Karl Mahlburg
Department of
Mathematics
Louisiana State University

email: mahlburg
(at) math (dot) lsu (dot) edu
Internet: www.math.lsu.edu/~mahlburg

Positions
 Louisiana State University.
Associate Professor (tenured),
2017 – 2021.
Assistant Professor, 2011 – 2017.
 Mathematical Sciences Research Institute /
Princeton University.
National Science
Foundationfunded 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
 The theory of automorphic forms, including modular
forms, mock modular forms and harmonic Maass
forms;
 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;
 Algebraic and finite combinatorics, including graph
theory, Catalantype structures, abelian sandpiles, combinatorial
probability
 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 extremevalue
variance estimator”, Louisiana State University Health Sciences Center,
Biostatistics Colloquium, October 28, 2019.
 “Characters of affine
Lie Algebras and SumProduct identities”, Hong Kong Number Theory Days,
July 16, 2019.
 “Quantum Invariants and
Quantum Modularity”, Hong Kong Number Theory Days, July 9, 2019.
 “Sumproduct 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
RealAnalytic 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 1418, 2017.
 Recent Developments in
Analytic Number Theory, Workshop, Mathematical Sciences Research
Institute, May 15, 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 68, 2015.
Grants and
Fellowships
 Louisiana Board of
Regents Enhancement Grant 04MATH14 (coPI), 2014 – 2016. PI:
Peter Wolenski,
LSU.
 NSF Conference Grant DMS1363265
(CoPI), 2014. PI: Ling Long, LSU.
 NSF Individual Research
Grant DMS1201435
(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 campuswide
 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 qseries, 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), UWMadison,
Spring 2005.
 Math
171 Recitations (Calculus with Algebra and Trigonometry I), UWMadison,
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,
qseries, 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 UWMadison 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
EtaQuotients and their Applications to Combinatorics”. LSU Digital
Commons
First Position after Ph.D.: Assistant Professor, Vermont Technical College
Professional
Activities
 CoOrganizer for
Conference: Southern
Number Theory Conference, held at LSU, Apr. 13–14, 2019.
 CoOrganizer and CoPI
for Conference: Southern
Number Theory Conference, held at LSU, Apr. 8–9, 2017.
 CoOrganizer and CoPI
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
ProblemSolving Seminar, LSU, 2011 – 2019.
 CoOrganizer 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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