Constantin Kogler

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

Since October 2022 I am working at Oxford and I have 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 as well as on self-similar measures. I rely on techniques from analysis, 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

Academic CV

Image Copyright: Heidelberg Laureate Forum Foundation.

Research

  1. On absolute continuity of inhomogeneous and contracting on average self-similar measures (with Samuel Kittle).
    (arxiv)
  2. Dimension of contracting on average self-similar measures (with Samuel Kittle).
    (arxiv)
  3. Entropy theory for random walks on Lie groups (with Samuel Kittle).
    (arxiv)
  4. Polynomial tail decay for stationary measures (with Samuel Kittle).
    (arxiv)
  5. Local limit theorem for random walks on symmetric spaces.
    To appear at Journal d'Analyse Mathématique. (arxiv)
  6. Effective density of non-degenerate random walks on homogeneous spaces (with Wooyeon Kim).
    IMRN 2024. (arxiv, journal)
  7. Effective p-adic ergodic theory, Diophantine approximation and spectral gap.
    Master Thesis. (204 pages, pdf)
  8. Closed geodesics on compact hyperbolic surfaces.
    Bachelor Thesis. (80 pages, pdf)
In preparation:
  1. Strong local limit theorem on hyperbolic space for Diophantine measures (with Wooyeon Kim).

Notes

Talks