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 Burns, Vaughn 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:

- RTG seminar, Geometry seminar, and Math Circle, University of
Michigan, March 2018

- Organiser, Conference on Thermodynamic formalism in dynamical
systems, ICMS, Edinburgh, June 2018

Talks:

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

- Math Department Colloquium, Michigan State University, February 2018

- Math Department Colloquium, University of North Texas (Denton),
December 2017

- Seminar, University of Houston, October 2017

- Speaker, Penn State Dynamical Systems Workshop, Pesin 70th
Birthday Event, October 2017

- Bowen's notebook problem session, Conference in honor of Rufus
Bowen, UBC (Canada), August 2017

- Special Session, Mathematical Congress of the Americas,
Montreal (Canada), July 2017

- Conference on Thermodynamic Formalism, Bremen (Germany), July 2017
- Dynamics seminar, Imperial College (UK), July 2017

- Special Session, Joint Mathematical Meetings, Atlanta, January 2017
- RTG Working Seminar on Geometry, Dynamics and Topology, University of Michigan, December 2016

- Speaker, Maryland-Penn State Workshop on Dynamical Systems, Penn State, November 2016
- Dynamics seminar, Penn State, September 2016
- Math Department Colloquium, City College of New York, September 2016
- Ergodic theory seminar, Ohio State, September 2016

- Speaker, Conference on statistical properties of nonequilibrium dynamical systems, SUSTC, Shenzhen, China, July 2016
- Ergodic theory seminar, Warwick University, July 2016

- Seminar, Wesleyan University, March 2016

- Geometry Seminar, Yale University, March 2016

- Seminar, University of Michigan, February 2016

- Dynamics seminar, University of Houston, December 2015

- Dynamics seminar, Brigham Young University, December 2015

- Analysis seminar, University of Utah, December 2015

- Mini-course Speaker, University of Warwick, 28-30 July 2015

- Speaker, LMS One Day Meeting, University of Bristol, 17 June 2015

- Special session speaker, AMS-EMS-SPM International Meeting (A=American, E=European, P=Portuguesa), Porto (Portugal), 10-13 June 2015
- Speaker, Conference in honor of Chernov, University of Alabama Birmingham, May 2015

- Dynamics seminar, University of Chicago, April 2015
- Center for Dynamics and Geometry Colloquium, Penn State, March 17 2015

- Special session speaker, AMS Sectional meeting, Michigan State University, March 14-15 2015
- Ohio State, Topology, Geometry, and Data Analysis seminar, December 2014
- Pingree Park Dynamics Workshop, Mini-course speaker, Pingree Park, Colorado, July 2014
- ICIAM (International Council for Industrial and Applied Mathematics) 2014 Scientific Workshop, Mathematical Biosciences Institute, Ohio State, May 2014
- St. Andrews (Scotland), Pure mathematics colloquium, April 2014
- University of Warwick, Ergodic theory seminar, April 2014

- British Mathematical Colloquium
(London, UK), Ergodic theory special session, April 2014

- AMS Eastern sectional meeting, University of Maryland
(Baltimore), Special session on 'Substitiution and tiling
dynamical systems', March 2014

- IUPUI, Ergodic Theory seminar, November 2013

- Midwest
Dynamical Systems Conference, University of Illinois Urbana-Champaign,
November 2013

- Mathematical Congress of the Americas, Guanajuato (Mexico), Special Session on Symbolic Dynamics, August 2013;
- PUC, Santiago (Chile), Conference on Thermodynamic Formalism and applications, July 2013;
- Harvard University, Dynamics Reading Group, March 2013;
- Yale University, Dynamics of Group Actions Seminar, March 2013;
- Boston University, Dynamical Systems Seminar, March 2013;
- Penn State, Dynamical Systems and Geometry seminar, January 2013;
- University of Houston, Dynamical Systems seminar, December 2012;
- Northwestern University, Dynamics Seminar, November 2012;
- University of Chicago, Dynamics seminar, November 2012;
- Conference on non-commutative geometry and ergodic theory, Ohio
State Univerity, 16th May 2012

- AMS Eastern sectional meeting, 17th March 2012, George Washington University, Special Session on Dynamics of Complex Networks, 'Topological pressure and a priori coding sequence density estimation in the human genome'
- Penn State Undergraduate Math Club, February 2012

- Math Department Colloquium, University of Southern California, January 20th 2012
- Joint Mathematics Meeting, Boston, Special session on uniformly and partially hyperbolic dynamical systems, January 2012, 'Uniqueness of Equilibrium States: Constructive techniques in a non-uniform, non-Markov setting'
- Penn State, Seminar on Mathematics in the Bio and Geo Sciences, November 2011, 'Topological pressure and a priori coding sequence density estimation in the human genome'
- Penn State, Dynamical Systems seminar, October 2011

