## Karl Mahlburg

320 Lockett Hall
Department of Mathematics

Louisiana State University
Baton Rouge, LA 70803

Office: (225) 578-1609
Department: (225) 258-1665

e-mail: mahlburg (at) math (dot) lsu (dot) edu
Internet: www.math.lsu.edu/~mahlburg

### Positions

• Louisisana State University.

Associate Professor, 2017
Tenure-track Assistant Professor, 2011 – 2017.

• Mathematical Sciences Research Institute / Princeton University.

National Science Foundation-funded Postdoctoral Fellow /  Visiting Research Fellow 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

 [23] K. Bringmann, J. Lovejoy, K. Mahlburg, "A partition identity and the universal mock theta functions $g_2$", to appear in Mathematical Research Letters. [22] K. Bringmann, K. Mahlburg, "Asymptotic formulas for stacks and unimodal sequences", Journal of Combinatorial Theory (A) 126 (2014), 194–215. arXiv [21] M. Di Nasso, I. Goldbring, R. Jin, S. Leth, M. Lupini, K. Mahlburg, "Progress on a sumset conjecture of Erdös", Canadian Journal of Mathematics, dx.doi.org/10.4153/CJM-2014-016-0. arXiv [20] K. Bringmann, J. Lovejoy, K. Mahlburg, "On q-difference equations for partitions without k-sequences", Proceedings of The Legacy of Ramanujan Conference, Ramanujan Mathematical Society Lecture Notes 20, 2013, pp. 129–137. [19] K. Mahlburg, C. Smyth, "Symmetric polynomials and symmetric mean inequalities" , Electronic Journal of Combinatorics 20 (2013), P34, 14 pp. [18] K. Bringmann, A. Folsom, K. Mahlburg, "Quasimodular forms and $s\ell(m|m)^\wedge$ characters", to appear in the Ramanujan Journal, special volume in honor of Basil Gordon. ( [17] K. Bringmann, K. Mahlburg, "Asymptotic inequalities for positive crank and rank moments", Transactions of the American Mathematical Society 366 (2014), 1073–1094. pdf ps [16] K. Bringmann, K. Mahlburg,  "Asymptotic formulas for coefficients of Kac-Wakimoto characters", Mathematical Proceedings of the Cambridge Philosophical Society 155 (2013), 51 - 72. [15] K. Bringmann, K. Mahlburg, R. Rhoades, "Taylor coefficients of mock-Jacobi forms and moments of partition statistics", Mathematical Proceedings of the Cambridge Philosophical Society, 157 (2014), 231–251. pdf ps [14] K. Bringmann, A. Holroyd, K. Mahlburg, M. Vlasenko, "k-run overpartitions and mock theta functions", Quarterly Journal of Mathematics (2013), 64 (2013), 1009–1021. doi:10.1093/qmath/has019. arXiv pdf ps [13] K. Bringmann, K. Mahlburg, A. Mellit, "Convolution bootstrap percolation models, Markov-type stochastic processes, and mock theta functions", International Mathematics Research Notices 2013; 971–1013. pdf ps [12] K. Bringmann, K. Mahlburg, "Improved bounds on metastability thresholds and probabilities for generalized bootstrap percolation", Transactions of the American Mathematical Society 364 (2012), 3829–3859. arXiv pdf ps [11] K. Bringmann, K. Mahlburg, R. Rhoades, "Asymptotics for crank and rank moments", Bulletin of the London Mathematical Society 43 (2011), 661–672. arXiv pdf ps [10] T. Kemp, K. Mahlburg, A. Rattan, C. Smyth, "Enumeration of noncrossing pairings on bit strings", Journal of Combinatorial Theory (A) 118 (2011), 129–151. arXiv [9] K. Bringmann, K. Mahlburg, "A generalization of the Hardy-Ramanujan circle method and applications to partitions without sequences", American Journal of Mathematics 133 (2011), 1151–1178. [8] K. Bringmann, K. Mahlburg, "Inequalities between crank and rank moments", Proc. Amer. Math. Soc. 137 (2009), no. 8, 2567–2574. pdf ps [7] K. Bringmann, F. Garvan, K. Mahlburg, "Partition statistics and quasiharmonic Maass forms", Int. Math. Res. Not., 2009, no. 1, 63–97. arXiv pdf ps [6] K. Mahlburg, "Partition congruences and the Andrews-Garvan-Dyson crank," Proceedings of the National Academy of Sciences 102 (2005), no. 43, 15373–76. pdf ps [5] K. Mahlburg, "More congruences for the coefficients of quotients of Eisenstein series,'  Journal of Number Theory 115 (2005), no. 1, 89–99. pdf ps [4] K. Mahlburg, 'The overpartition function modulo small powers of 2,' Discrete Mathematics 286 (2004), no. 3, 263–267. pdf ps [3] K. Mahlburg, K. Ono, "Arithmetic of certain hypergeometric modular forms," Acta Arithmetica 113 (2004), no. 1, 39–55. pdf ps [2] J. Getz, K. Mahlburg, "Partition identities and a theorem of Zagier," Journal of Combinatorial Theory (A) 100 (2002), 27–43. pdf ps [1] A. Benjamin, G. Levin, K. Mahlburg, J. Quinn, "Random approaches to Fibonacci identities," The American Mathematical Monthly 107 (2000), 511–16.

### Colloquia and Plenary Talks

• "Asymptotic formulas for unimodal sequences", Colloquium, College of Charleston, September 12, 2014.

• "Inequalities for positive crank and rank moments", Delegate speaker, Legacy of Ramanujan Conference, University of Delhi, India, December 19, 2012.

• "Percolation, probability, and partitions", Colloquium, University of North Texas, May 2, 2011.
• "Percolation, probability, and partitions", Colloquium, Wesleyan University, April 21, 2011.
• "Noncrossing partitions and general Catalan objects", Colloquium, University of Talca, Chile, December 9, 2010.

• “Partitions, probability, and percolation”, Prospects in q-series and modular forms Conference, University College, Dublin, Ireland, July 14, 2010.

• “Asymptotics for crank and rank moments”, International Conference on number theory and mock theta functions, SASTRA University, Kumbakonam, India, December 22, 2009.

• "The arithmetic of the coefficients of automorphic forms and applications in number theory", Colloquium, University of Talca, Chile, March 3, 2009.

• "Modular forms in number theory," Mathematics Colloquium, Harvey Mudd College, December 7, 2006.

• "The Andrews-Garvan-Dyson crank and partition congruences," Colloquium, Temple University, January 23th, 2006.

• "The Andrews-Garvan-Dyson crank and partition congruences," Plenary address, International Conference on Number Theory and Mathematical Physics and SASTRA Ramanujan Award Presentation, Kumbakonum, India, December 20-22, 2005.

### Selected Seminars and Invited Talks

• "Analytic and Combinatorial study of Schur's Second Partition Theorem", Combinatorics Seminar, University of Minnesota, May 2, 2014.

• "Schur's partition theorem and mixed mock modular forms", Number Theory Seminar, University of Illinois, November 19, 2013.

• "Markov processes and q-series", Symposium on modular forms, mock theta functions, and applications, University of Cologne, Germany, March 1, 2012.
• "Coefficient asymptotics for Kac-Wakimoto characters", NY Workshop on the Symmetric Group, Graduate Center of the City University of New York, September 9, 2011.
• "Mock Jacobi forms and moment asymptotics", School and Conference on Modular Forms and Mock Modular Forms and their Applications in Arithmetic, Geometry and Physics, The Abdus Salam International Center for Theoretical Physics, Trieste, Italy, March 14, 2011.
• "Mock modular forms and coefficient asymptotics for characters of affine Lie superalgebras", First International Meeting of the American Mathematical Society and the Socidedad de Matematica de Chile, Universidad of Frontera, Pucón, Chile, Dec. 17, 2010.

• "Percolation, Probability, and Partitions", Number Theory Seminar, Yale University, October 19, 2010.
• "q-series, a mock theta function, and probability", Number Theory Seminar, Max Planck Institue, Bonn, July 28, 2010.

• “Percolation, Probability, and Partitions”, Research Seminar, Microsoft Research Theory Group, Seattle, May 13, 2010.

• "Mock theta functions, q-series, combinatorial probability, and percolation models", Algebra Seminar, Emory University, February 4, 2010.

• "Asymptotics for crank and rank moments", International Conference on mock theta functions and applications in combinatorics, algebraic geometry, and mathematical physics, Max Planck Mathematical Institute, May 26, 2009.

• "Asymptotics for crank and rank moments", Number Theory Seminar, Johns Hopkins University, April 14, 2009.

• "Arithmetic of the coefficients of automorphic forms", Number Theory Seminar, Princeton University, October 23, 2008.

• "Asymptotics for partitions without sequences," Quebec-Vermont Number Theory Seminar, McGill University, April 17, 2008.

• "Partitions statistics and weak Maass forms," Number Theory Seminar, Massachusetts Institute of Technology, October 11, 2007.

• "Durfee symbol congruences and higher rank moments," Combinatorics Seminar, Pennsylvania State University, August 22, 2007.

• "The Andrews-Garvan-Dyson crank and partition congruences," Algebra Seminar, Massachusetts Institute of Technology, October 11, 2006.

• "The Andrews-Garvan crank and partition congruences," Joint Combinatorics and Number Theory Seminar, Ohio State University, May 11th, 2005.

• "The Andrews-Garvan crank and partition congruences," Combinatorics Seminar, University of Pennsylvania, March 29th, 2005.

• "Cranks revisited and higher partition congruences," Special Year in Mathematics Additive Number Theory Conference, University of Florida, Gainesville, November 2004.

• "Partition identities and a theorem of Zagier," Combinatorics Seminar, University of Wisconsin-Madison, Spring 2002.

### Grants and Fellowships

• Louisiana Board of Regenets 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 Program, 2006.

• Recommended for National Science Foundation Postdoctoral Research Fellowship, 2006.

• National Science Foundation VIGRE Fellowship, 2001 – 02, 2005 – 2006.

• National Science Foundation Graduate Research Fellowship, 2002 – 2005.

### Honors and Awards

• Inaugural PNAS Paper of the Year Award, presented at the National Academy of Sciences, 2006.

• Excellence in Mathematical Research Award, University of Wisconsin Mathematics Department, 2005.

### Teaching

• MATH 4181 (Elementary Number Theory), Louisiana State University, Fall 2001.
• 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.

### Directed Research and Advising

• 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.

### Professional Activities

• 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 – );

• Co-Organizer for Putnam Examination Problem Sessions, LSU, 2011 – .

• Co-Organizer for Algebra and Number Theory Seminar, LSU, 2011 – .

• Student member of Graduate Program Committee, UW-Madison, 2005 – 2006.

• Member of The American Mathematical Society, 2003 – .

• Member of the UW-Madison Teaching Assistant's Association, 2005.

• Reviewer for the American Mathematical Society Mathematical Reviews Database (15 reviews written).

• Advances in Mathematics, American Mathematical Monthly, Annals of Combinatorics, Ars Combinatoria, Discrete Mathematics, Electronic Journal of Combinatorics, European Journal of Combinatorics, INTEGERS - Electronic Journal of Combinatorial 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, London Mathematical Society, Mathematical Research Letters, Proceedings of the American Mathematical Society, Proceedings of the National Academy of Sciences, The Ramanujan Journal; (33 total papers refereed).