Constantin Kogler

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

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

Image Copyright: Heidelberg Laureate Forum Foundation.

Research

1. On absolute continuity of inhomogeneous and contracting on average self-similar measures (with Samuel Kittle).
   (84 pages, arxiv, pdf)
2. Effective density of non-degenerate random walks on homogeneous spaces (with Wooyeon Kim).
   IMRN 2024. (21 pages, arxiv, journal)
3. Local limit theorem for random walks on symmetric spaces.
   To appear at Journal d'Analyse Mathématique. (46 pages, arxiv)
4. Effective p-adic ergodic theory, Diophantine approximation and spectral gap.
   Master Thesis. (204 pages, pdf)
5. Closed geodesics on compact hyperbolic surfaces.
   Bachelor Thesis. (80 pages, pdf)

In preparation:

6. Dimension theory for contracting on average self-similar measures (with Samuel Kittle).
7. Strong local limit theorem on hyperbolic space for Diophantine measures (with Wooyeon Kim).

Notes

• Topics on Linear Groups. Graduate course by Emmanuel Breuillard at Oxford in Trinity Term 2023.

Talks

• 21th October 2024: Institute for Advanced Study. Informal Dynamics Seminar.
  Title: Absolute Continuity of Self-Similar Measures.
• 14th October 2024: University of Oxford. Junior Number Theory Seminar.
  Title: Self-Similar Sets and Measures. Notes.
• 9th October 2023: University of Warwick. DAGGER Seminar.
  Title: Ergodic actions, random walks and additive combinatorics.
• 17th January 2023: University of Warwick. Ergodic Theory and Dynamical Systems Seminar.
  Title: Random Walks on non-compact Lie groups. Slides.
• 8th June 2022: University of Oxford. Junior Topology and Group Theory Seminar.
  Title: Random Walks on Lie Groups and Diophantine Approximation.
• 6th May 2022: University of Cambridge. Junior Geometry Seminar.
  Title: Random Walks on Lie Groups and Diophantine Approximation.
• 24th November 2021: University of Cambridge. S^3 seminar.
  Title: Expander Graphs. Slides.
• 13th October 2021: Oberwolfach Arbeitsgemeinschaft.
  Title: Spectral Gap for Compact Lie Groups. Slides.

Gallery

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

• Random walks on modular surface.
  
• Random walks on hyperbolic space.
  
• Closed geodesics on the modular surface.
  
• Equidistributing orbits on the modular surface.
  
• Periodic trajectories in the equilateral triangle.
  
• Periodic trajectories in the regular pentagon.
  
• Periodic trajectories in the regular hexagon.
  
• Periodic trajectories in the regular octagon.
  
• Closed and simple closed geodesics on the regular tetrahedron.
  
• Simple geodesics on the cube.
  
• Simple geodesics on the octahedron.