Click here for my homepage and contact
information. Last updated: December 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
20092012, 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 active in Outreach, particularly in developing programs
for mathematics and STEM education for K12 students from
underrepresented groups. I am a regular contributor of mathematical
content to various activities run by the Ohio State Young
Scholars Program. In particular, I have regularly contributed
activities to their 9th grade visitation day, and the YSP Summer
Academy for rising 12th graders. I was one of the mathematics director (with my
colleagues John Johnson and Adriana Dawes) for the 2013 '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 workshop on best practices in Graduate Advising at Ohio
State in June 2019; an AIM workshop on 'Equilibrium states for dynamical
systems arising from geometry' in July 2019; a workshop on
dynamical systems
Thermodynamic Formalism: Ergodic Theory and Geometry at Warwick
University celebrating the 60th birthday of Mark Pollicott 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 am coPI on NSF conference grant DMS  1856176 'Midwest Dynamical
Systems Conferences 2019/2020' with Laura DeMarco (PI) and Roland
Roeder. The website for the Midwest Dynamics conference series is here
I previously received NSF support from a 'standard' grant held from 20112015.
I was a participant in an AIM SQuaRE
with Keith Burns, Vaughn
Climenhaga and Todd
Fisher from 20132016. The project was entitled "Equilibrium states for geodesic
flows in nonpositive curvature".
Preprints: (Available at my arXiv
page here)
1. 'Strong symbolic dynamics for geodesic flow on CAT(1) spaces and
other metric Anosov flows'
Joint work with Dave Constantine
and JeanFrancois Lafont
arXiv version here, 25 pages.
Published Papers and Papers Accepted for Publication:
1. 'Measures of maximal entropy for suspension flows over the full shift'
Joint work with Tamara Kucherenko
arXiv version here, 12 pages, To appear
in 'Mathematische Zeitschrift'.
2. 'Unique equilibrium states for geodesic flows in nonpositive
curvature'
Joint work with Keith Burns, Vaughn
Climenhaga and Todd
Fisher
Arxiv version here, 50 pages, Published in 'GAFA', 2018, Vol. 28 issue 5, 12091259.
3. 'The weak specification property for geodesic flows on CAT(1)
spaces'
Joint work with Dave Constantine
and JeanFrancois Lafont
arXiv version here, 30
pages, 2 figures, To appear in Groups, Geometry and Dynamics.
4. 'Fat flats in rank one manifolds'
Joint work with Dave Constantine, JeanFrancois Lafont and Ben McReynolds
Arxiv version here, 23
pages, 1 figure, To appear in 'Michigan Mathematical Journal'.
5. 'Unique equilibrium states for BonattiViana diffeomorphisms'
Joint work with Vaughn
Climenhaga and Todd Fisher
Arxiv version here, 46
pages, Published in 'Nonlinearity', 2018, Vol. 31 issue 6, p,25322577.
6. 'Generalized betatransformations and the entropy of unimodal maps'
Arxiv version here, 24 pages, Published
in 'Commentarii Mathematici Helvetici', 2017, Vol. 92 issue 4, p.777800.
7. 'A suspension flow over the full shift with two distinct measures
of maximal entropy'
Joint work with Tamara Kucherenko
6 pages, Published in 'Topology
Proceedings', 2018, Vol. 52, p.321328.
8. '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'.
9. 'Unique equilibrium states for flows and homeomorphisms with nonuniform structure'
Joint work with Vaughn
Climenhaga, Arxiv version here
Published in 'Advances in Mathematics', 2016, Vol. 303, p.745799.
10. 'Large deviations for systems with nonuniform structure'
Joint work with Vaughn
Climenhaga and
Kenichiro Yamamoto, Arxiv version here
Published in 'Transactions of the
American Mathematical Society', 2017, Vol 369, p.41674192.
11. '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 12, p.4569
12. '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.18161831
13. '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.401427.
14. 'Intrinsic ergodicity beyond specification : betashifts, Sgap
shifts, and their factors'
Joint work with Vaughn
Climenhaga,
Arxiv version here
Published in the 'Israel Journal
of Mathematics' 2012, Vol.192 part 2, 785817.
15. 'Irregular sets, the betatransformation and the almost
specification property'
Published in 'Transactions of the
American Mathematical Society', 2012, Vol. 364 no. 10, p. 53955414.
