This conference is part of the regional research conference series sponsored by the National Science Foundation (NSF) and the Conference Board of the Mathematical Sciences (CBMS).

In his lecture series, Professor Garvan plans to address the following major themes: Extending Ramanujan’s classical partition congruences, furthering the combinatorics of partition congruences, extending partition statistics and cranks, and ranks and mock modular forms. The work will include these topics in the context of number theory, combinatorics, physics, and other areas. Much of the recent work has been motivated by data obtained from innovative use of both the mathematical theory and the use of computer algebra systems that Professor Garvan has pioneered. The conference is expected to result in a further interweaving of computational number theory with the included topics.

Dr. Frank Garvan will deliver ten lectures over the duration of the conference on the topics of partition ranks and cranks, mock theta functions and mock modular forms, and computer algebra. In addition, several eminent scholars in this area of research have accepted preliminary invitations to deliver one-hour lectures on related material.

An excerpt from a 1996 interview with Freeman Dyson that could have served as an introduction to this conference.

CONFERENCE LECTURE VIDEOS

Monday, May 16, 2022

Frank Garvan, Lecture 1: Ramanujan's Partition Congruences
Madeline Dawsey: Ranks, Cranks, and Partition Congruences
George Andrews: Partition Identities for k-Regular Partitions with Distinct Parts
Frank Garvan, Lecture 2: The Combinatorics of Partition Congruences

Tuesday, May 17, 2022

Frank Garvan, Lecture 3: Mahlburg, Bringmann, and Ono's Rank and Crank Congruences, Part 1.
Ae Ja Yee: Partition rank and crank from a combinatorial point of view
Frank Garvan, Lecture 4: Mahlburg, Bringman, and Ono's rank and crank congruences, Part 2.

Wednesday, May 18, 2022

Frank Garvan, Lecture 5: Ramanujan's Mock Theta Functions
Peter Paule: Differential Equations and Modular Forms
Larry Rolen: Recent problems in partitions and other combinatorial functions
Frank Garvan, Lecture 6: Transformation Properties of Dyson's Rank Function

Thursday, May 19, 2022

Frank Garvan, Lecture 7: Holomorphic Projection
Peter Paule: RISC Computer Algebra Packages for q-series
Frank Garvan, Lecture 8: Zagier's Higher Order Mock Theta Functions

Friday, May 20, 2022

Frank Garvan, Lecture 9: The Hurwitz Class Number, Mock Theta Functions, and the Unimodal Sequence Conjectures
Christopher Jennings-Shaffer: Bailey's Lemma, Bailey pairs, and so on
Frank Garvan, Lecture 10: Congruences for the Rank and Crank Parity Functions

Organizing Committee:
Tim Huber, University of Texas Rio Grande Valley
Brandt Kronholm, University of Texas Rio Grande Valley
Andrew Sills, Georgia Southern University

This material is based upon work supported by the National Science Foundation under Grant Number 2132649.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Additional support for this conference is provided by the National Security Agency.