropy of supersymmetric black holes in string theory compactifications can be related to that of a D- or M-brane system, which in many cases can be further reduced to a two-dimensional conformal field theory (CFT). For black holes in M-theory...

Abstract: https://www.ias.edu/sites/default/files/abstact_kasjan.pdf

"Saturons" are macroscopic objects that exhibit maximal micristate degeneracy within the validity of a given quantum  field theoretic description.  Due to this feature, saturons and black holes belong to the same universality class with common key...

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...