Preprint version here
16. '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
17. 'The irregular set for maps with the specification property has full
topological pressure'
Published in 'Dynamical Systems :
An International Journal', 25(1), 2010, p.2551.
Preprint version here
18. 'A variational principle for topological pressure for certain
noncompact sets'
Published in 'Journal of the
London Mathematical Society', December 2009, Volume 80, part 3,
p585602.
Preprint version here
19. 'A thermodynamic definition of topological pressure for
noncompact sets'
Published in 'Ergodic Theory and
Dynamical Systems', 31(2) 2011, pp. 527547
Preprint version here
Upcoming Talks and travels:
 Minicourse (6 part) 'Beyond
Bowen's specification property', joint with Vaughn Climenhaga, Beyond
Uniform Hyperbolicity Conference, Luminy (France), May 2019
 Speaker, Maryland Conference on Dynamical Systems, University
of Maryland, April 2019

Participant/Organizer, Workshop on Thermodynamic Formalism, AIM,
San Jose CA, July
2019

Participant/Organizer, Workshop on Thermodynamic Formalism: Ergodic
theory and geometry, University of Warwick, July 2019
Talks, etc:
For abstracts of the talks (when I was organised enough to add them to
this list), click here
 Speaker, Groups Geometry and Dynamics 1day conference,
Indianapolis, February 2019
 Dynamics seminar, University of Houston, February 2019
 Dynamics seminar, Brigham Young University, December 2018
 Geometry and Topology seminar, Boston College, September 2018
 Speaker, William Rowan Hamilton Workshop on Geometry and
Topology, Dublin (Ireland), JulyAugust 2018
 Organizer, Conference on Thermodynamic formalism in dynamical
systems, ICMS, Edinburgh, June 2018
 RTG seminar, Geometry seminar, and Math Circle, University of
Michigan, March 2018
 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, MarylandPenn 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
 Minicourse Speaker, University of Warwick, 2830 July 2015
 Speaker, LMS One Day Meeting, University of Bristol, 17 June 2015
 Special session speaker, AMSEMSSPM International Meeting
(A=American, E=European, P=Portuguesa), Porto (Portugal), 1013 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 1415 2015
 Ohio State, Topology, Geometry, and Data Analysis seminar, December 2014
 Pingree Park Dynamics Workshop, Minicourse 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 UrbanaChampaign,
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 noncommutative 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 nonuniform,
nonMarkov 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
 GoettingenPenn 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: Betashifts, the Bowen property and Beyond'
 University of Washington, Rainwater Seminar (Dynamics and
Analysis), April 2011, 'Distinguished invariant measures for
Betashifts and their factors'
 Microsoft Research, April 2011, 'Distinguished invariant measures
for
Betashifts and their factors'
 University of Maryland, Dynamical Systems conference, April 2011,
'Uniqueness of equilibrium states: Betashifts, the Bowen property and
Beyond'
 University of Toronto, Dynamics seminar, February 14th, 2011,
'Subshift factors of the betashift are
intrinsically ergodic'
 Penn State, Logic seminar, December 2010, 'Topological pressure
for noncompact sets, Kamae entropy and Kolmogorov complexity'
 University of Richmond (2010 AMS Fall Southeastern
meeting), November 2010, 'Subshift factors of the betashift
are intrinsically ergodic'
 Penn State 'Workshop in Dynamical Systems and Related
Topics', October 2010, 'Subshift factors of the betashift 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 betashifts
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 betatransformations and quasihyperbolic
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
noncompact 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, MarylandPenn State Workshop on Dynamical Systems, October
2008: 'The Liouville entropy of a 3manifold is not
monotonic along the Ricci flow'
 University of
Maryland, MarylandPenn 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
NonCompact Sets'
 Manchester University, Dynamical Systems Seminar, November
2007:
‘A Thermodynamic Definition of Topological Pressure for NonCompact
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'
Conferences Organised:
Workshop on Thermodynamic Formalism, ICMS, Edinburgh (Scotland), June
2018. The conference website is here. With Thomas Jordan,
Omri Sarig and Mike Todd.
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. With Keith Burns.
Chaotic
Properties of Dynamical Systems, University of
Warwick, August 2007. With Thomas Jordan.
Past Awards and Grants:
 20112015, 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'
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,
20132014; Coorganiser 20162017
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’, ‘NonLinearity’
and ‘Topology and its Applications’
Coorganiser (with Mark Pollicott) of Dynamical Systems
seminar, University of Warwick, 20082009