Click here for my homepage and contact information. Last updated: February 16th 2018.

About me (in brief):

I am currently Associate Professor in the Mathematics Department of Ohio State University, where I am a member of the Ergodic theory group. From 2009-2012, I was Chowla Research Assistant Professor at Penn State, where I was a member of the Penn State Center for Dynamics and Geometry.  I completed my PhD in Mathematics at the University of Warwick in 2009, supervised by Professors Mark Pollicott and Peter Walters. My research area is ergodic theory and dynamical systems. I am the organiser of the Ohio State ergodic theory and probability seminar. My research is currently supported by an NSF CAREER award.

I'm also interested in Outreach, particularly in developing programs for mathematics and STEM education for K-12 students from under-represented groups. In Summer 2013, I started working with the Ohio State Young Scholars Program to develop, and deliver, the mathematical content for the 'Building Mathematical Capacity Summer Experience' summer camp for rising 10th graders.

I was an organiser/mentor (with Jon Chaika, Vaughn Climenhaga, Boris Hasselblatt and Bryna Kra) for an AMS 2017 Mathematics Research Community. See here for more details. I am an organiser for a few upcoming conferences and workshops: a conference on Thermodynamic Formalism in June 2018 at ICMS in Edinburgh; an AIM workshop on 'Equilibrium states for dynamical systems arising from geometry' in July 2019; a large workshop on dynamical systems at Warwick University in July 2019.

Research Interests (in brief):

My main research area is ergodic theory and dynamical systems, particularly the 'entropy theory' of this subject. I am particularly interested in connections between dynamical systems and other areas of mathematics. Recently, my work has particularly focused on connections between dynamical systems and geometry. I have also worked on the implementation of ideas related to my pure research in the applied setting of Bioinformatics.


Grants:

I currently hold an NSF CAREER award, which started in Summer 2015. The project is entitled: 'Entropy in dynamics: connections with geometry, algebraic numbers, and bioscience'.

I previously received NSF support from a 'standard' grant held from 2011-2015.

I was a participant in an AIM SQuaRE with Keith BurnsVaughn Climenhaga and Todd Fisher from 2013-2016. The project was entitled "Equilibrium states for geodesic flows in nonpositive curvature".


Preprints: (Available at my arXiv page here)

1. 'Unique equilibrium states for geodesic flows in nonpositive curvature'
       Joint work with Keith Burns, Vaughn Climenhaga and Todd Fisher
       Arxiv version here, 49 pages, 2 figures.

2. 'The weak specification property for geodesic flows on CAT(-1) spaces'
       Joint work with Dave Constantine and Jean-Francois Lafont
       Arxiv version here, 28 pages, 2 figures.

3. 'Measures of maximal entropy for suspension flows over the full shift'
       Joint work with Tamara Kucherenko
       Arxiv version here, 12 pages.


Published Papers and Papers Accepted for Publication:


1. 'Fat flats in rank one manifolds'
       Joint work with Dave Constantine, Jean-Francois Lafont and Ben McReynolds
       Arxiv version here, 23 pages, 1 figure, To appear in 'Michigan Mathematical Journal'.

2. 'Unique equilibrium states for Bonatti-Viana diffeomorphisms'
       Joint work with Vaughn Climenhaga and Todd Fisher
       Arxiv version here, 46 pages, To appear in 'Nonlinearity'.

3. 'Generalized beta-transformations and the entropy of unimodal maps'
       Arxiv version here, 21 pages, To appear in 'Commentarii Mathematici Helvetici'.

4. 'A suspension flow over the full shift with two distinct measures of maximal entropy'
       Joint work with Tamara Kucherenko
       6 pages, To appear in 'Topology Proceedings'.

5. 'Unique equilibrium states for Mane diffeomorphisms'
       Joint work with Vaughn Climenhaga and Todd Fisher
       Arxiv version here, 27 pages, To appear in 'Ergodic Theory and Dynamical Systems'.

6. 'Unique equilibrium states for flows and homeomorphisms with non-uniform structure'
       Joint work with Vaughn Climenhaga, Arxiv version here
       Published in 'Advances in Mathematics', 2016, Vol. 303, p.745-799.

