Click here for my homepage and contact information.

About me (in brief):

I am currently a Chowla Research Assistant Professor in the Mathematics Department of Penn State University. I am 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, dynamical systems and geometry. I am an organiser of the Center for Dynamics and Geometry seminar at Penn State. My research is supported by an NSF grant. From Fall 2012, I will be Assistant Professor at the Ohio State University.

Research Interests (in brief):

My main research area are ergodic theory, dynamical systems and geometry.  Within this huge field, I have a number of specialities -  At the intersection of ergodic theory and dynamical systems, I study symbolic dynamics, thermodynamic formalism and dimension theory. At the intersection of dynamical systems and geometry, I study geodesic flows and dynamical invariants of manifolds. I have recently worked on the implementation of ideas related to my pure research in the applied setting of Bioinformatics.

I am currently very interested in a series of questions related to the evolution of ergodic properties of surfaces (and higher-dimensional manifolds) under geometric flows such as the Ricci flow. Another ongoing project is to develop the theory of thermodynamic formalism in the context of the Teichmuller flow and various related discrete times systems.  Both of these projects rely on, and are inspired by, the rich interplay between dynamics and geometry.

Current Grants:

I am the Principle Investigator for NSF grant DMS-1101576. The project is entitled 'Thermodynamic Formalism and Dynamical Systems Arising from Geometry'.

Preprints: (Also available at my arXiv page here)

1. 'Intrinsic ergodicity via obstruction entropies'
       Joint work with Vaughn Climenhaga, Arxiv version here

2. 'Topological pressure and coding sequence density estimation in the human genome'
       Joint work with David Koslicki, Arxiv version here


Published Papers and Papers Accepted for Publication:


1. 'Equilibrium states beyond specification and the Bowen property'
       Joint work with Vaughn Climenhaga, Arxiv version here
       To appear in 'Journal of the London Mathematics Society'

2. 'Intrinsic ergodicity beyond specification : beta-shifts, S-gap shifts, and their factors'
       Joint work with Vaughn Climenhaga, Arxiv version here
       To appear in the 'Israel Journal of Mathematics' 

3. 'Irregular sets, the beta-transformation and the almost specification property'
       To appear in 'Transactions of the American Mathematical Society', published online.
       Preprint version here

4. '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

5. '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

6. '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

7.  '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


Thesis:

Broadly speaking, the subject of my thesis was dimension theory in dynamical systems and thermodynamic formalism. For a little informal information about my thesis, click here. For the formal abstract, click here. For the whole thing, click Thesis. The main results from my thesis are included in some of the publications and preprints listed above. The thesis version contains extra exposition and includes an additional 'Techniques' chapter.

Upcoming Talks:

To be announced Talks Given:

For abstracts of the talks, click here

Conferences Organised:

Chaotic Properties of Dynamical Systems, 20-24 August 2007, University of Warwick.

Past Awards and Grants:
Other Scholarly Activities:
Invited Research Visits:

Northwestern University, July 2010
Northwestern University, October 2008                          
Penn State University, March 2008.