Constantin Kogler

I'm a member at the School of Mathematics of the Institute for Advanced Study. My research is generously funded by a Postdoc Mobility Fellowship of the Swiss National Science Foundation (Grant number 235409).

Email address: lastname at ias.edu

I recently completed my PhD at the University of Oxford under the supervision of Emmanuel Breuillard and also mentored by Péter Varjú. During the first two years of my doctoral studies, I was based at the University of Cambridge as part of the CCIMI cohort. Prior to my doctorate, I earned a master’s degree in mathematics from ETH Zürich in 2020.

My research focuses on random walks on Lie groups and (locally) symmetric spaces, as well as on self-similar measures. I draw on tools from analysis, additive combinatorics, and number theory (particularly Diophantine approximation). I'm also interested in effective methods in homogeneous dynamics.

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.
   Journal d'Analyse Mathématique 2025. (arxiv, journal)
6. Effective density of non-degenerate random walks on homogeneous spaces (with Wooyeon Kim).
   IMRN 2024. (arxiv, journal)

Theses:

1. Topic in Random Walks on Lie Groups.
   PhD Thesis. (204 pages, pdf)
2. Effective p-adic ergodic theory, Diophantine approximation and spectral gap.
   Master Thesis. (204 pages, pdf)
3. Closed geodesics on compact hyperbolic surfaces.
   Bachelor Thesis. (80 pages, pdf)

Notes

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

Talks

• 4th July 2025: 21st Annual Berlin-Oxford Meeting on Applied Stochastic Analysis
  Title: Stationary Measures for Random Walks on Lie Groups. Slides.
• 4th June 2025: Université Sorbonne Paris Nord (LAGA).
  Title: Dimension and Absolute Continuity of Self-Similar Measures.
• 2nd April 2025: ETH Zürich. Ergodic Theory and Dynamical Systems Seminar.
  Title: Dimension and Absolute Continuity of Self-Similar Measures.
• 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.

• Self-affine measures.
  
• Bernoulli convolutions.
  
• 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.