7. 'Large deviations for systems with non-uniform structure'
       Joint work with Vaughn Climenhaga and Kenichiro Yamamoto, Arxiv version here
       Published in 'Transactions of the American Mathematical Society', 2017, Vol 369, p.4167-4192.

8. 'Coding sequence density estimation via topological pressure'
       Joint work with David Koslicki, Arxiv version here
       Published in the 'Jounal of Mathematical Biology', 2015, Vol.70 issue 1-2, p.45-69

9. 'Intrinsic ergodicity via obstruction entropies'
       Joint work with Vaughn Climenhaga, Arxiv version here
       Published in 'Ergodic Theory and Dynamical Systems', 2014 Vol 34 issue 6, p.1816-1831

10. 'Equilibrium states beyond specification and the Bowen property'
       Joint work with Vaughn Climenhaga, Arxiv version here
       Published in 'Journal of the London Mathematical Society', 2013, Vol. 87 part 2, p.401-427.

11. 'Intrinsic ergodicity beyond specification : beta-shifts, S-gap shifts, and their factors'
       Joint work with Vaughn Climenhaga, Arxiv version here
       Published in the 'Israel Journal of Mathematics'  2012, Vol.192 part 2, 785-817.

12. 'Irregular sets, the beta-transformation and the almost specification property'
       Published in 'Transactions of the American Mathematical Society', 2012, Vol. 364 no. 10, p. 5395-5414.
       Preprint version here

13. 'A criterion for topological entropy to decrease under normalised Ricci flow'
       Published in 'Discrete and continuous Dynamical Systems, series A', 30(4), 2011.
       Arxiv version here

14. 'The irregular set for maps with the specification property has full topological pressure' 
        Published in 'Dynamical Systems : An International Journal', 25(1), 2010, p.25-51.
        Preprint version here

15. 'A variational principle for topological pressure for certain non-compact sets' 
        Published in 'Journal of the London Mathematical Society', December 2009, Volume 80, part 3, p585-602.
        Preprint version here

16.  'A thermodynamic definition of topological pressure for non-compact sets'
        Published in 'Ergodic Theory and Dynamical Systems', 31(2) 2011, pp. 527-547
        Preprint version here



Upcoming Talks and travels: 

Talks:


For abstracts of the talks (when I was organised enough to add them to this list), click here
Conferences Organised:

Midwest Dynamical Systems Meeting at Ohio State, October 2015. The conference website is here. An archive of past MWDS conferences is here.

AMS special session on Dynamical Systems:Thermodynamic formalism and connections with geometry, Western sectional meeting in Boulder, Colorado, April 2013.

Chaotic Properties of Dynamical Systems, University of Warwick, August 2007.

Past Awards and Grants:
Thesis:

Broadly speaking, the subject of my thesis was dimension theory in dynamical systems and thermodynamic formalism. The main results from my thesis are included in some of the early publications and preprints listed above. The whole thing is here: Thesis.


Other Scholarly Activities:
  • Organiser of the Ohio State Ergodic Theory and Probability Seminar, 2012 - Present

  • Organiser of the Ohio State Math Department Colloquium, 2013-2014; Co-organiser 2016-2017

  • Organiser of the Penn State Center for Dynamics and Geometry seminar, 2009 - 2011

  • Reviewer for the National Science Foundation (USA) and FONDECYT (Chile)

  • Reviewer for journals including 'Inventiones Mathematicae', 'Transactions of the American Mathematical Society', 'Journal of the European Mathematical Society', 'Proceedings of the American Mathematical Society', 'Advances in Mathematics', 'Israel Journal of Mathematics', ‘Monatshefte fur Mathematik’, 'Journal of the London Mathematical Society', 'Journal of Functional Analysis', 'Dynamical Systems: An International Journal', ‘AMS Contemporary Math Series’, 'Journal of Modern Dynamics', ‘Ergodic Theory and Dynamical Systems’, ‘Stochastics and Dynamics’, ‘Geometry and Topology’, ‘Non-Linearity’ and ‘Topology and its Applications’

  • Co-organiser (with Mark Pollicott) of Dynamical Systems seminar, University of Warwick, 2008-2009