Research
Research
My research has focused on the combinatorial and statistical properties of integer partitions and related objects, using techniques from hypergeometric q-series, automorphic forms, probability and combinatorics. My research is funded by the Simons Foundation, award number SFI-MPS-TSM-00013780.
Preprints/in preparation:
W. Bridges and K. Bringmann, "Limit shapes for Andrews-Gordon-Bressoud partitions," in preparation
W. Bridges, K. Bringmann and C. Nazaroglu, "Statistics for random representations of Lie algebras," submitted. arXiv:2503.02822
W. Bridges, J. Franke and J. Stumpenhusen, "On the proportion of coprime fractions in number fields," submitted. arXiv:2311.01346
Published/accepted:
W. Bridges, "Distribution of the sum of reciprocal parts for distinct parts partitions," Annals of Combinatorics (2025). arXiv:2503.03899
W. Bridges, W. Craig, A. Folsom and L. Rolen, "Zeros of hook length polynomials and related questions," Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 21 (2025). arXiv:2408.16902
W. Bridges and K. Bringmann, "A Rademacher-type exact formula for partitions without sequences," The Quarterly Journal of Mathematics 75 (2024). arXiv:2304.01377
W. Bridges, B. Brindle, K. Bringmann and J. Franke, "Asymptotic expansions for partitions generated by infinite products," Mathematische Annalen 390 (2024). arXiv:2303.11864
W. Bridges and K. Bringmann, "Log-concavity for unimodal sequences," Research in Number Theory 6 (2024). arXiv:2307.05120
W. Bridges, J. Franke and J. Males, "Sign changes in statistics for plane partitions," Journal of Mathematical Analysis and Applications 530 (2024). arXiv:2207.14590
W. Bridges and K. Bringmann, "Taylor coefficients of false Jacobi forms and ranks of unimodal sequences," Advances in Mathematics 426 (2023). arXiv:2208.11942
W. Bridges and Ali Uncu, "Weighted cylindric partitions," Journal of Algebraic Combinatorics 56 (2022). arXiv:2201.03047
W. Bridges, J. Franke and T. Garnowski, "Asymptotics for the twisted eta-product and applications to sign changes in partitions,"Research in the Mathematical Sciences 9 (2022). arXiv:2111.04183
W. Bridges and K. Bringmann, "Statistics for unimodal sequences,"Advances in Mathematics 401 (2022). arXiv:2106.02334
W. Bridges, "Partitions into distinct parts with bounded largest part," Research in Number Theory 6 (2020). arXiv:2004.12036
W. Bridges, "Limit shapes for unimodal sequences,"International Journal of Number Theory 19 (2023). arXiv:2001.06878
W. Bridges, "Partition inequalities and applications to sum-product conjectures of Kanade-Russell," Integers 20 (2020). arXiv:1903.07587
Notes:
W. Bridges and W. Craig, "On the distribution of the norm of partitions," Ramanujan Journal 66 (2025). arXiv:2308.00123
W. Bridges, K. Bringmann and J. Franke, "On the number of irreducible representations of su(3),"Acta Arithmetica 215 (2024). arXiv:2308.02319
Ph.D. Thesis:
"Combinatorial and asymptotic statistical properties of partitions and unimodal sequences,'' LSU Digital Commons
Simons Foundation: award number SFI-MPS-TSM-00013780 (2025-2030)
Some of these may be future events!
