# Indefinite Theta Functions and Applications in Physics & Geometry

## Hamilton Mathematics Institute, Trinity College Dublin

### Dates: June 6-9, 2017

### Speakers:

**Organizers:**
Jan Manschot (HMI/TCD)

Larry Rolen (HMI/TCD)

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Description of the workshop:

Modular forms have been of major significance in various subjects, such as number theory, algebraic geometry and theoretical physics. The aim of this workshop is to bring together researchers on modular forms and their applications. The workshop will pay specific attention to indefinite theta functions, which play a key role in the modern understanding of Ramanujan’s mock theta functions, as well as in conformal field theory, BPS state counting and wall-crossing of moduli invariants. The workshop will include lectures by five leading international experts, who will each deliver two talks. We hope that the lecture program will be of particular interest to young researchers in the field, including Phd students and postdocs.

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Schedule:

**Tuesday:**

10:30-11:00 Coffee and registration

11:00-12:00 Zwegers:(Indefinite) Theta Functions: an introduction

12:00-14:00 Lunch

14:00-15:00 Zwegers: Explicit construction of theta functions for quadratic forms of general signature

15:00-15:30 Coffee break

15:30-16:00 Stephan Ehlen: A completion of a generating series of Duke-Imamoglu-Toth

**Wednesday: **

9:30-10:30 Pioline: Indefinite theta series and generalized error functions I

10:30-11:00 Coffee

11:00-12:00 Creutzig: Introduction to the modular aspects of logarithmic conformal field theory I

12:00-14:00 Lunch

14:00-15:00 Kudla: Integrals of theta forms I

15:00-15:30 Coffee break

15:30-16:00 Michael Griffin: Umbral Moonshine

**Thursday: **

9:30-10:30 Pioline: Indefinite theta series and generalized error functions II

10:30-11:00 Coffee

11:00-12:00 Creutzig: Introduction to the modular aspects of logarithmic conformal field theory II

12:00-14:00 Lunch

14:00-15:00 Hikami: Quantum modular forms I: Introduction to quantum invariants of knots and 3-manifolds

15:00-15:30 Coffee break

15:30-16:00 Yingkun Li: Another sum expression for the Appell-Lerch sum

**Friday:**

9:30-10:30 Hikami: Quantum modular forms II: Asymptotics of quantum invariants

10:30-11:00 Coffee

11:00-12:00 Kudla: Integrals of theta forms II

12:00-14:00 Lunch

### Supported by HMI, SFI, Simons Foundation, TCD Maths

###
Registration:

Registration is free of charge but **mandatory**. Please email theta@maths.tcd.ie to register by ** May 29th**. The application deadline for funding has passed.

**Participants are listed here**

The lectures will take place in the Maxwell Lecture Theatre.
Map with suggested restaurants
** Please check out our informational poster!****
**