## Karl Mahlburg
320 Lockett Hall |
Office: (225) 578-1609 |

**Louisiana State University.**Associate Professor (tenured), 2017 –

Tenure-track 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.

**University of Wisconsin at Madison.**

Ph.D.**in Mathematics**, 2006

Advisor: Ken OnoThesis: "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.

- 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, Catalan-type structures, abelian sandpiles, combinatorial probability
- Nonstandard analysis and analytic number
theory

See Publications page for full
list of **38** refereed journal articles and **3 **preprint(s).

- “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.

**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.

- 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.

- 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.

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

Current Employment: Chief Technical Officer at CleverSolve

- Irfan Alam
- Expected Ph.D. 2020
- Shashika
Petta Mestrige
- Walter
Bridges

- 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 – .
- Co-Organizer for Algebra and Number Theory
Seminar, LSU, 2011 – 2013.
- Member of The American
Mathematical Society, 2002 – .
- 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; (5 grants reviewed).
- Reviewer for the American Mathematical Society Mathematical Reviews Database
(15 reviews written).

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