Positions

• Louisiana State University.
  
  Associate Professor (tenured), 2017 – 2021.
  Assistant Professor, 2011 – 2017.
• Mathematical Sciences Research Institute / Princeton University.
  
  National Science Foundation-funded Postdoctoral Fellow / Visiting Research Fellow (administered by MSRI), 2009 – 2011.
• Massachusetts Institute of Technology.
  
  C.L.E. Moore Instructor, 2006 – 09.

Education

• University of Wisconsin at Madison.
  
  Ph.D. in Mathematics, 2006
  Advisor:  Ken Ono
  Thesis: "Congruences for the coefficients of modular forms and applications to number theory."  (pdf)
  
  M.S. in Mathematics, 2003.
• Harvey Mudd College.
  
  B.S. in Mathematics with Highest Distinction, 2001. 

Research Interests

1. The theory of automorphic forms, including modular forms, mock modular forms and harmonic Maass forms;
2. Applications of automorphic forms to other areas of mathematics, including the theory of partitions and basic hypergeometric series, bootstrap percolation models, affine Lie superalgebras, Markov processes;
3. Algebraic and finite combinatorics, including graph theory, Catalan-type structures, abelian sandpiles, combinatorial probability
4. Nonstandard analysis and analytic number theory   

Publications

See Publications page for full list of 41 refereed journal articles and 0 preprint(s).

Selected Talks, Conferences, and Workshops

• “Statistics for unimodal sequences of integers”, Special Session on Partition Theory and Related Topics, American Mathematical Society Sectional Meeting, University of Florida, Gainesville, November 2, 2019.
• “The extreme-value variance estimator”, Louisiana State University Health Sciences Center, Biostatistics Colloquium, October 28, 2019.
• “Characters of affine Lie Algebras and Sum-Product identities”, Hong Kong Number Theory Days, July 16, 2019.
• “Quantum Invariants and Quantum Modularity”, Hong Kong Number Theory Days, July 9, 2019.
• “Sum-product identities, partition identities, and affine Lie algebras”, Seminar, Research Institute for Symbolic Computation, January 30, 2019.
• “Statistics for unimodal sequences”, SFB Colloquium, Research Institute for Symbolic Computation, January 29, 2019.
• "Quantum dimensions and characters for vertex operator algebras", Conference on Modular Forms and Related Topics, American University of Beirut, May 28, 2018.
• "Asymptotic analysis of partial theta functions", Special Session on Real-Analytic Automorphic Forms, American Mathematical Society Sectional Meeting, University of North Texas, Denton, September 9, 2017.
• Nonstandard Methods in Combinatorial Number Theory, Workshop, American Institute of Mathematics, August 14--18, 2017.
• Recent Developments in Analytic Number Theory, Workshop, Mathematical Sciences Research Institute, May 1--5, 2017.
• "Alladi's work on Schur's second partition theorem and universal mock theta functions", Alladi 60 Conference, University of Florida, March 20, 2016.
• "Classical partition identities and automorphic forms. I. Introduction to classical partition identities. II. Automorphic properties. III. Additional discussion."  Number Theory Seminar, Korea Institute for Advanced Study, July 6--8, 2015.

Grants and Fellowships

• Louisiana Board of Regents Enhancement Grant 04MATH-14 (co-PI), 2014 – 2016.  PI: Peter Wolenski, LSU.
• NSF Conference Grant DMS-1363265 (Co-PI), 2014.  PI: Ling Long, LSU.
• NSF Individual Research Grant DMS-1201435 (PI), 2012 – 2015.
• Louisiana State University Council on Research Summer Stipend, 2012.
  
  
• Humboldt Foundation Foreign Research Fellowship, 2010 – 2012.
  
  
• NSA Young Investigator Grant (PI), 2008 – 2010.
  
  
• Clay Math Foundation Liftoff Fellow, 2006.
  
  
• Recommended for National Science Foundation Postdoctoral Research Fellowship, 2006.
  
  
• National Science Foundation Graduate Research Fellowship, 2002 – 2005.
  
  

Honors and Awards

• LSU Alumni Association Faculty Excellence Award, 2018 (ceremony)
  Recognizes outstanding teaching, research, and service; 4 awards given annually campus-wide
• Tiger Athletic Foundation Undergraduate Teaching Award, 2018
  
  
• Inaugural PNAS Paper of the Year Award, presented at the National Academy of Sciences, 2006.
  
  

Teaching

• MATH 7230 (Class Field Theory), LSU, Fall 2019.
• MATH 7230 (Algebraic Number Theory), LSU, Fall 2018.
• MATH 4345 (Special Functions), LSU, Fall 2018 Fall 2019.
• MATH 7230 (Partitions, Hypergeometric q-series, and Modular Forms), LSU, Fall 2017.
• MATH 4158 (Foundations of Mathematics), LSU, Fall 2016 Fall 2017.
  
  
• MATH 4200 (Abstract Algebra I), LSU, Fall 2015.
• MATH 7230 (Analytic Number Theory), LSU, Spring 2014 Spring 2018.
• MATH 7210 (Algebra I), LSU, Fall 2013 Fall 2014 Fall 2015.
• MATH 3903 (Methods of Problem Solving), LSU, Fall 2013 Fall 2014 Fall 2015 Fall 2016 Fall 2017 Spring 2018 Fall 2018 Fall 2019.
• MATH 7290 (Elliptic Curves and Modular Forms), LSU, Spring 2013.
• MATH 3355 (Probability), LSU, Fall 2012 Fall 2017.
• MATH 2020 (Solving Discrete Problems), LSU, Fall 2011 Fall 2012.
  