- Goettingen-Penn State International Summer School on Dynamical Systems, Goettingen, Germany, August 2011
- University of Warwick, Dynamical Systems seminar, August 2011

- Equadiff 2011 at University of Loughborough, UK, Special session on Statistical properties of dynamical systems, August 2011
- City University of New York, May 2011, 'Uniqueness of equilibrium states: Beta-shifts, the Bowen property and Beyond'
- University of Washington, Rainwater Seminar (Dynamics and Analysis), April 2011, 'Distinguished invariant measures for Beta-shifts and their factors'
- Microsoft Research, April 2011, 'Distinguished invariant measures for Beta-shifts and their factors'
- University of Maryland, Dynamical Systems conference, April 2011, 'Uniqueness of equilibrium states: Beta-shifts, the Bowen property and Beyond'
- University of Toronto, Dynamics seminar, February 14th, 2011, 'Subshift factors of the beta-shift are intrinsically ergodic'
- Penn State, Logic seminar, December 2010, 'Topological pressure for non-compact sets, Kamae entropy and Kolmogorov complexity'
- University of Richmond (2010 AMS Fall Southeastern meeting), November 2010, 'Subshift factors of the beta-shift are intrinsically ergodic'
- Penn State 'Workshop in Dynamical Systems and Related Topics', October 2010, 'Subshift factors of the beta-shift are intrinsically ergodic'
- Rice university, Ergodic theory seminar, April 2010, 'A criterion for topological entropy to decrease under normalised Ricci flow'
- Rice university, Special ergodic theory seminar for graduate
students, April 2010, 'Dynamical properties of arbitrary beta-shifts
and related systems via weak specification properties'

- University of Maryland, Dynamics seminar, March 2010, 'A criterion for topological entropy to decrease under normalised Ricci flow'
- University of Maryland, Student dynamics seminar March 2010,
'Weak
specification properties for beta-transformations and quasi-hyperbolic
toral automorphisms'

- Northwestern University, February 2010, 'A criterion for topological entropy to decrease under normalised Ricci flow'
- Penn State, February 2010, Working geometry seminar
(expository), 'Interpretation and applications of topological entropy
in geometry'

- Yale University, February 2010, 'A criterion for topological entropy to decrease under normalised Ricci flow'
- Penn State, December 2009, title 'Monotonicity of topological entropy under normalised Ricci flow'
- Penn State, Dynamical Systems seminar, October 2009: 'The irregular set for the beta transformation carries full topological entropy (= log beta) and full Hausdorff dimension (=1)'
- Boston University, Dynamical Systems seminar, October
2009 : 'The irregular
set for the beta transformation carries full topological entropy (= log
beta) and full Hausdorff dimension (=1)'

- University of Surrey, Seminar (part of themed semester in ergodic theory), March 2009: 'Another look at topological pressure for non-compact sets'
- Warwick Mathematics Institute, London Mathematical Society one day ergodic theory meeting, January 2009: 'The irregular set for the beta transformation carries full topological entropy (= log beta)'
- Northwestern University, Dynamical Systems Seminar, October 2008: 'The irregular set for the beta transformation carries full topological entropy (= log beta)'
- Penn State
University, Maryland-Penn State Workshop on Dynamical Systems, October
2008: 'The Liouville entropy of a 3-manifold is not
monotonic along the Ricci flow'

- University of
Maryland, Maryland-Penn State Workshop on Dynamical Systems, March
2008: 'The Irregular Set for Maps with the
Specification Property Carries Full Topological Pressure'

- Warwick Mathematics Institute, Dynamical Systems Seminar,
January
2008: ‘A Thermodynamic Definition of Topological Pressure for
Non-Compact Sets'

- Manchester University, Dynamical Systems Seminar, November
2007:
‘A Thermodynamic Definition of Topological Pressure for Non-Compact
Sets'

- Warwick
Mathematics Institute, Conference ‘Chaotic Properties of Dynamical
Systems’, August 2007: ‘The Irregular Set for Maps with
the Specification Property carries Full Entropy’

- Warwick Mathematics Institute, Postgraduate Seminar,
November 2006: 'The Multifractal Miracle: Multifractal Analysis in
Symbolic Dynamics'

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:

- 2011-2015, NSF "standard" grant

- August 2007, ASSEC Conference Competition, Winner (with Thomas Jordan) of University of Warwick ASSEC (American Study and Student Exchange Committee) Conference Competition to organise conference 'Chaotic Properties of Dynamical Systems', Warwick Mathematics Institute.

- August 2007, Awarded London Mathematical Society Scheme 1 Conference Grant to support the conference 'Chaotic Properties of Dynamical Systems'

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: