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

Education


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), 194215. arXiv pdf ps
[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 pdf ps
[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. 129137. pdf ps
[19] K. Mahlburg, C. Smyth, "Symmetric polynomials and symmetric mean inequalities" , Electronic Journal of Combinatorics 20 (2013), P34, 14 pp. pdf ps
[18] K. Bringmann, A. Folsom, K. Mahlburg, "Quasimodular forms and $s\ell(m|m)^\wedge$ characters", to appear in the Ramanujan Journalspecial volume in honor of Basil Gordon. (pdf ps)
[17] K. Bringmann, K. Mahlburg, "Asymptotic inequalities for positive crank and rank moments", Transactions of the American Mathematical Society 366 (2014), 10731094. arXiv 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. pdf ps
[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), 231251. 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), 10091021. 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; 9711013. 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), 661672. 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 pdf

[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), 11511178. pdf ps

[8]

K. Bringmann, K. Mahlburg, "Inequalities between crank and rank moments", Proc. Amer. Math. Soc. 137 (2009), no. 8, 25672574. pdf ps

[7]

K. Bringmann, F. Garvan, K. Mahlburg, "Partition statistics and quasiharmonic Maass forms", Int. Math. Res. Not., 2009, no. 1, 6397. 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, 1537376. pdf ps

[5]

K. Mahlburg, "More congruences for the coefficients of quotients of Eisenstein series,'  Journal of Number Theory 115 (2005), no. 1, 8999. pdf ps

[4]

K. Mahlburg, 'The overpartition function modulo small powers of 2,' Discrete Mathematics 286 (2004), no. 3, 263267. pdf ps

[3]

K. Mahlburg, K. Ono, "Arithmetic of certain hypergeometric modular forms," Acta Arithmetica 113 (2004), no. 1, 3955. pdf ps

[2]

J. Getz, K. Mahlburg, "Partition identities and a theorem of Zagier," Journal of Combinatorial Theory (A) 100 (2002), 2743. pdf ps

[1]

A. Benjamin, G. Levin, K. Mahlburg, J. Quinn, "Random approaches to Fibonacci identities," The American Mathematical Monthly 107 (2000), 51116.


Colloquia and Plenary Talks


Selected Seminars and Invited Talks


Grants and Fellowships

Honors and Awards


Teaching

Directed Research and Advising

Professional Activities



Karl Mahlburg