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**NSF/CBMS Research Conference **

**Ramanujan’s ranks, Mock Theta Functions, and Beyond**

**NSF/CBMS Research Conference**

**Ramanujan’s ranks, Mock Theta Functions, and Beyond**

**May 16-20, 20****22**

**The University of Texas Rio Grande Valley**

**School of Mathematical and Statistical Sciences**

**Edinburg, Texas, USA**

**Principal Speaker**

**Frank Garvan**

** University of Florida **

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.