Research



I am interested in ergodic theory and dynamical systems, specifically, symbolic dynamics and related areas of statistical physics and probability.





Arnold's Cat Map on a Cherry
(Wikipedia)


Publications and Online preprints

  • Kirszbraun-type Theorems For Graphs with Igor Pak and Martin Tassy (2017).[ arXiv ]
  • Rational ergodicity of Step function Skew Products with Jon Aaronson and Michael Bromberg, Accepted in J. Mod. Dyn. (2017).[ arXiv ]
  • Mixing Properties for Hom-Shifts and the Distance between Walks on Associated Graphs with Brian Marcus, Accepted in Pacific J. Math. (2017). [ arXiv ]
  • Four-Cycle Free Graphs, the Pivot Property and Entropy Minimality, Accepted in Ergodic Theory Dynam. Systems (2015). [arXiv]
  • A Generalisation of the Hammersley-Clifford Theorem, Accepted in Trans. Amer. Math. Soc. (2016). [arXiv]
  • Markov Random Fields, Markov Cocycles and the 3-coloured Chessboard with Tom Meyerovitch, Accepted in Israel J. Math. 215 (2015), 909-964. [arXiv] [Journal]
  • One Dimensional Markov Random Fields, Markov Chains and Topological Markov Fields with Guangyue Han, Brian Marcus, Tom Meyerovitch and Ronnie Pavlov, Accepted in Proc. Amer. Math. Soc. 142 (2014), 227-242. [arXiv] [Journal]

  • Notes and Essays
  • Markov Random Fields, Gibbs States and Entropy Minimality PhD Thesis at the University of British Columbia, 2015. [Thesis]
  • Undecidability in Tiling problems Written as part of a project in a course on the theory of Computation [Essay]
  • Markov Random Fields and Measures with Nearest Neighbour Potentials Msc Thesis at the University of British Columbia, 2011. [Essay][Errata]

  • Selected Presentations
  • Irrational rotations, random affine transformations and the central limit theorem at the University of California in Los Angeles, the Weizmann Institute, Technion Institute of Technology, Tata Institute of Fundamental Research in Mumbai, Indian Institute of Technology in Mumbai, 2017. [Link 1] [Link 2]
  • Some Strange Universality Results for Hom-Shifts At the Bangalore Probability Seminar, IISc, 2016. [Link]
  • Four Talks on Hom-Shifts At the Transversal Aspects of Tilings, Oléron, 2016. [1],[2], [3] and [4]
  • An Introduction to Hom-Shifts At the Workshop on Dynamical Systems and Related Topics in the University of Maryland, College Park, 2016. [Link]
  • Distance between Walks on Graphs At the Dartmouth College, the University of Denver, the University of Kansas and the Wright University, 2016. [Link]
  • Four-cycle Free Graphs and Entropy Minimality At the Tel Aviv University, the Tata Institute of Fundamental Research in Mumbai in 2015, the Workshop on Symbolic Dynamics on Finitely Presented Groups in Santiago, the Pingree Park Dynamics Workshop in Denver and the Dynamics Seminar in the University of Victoria in 2014. [Link]
  • Pivot Property for Hom(ℤd, H) At the Workshop on Combinatorics and Applications in Shanghai, April, 2015. [Link]
  • Graph Foldings and Markov Random Fields At the Indian Statistical Institute, Kolkata, August, 2014. [Link]
  • Graph Foldings and Markov Random Fields At the Combinatorics Seminar in the Dartmouth College, February, 2014. [Link]
  • Markov Random Fields and the 3-coloured Chessboard At the Symbolic Dynamics Special Session in the Mathematical Congress of the Americas, 2013. [Link]
  • Markov Random Fields and the 3-coloured Chessboard At the Symbolic Dynamics Special Session in the Mathematical Congress of the Americas, 2013. [Link]
  • Markov Random Fields and the Pivot Property (with a short introduction to symbolic dynamics) At the Indian Statistical Institute in Bangalore, July, 2013. [Link]
  • Markov Random Fields, Markov Cocycles and the Pivot Property At the Automata Theory and Symbolic Dynamics Workshop in Vancouver, 2013. [Link]