Click here for my homepage and contact information. Last updated: June 12th 2017.

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.

In 2017-2018, I will be an organiser/mentor (with Jon Chaika, Vaughn Climenhaga, Boris Hasselblatt and Bryna Kra) for an AMS Mathematics Research Community. See here for more details.

Research Interests (in brief):

My main research area is ergodic theory and dynamical systems, particularly the 'entropy theory' of this subject.  I have also recently 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. 'Fat flats in Rank-one manifolds''
Joint work with Dave Constantine, Jean-Francois Lafont and Ben McReynolds
Arxiv version here, 23 pages, 1 figure

3. 'Unique equilibrium states for Bonatti-Viana diffeomorphisms'
Joint work with Vaughn Climenhaga and Todd Fisher
Arxiv version here, 40 pages

4. 'Unique equilibrium states for Mane diffeomorphisms'
Joint work with Vaughn Climenhaga and Todd Fisher
Arxiv version here, 27 pages

5. 'The weak specification property for geodesic flows on CAT(-1) spaces'
Joint work with Dave Constantine and Jean-Francois Lafont
Arxiv version here, 33 pages, 2 figures


Published Papers and Papers Accepted for Publication:


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

2. '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.

3. 'Large deviations for systems with non-uniform structure'
       Joint work with Vaughn Climenhaga and Kenichiro Yamamoto, To appear in Trans. Amer. Math. Soc., Arxiv version here

4. '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

5. '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

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

7. '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.

8. '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

9. '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

10. '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

11. '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

12.  '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: 

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 from 30th October to 1st November. 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, 20-24 August 2007, University of Warwick.

    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: