Aitor Azemar

I am a last year PhD student at the university of Glasgow, supervised by Maxime Fortier Bourque and Vaibhav Gadre.

I can be contacted at name dot surname at glasgow dot ac dot uk.

Research interests

I am mostly interested in using probability to study geometric aspects of objects. Lately I have been looking into applying techniques from dynamics to complex networks.

Currently thinking about

Density repelling random walk

Nowhere density of Busemann points within horofunction compactification of Teichmüller space.

Singularity of harmonic measures for uniform lattices.

Papers

  1. Mathematical modelling of a silicon carbide (SiC) pilot furnace , joint with James Andrews, Atrayee Bhattacharya, Charlie Egan, Andrew Lacey, Brady Metherall, Nicholas Ryan, MIIR, to appear.
  2. Stationary measures on the circle from hyperbolic surfaces with cusps cannot be straightened by quasi-symmetries, joint with Vaibhav Gadre, preprint.
  3. Bounds for the random walk speed in terms of the Teichmüller distance, preprint.
  4. Random walk speed is a proper function on Teichmüller space, joint with Vaibhav Gadre, Sébastien Gouëzel, Thomas Haettel, Pablo Lessa, Caglar Uyanik, Journal of Modern Dynamics, to appear.
  5. A qualitative description of the horoboundary of the Teichmüller metric, Algebraic & Geometric Topology, to appear.
  6. Statistical hyperbolicity for harmonic measure, joint with Vaibhav Gadre and Luke Jeffreys, Int. Math. Res. Not. IMRN (2022), no. 8, 6289-6309.
  7. Random walks on convergence groups, Groups Geom. Dyn. 16 (2022), no. 2, pp. 581–612 
     
    I attributed the proof that the isometry groups of a Gromov hyperbolic space acts as a convergence group on its boundary to Bowditch (1996).
    
    This is more commonly attributed to Tukia (1994). Furthermore, Woess did publish the same result one year prior (1993).
    
    The same paper by Woess discusses the Dirichlet problem in a similar context, so it should also have been cited in Section 4.2.

Presentations

  1. European Study Group with Industry, University of Edinburgh
  2. Teichmüller spaces and geodesic currents, NCNGT, Part1, Part2
  3. Geometry and Topology seminar, Indian Institute of Science
  4. Geometry and Topology seminar, University of Bristol
  5. Geometry and Topology seminar, University of Glasgow
  6. Post Graduate Research seminar, University of Glasgow

CV

Tikz examples