  
• MATH 4181 (Elementary Number Theory), LSU, Fall 2011.
  
  
• Math 18.01 (Single Variable Calculus), MIT, Spring 2009.
  
  
• Math 18.781 (Introduction to the Theory of Numbers), MIT, Fall 2008.
  
  
• Math 18.786 (Algebraic Number Theory), MIT, Spring 2008.
  
  
• Math 18.02 (Multivariable Calculus) Recitations, MIT, Fall 2007.
  
  
• Math 18.02A (Multivariable Calculus), MIT, Spring 2007.
  
  
• Math 18.01A/18.02A (Calculus) Recitations, MIT, Fall 2006.
  
  
• Math 217 Recitations (Calculus with Algebra and Trigonometry II), UW-Madison, Spring 2005.
  
  
• Math 171 Recitations (Calculus with Algebra and Trigonometry I), UW-Madison, Fall 2004.
  
  

Research Advising and Directed Reading

Undergraduate Students:
            Brandon Roberts, Directed Reading: “Algebraic Geometry”, LSU, Spring 2019
            Brandon Roberts, Directed Reading: “Analytic Number Theory”, LSU, Fall 2018.
            Thomas Ayton, Abel Lopez, Connor Sanford, Aubrey Stewart, Richard Tuminello: Submitted solutions to Problems in The American Mathematical Monthly, MATH 3903, LSU, Spring 2018.
            Derek Walker, Directed Reading: “Elementary Number Theory”, LSU, Spring 2015
            Paxton Turner, Directed Reading: "Partitions, q-series, and Analytic Techniques in Number Theory", LSU, Fall 2013.
            Ethan Sterling, Directed Research: "The Bounded Thrackle Conjecture", Undergraduate Research Opportunities Program, MIT, Summer 2008.
            Matthew Garcia, Directed Reading: "An Adelic Approach to Class Field Theory", Undergraduate Research Opportunities Program, MIT, Spring 2008.
            Alex Arkhipov, Directed Reading/Research: "Combinatorial Partition Theory", Undergraduate Research Opportunities Program, MIT, Summer 2007.
            Assistant Instructor for UW-Madison Research Experience for Undergraduates, Summer 2005, 2006.

Graduate Students:

• Richard Frnka - Ph.D. awarded May 2017
  Dissertation: "Asymptotic formulae for unimodal sequences with congruence relations" ETD link
  
  First Position after Ph.D.: Chief Technical Officer at CleverSolve

• Walter Bridges – Ph.D. awarded August 2020.
  Dissertation: “Combinatorial and Asymptotic Statistical Properties of Partitions and Unimodal Sequences and Unimodal Sequences”. LSU Digital Commons
  
  First Position after Ph.D.: Postdoctoral Researcher, University of Cologne, Germany
  
  
• Irfan Alam – Ph.D. awarded August 2021.
  Dissertation: “Applications of Nonstandard Analysis in Probability and Measure Theory”. LSU Digital Commons
  
  First Position after Ph.D.: Hans Rademacher Instructor, University of Pennsylvania

• Shashika Petta Mestrige – Ph.D. awarded December 2021.
  Dissertation: “Congruences Between Coefficients of a Class of Eta-Quotients and their Applications to Combinatorics”. LSU Digital Commons
  
  First Position after Ph.D.: Assistant Professor, Vermont Technical College

 

Professional Activities

• Co-Organizer for Conference: Southern Number Theory Conference, held at LSU, Apr. 13–14, 2019.
• Co-Organizer and Co-PI for Conference: Southern Number Theory Conference, held at LSU, Apr. 8–9, 2017.
• Co-Organizer and Co-PI for Conference: Applications of Automorphic Forms in Number Theory and Combinatorics, held at LSU, Apr. 12–15, 2014.
• Departmental Committees at LSU: Internal Review Committee (2012 – 2013); Executive Committee (2012 – 2013, 2015 – 2016);
• Organizer for Undergraduate Problem-Solving Seminar, LSU, 2011 – 2019.
• Co-Organizer for Algebra and Number Theory Seminar, LSU, 2011 – 2013.
• Member of The American Mathematical Society, 2002+, intermittently.
• Member of the Mathematical Association of America, 2018 – .
• Referee work for: Advances in Mathematics; American Mathematical Monthly; Annals of Combinatorics; Ars Combinatoria; Arxiv der Mathematik; Colloquium Mathematicum; Discrete Mathematics; Electronic Journal of Combinatorics; European Journal of Combinatorics; Forum of Mathmematics, Sigma; INTEGERS - Electronic Journal of Combinatorial Number Theory; International Journal of Number Theory; Journal für die Reine und Angewandte Mathematik; Journal of Combinatorial Theory Series A; Journal of Cryptology; Journal of Integer Sequences; Journal of Number Theory; Journal of the London Mathematical Society;  Mathematical Proceedings of the Cambridge Philosophical Society; Mathematical Research Letters; Proceedings of the American Mathematical Society; Proceedings of the National Academy of Sciences; The Ramanujan Journal; Springer Conference Proceedings in Mathematics (51 total papers refereed).
• Grant Reviews for: National Science Foundation, National Security Agency.
• Reviewer for the American Mathematical Society Mathematical Reviews Database.

 

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