Constantin Kogler

I'm a PhD student in mathematics under the supervision of Emmanuel Breuillard (Oxford) and Péter Varjú (Cambridge).

Since October 2022 I'm working at Oxford, yet I've spent the first two years of my PhD at Cambridge, where I was part of the CCIMI-cohort. Before coming to the UK, I completed in 2020 a masters degree at ETH Zürich studying mostly under Manfred Einsiedler.

I work on random walks on Lie groups and (locally) symmetric spaces. My approach to random walks is analytic and therefore I utilize harmonic analysis and the theory of unitary representations. Furthermore, I rely on techniques from additive combinatorics and number theory, particularly Diophantine approximation. From my time at ETH, I'm also interested in effective methods in homogeneous dynamics (see my master thesis).

Email address: lastname at maths.ox.ac.uk

Image Copyright: Heidelberg Laureate Forum Foundation.

Research

https://arxiv.org/abs/2211.11128. Local limit theorem for random walks on symmetric spaces.

My Theses

Master Thesis. Effective p-adic Ergodic Theory, Diophantine Approximation and Spectral Gap.
Bachelor Thesis. The main result is Selberg's trace formula.

Talks

Talk on Expander Graphs. Given at S^3 student seminar in Cambridge.
Spectral Gap for Compact Lie Groups. Given at the Oberwolfach-Arbeitsgemeinschaft in October 2021.
Duke's Theorem 1. Notes for my first talk on the proof by Einsiedler, Lindenstrauss, Michel and Venkatesh of Duke's Theorem.
Duke's Theorem 2. Second talk on Duke's Theorem.
Linear Algebra. Collected notes (in german) of my Linear Algebra exercise class in Fall 2018.

Gallery

Below a collection of images is shown. Here you find my posters.