2026 Gainesville International Number Theory Conference: In Honor of Krishna Alladi's 70th Birthday, University of Florida, March 2026
21st SASTRA Ramanujan Conference, Sastra University, India, December 2025
AMS Fall Central Sectional Meeting: Special Session on Recent Trends in Discrete and Continuous Probability, St. Louis University, October 2025
AMS Fall Southeastern Sectional Meeting: Special Session on Random Structures in Combinatorics and Number Theory, Tulane University, October 2025
AMS Fall Southeastern Sectional Meeting: Special Session on Experimental Mathematics, Tulane University, October 2025
AMS Fall Southeastern Sectional Meeting: Special Session on Modular Forms in Combinatorics and Number Theory, Tulane University, October 2025
AMS Fall Western Sectional Meeting: Special Session on Recent Developments in Areas Influenced by Ramanujan's Mathematics, University of Denver, August 2025
Integers Conference: In Honor of the 80th Birthdays of Melvyn Nathanson and Carl Pomerance, University of Georgia, May 2025
37th Automorphic Forms Workshop, University of North Texas, April 2025
Specialty Seminar in Partition Theory, q-Series and Related Topics: Michigan Tech University, USA, March 2025
Algebra and Number Theory Seminar, Louisiana State University, January 2025
Number Theory Seminar, Vanderbilt University, October 2024
AMS Fall Central Section Meeting: Special Session on Additive Number Theory and Modular Forms, San Antonio, TX, USA, September 2024
Algebra Seminar, University of North Texas, August 2024
Mini Symposium on Algebra and Applications, (online), Kutaisi International University, Republic of Georgia, June 2024
The legacy of Ramanujan: Celebrating the 85th Birthdays of George Andrews and Bruce Berndt, Pennsylvania State University, USA, June 2024
Texas-Oklohoma Representations and Automorphic Forms XIII, TORA XIII, University of North Texas, USA, April 2024
AMS Joint Mathematics Meetings: Special Session on Partition Theory and q-Series, San Fransisco, USA, January 2024
Number Theory and Combinatorics Seminar: University of Texas at Tyler, November 2023
Specialty Seminar in Partition Theory, q-Series and Related Topics: Michigan Tech University, USA, October 2023
Mini Symposium on Algebra and Applications, (online), Kutaisi International University, Republic of Georgia, July 2023
35th Automorphic Forms Workshop, Louisiana State University, USA, May 2023
Algorithmic Combinatorics and Computer Algebra Seminar: Research Institute for Simbolic Computation, Johannes Kepler Universität, Hagenburg, Austria, March 2023
Workshop on Cylindric Partitions: Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria, November 2022
Ramanujan and Euler: Partitions, Mock Theta Functions and q-Series, (online), July 2022
-invited talk + 3 school lectures
Workshop on Integer Partitions, Nesin mathematics village, near Selçuk, Turkey, June 2022
-series of 5 lectures
100 Years of Mock Theta Functions: New Directions in Partitions, Modular Forms and Mock Theta Functions, Vanderbilt University, USA, May 2022
Early Number Theory Researchers Seminar (ENTR), Darmstadt and Cologne, Germany, May 2022
AMS Joint Mathematics Meetings: Special Session on Modular Forms and Combinatorics, Seattle, Washington, USA, April 2022
AMS Joint Mathematics Meetings: Special Session on Early Career Number Theory Research with Combinatorics, Modular Forms, and Basic Hypergeometric q-Series, Seattle, Washington, USA, April 2022
University of Cologne Number Theory Seminar: November 2021
Specialty Seminar in Partition Theory, q-Series and Related Topics: Michigan Tech University, USA, October 2021
Number Theory Lunch Seminar: Max Plank Institute for Mathematics, Bonn, Germany, June 2021
LSU Algebra and Number Theory Seminar: October 2020
Vanderbilt Number Theory Seminar: September 2020
AMS Joint Mathematics Meetings: Special Session on Interactions Between Partitions, Basic Hypergeometric Series and Modular Forms, Denver, Colorado, USA, January 2020
AMS Fall Southeastern Sectional Meeting: Special Session on Experimental Mathematics in Number Theory and Combinatorics, University of Florida, USA, November 2019
Analytic and Combinatorial Number Theory, A Conference in Honor of Bruce Berndt's 80th Birthday, University of Illinois, USA, June 2019
Southern Regional Number Theory Conference, Louisiana State University, USA, April 2019
Texas-Oklohoma Representations and Automorphic Forms X, TORA X, University of North Texas, USA, April 2019
33rd Automorphic Forms Workshop, Duquesne University, Duquesne University, USA, March 2019
International Conference on Modular Forms and q-Series, University of Cologne, Germany, March 2024
Workshop on Integer Partitions, Nesin mathematics village, Selçuk, Turkey, June 2022
Southern Regional Number Theory Conference, Louisiana State University, USA, March 2020
Advances in Applied Mathematics
Advances in Mathematics
American Mathematical Monthly
Annals of Combinatorics
Bulletin of the Australian Mathematical Society
Canadian Journal of Mathematics
European Journal of Combinatorics
Hardy-Ramanujan Journal
International Journal of Number Theory
Journal of Combinatorial Theory Series A
Journal of Mathematical Analysis and Applications
Journal of the Mathematical Society of Japan
Journal of Number Theory
MathSciNet reviews
Proceedings of the American Mathematical Society
Ramanujan Journal
Random Structures and Algorithms
Research in the Mathematical Sciences
Research in Number Theory
Undergraduates
Nikhil Verma, TAMS Early Summer Researchers, University of North Texas, Summer 2025
Luca Sommer, Bachelor Thesis: "Über die Irrationalität von ζ- und β-Werten" (On the Irrationality of ζ- and β-Values), University of Cologne, Winter 2022/23
Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria, March, 2023
Vanderbilt University, October, 2024
NSF-CBMS Conference: L-functions and Multiplicative Number Theory, University of Mississippi USA, May 2019
Connecticut Summer School in Number Theory, CTNT, University of Connecticut, USA, June 2018