CRM: Centro De Giorgi
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New developments in the theory of modular forms over function fields

5 November 2018 - 9 November 2018


VIDEO: a playlist of the talks is available on Youtube.

The theory of modular forms goes back to the 19th century, and has since become one of the cornerstones of modern number theory. Historically, modular forms were first defined and studied over the complex numbers, but in the 1960s, with the formulation of the Langlands program, it became apparent that the development of a theory of modular forms over function fields will also have major arithmetic applications. A tremendous breakthrough in this direction came with the work of Drinfeld, who in the 1970s, in an attempt to prove the Langlands conjecture over function fields, introduced what are now called Drinfeld moduli spaces. The purpose of the conference will be to bring together mathematicians working on function field arithmetic, and the theory of modular forms in general, to discuss the latest developments in the theory of automorphic and Drinfeld modular forms, and to explore possible new directions of research. We anticipate an active participation of younger researchers for whom this conference will provide a convenient venue to present their work. This conference can also be considered as a sequel of the event « Zeta functions and L-series in positive characteristic » organized by Pellarin and Taelman at the CRM in the period 26 - 30 November 2012, which was followed by the workshops « On function fields, zeta functions and Drinfeld modular forms » , 22-26 June 2015 (at the Imperial College, London), « Analogies between number field and function field » 27 June - 1 July, 2016, Lyon and « Arithmetic of function fields », June 26 - 30, 2017, Münster.

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The intensive period was partially supported by:

logo Foundation Compositio Mathematica.

Research Directions

Preliminary list of speakers

# Gebhard Böckle (Heidelberg University, Germany)

# Gunther Cornelissen (Utrecht University, Netherlands)

# Ernst-Ulrich Gekeler (Saarland University, Germany)

# Tim Gendron (UNAM, Mexico)

# Urs Hartl (University of Münster, Germany)

# Masanobu Kaneko (Kyushu University, Japan)

# Ken Ono (Emory University, USA)

# Matthew Papanikolas (Texas A&M University, USA)

# Richard Pink (ETH Zurich, Switzerland)

# Ariel Shnidman (CCR-Princeton, USA)

# Douglas Ulmer (University of Arizona, USA)

# Fu-Tsun Wei (National Central University, Taiwan)

# Jing Yu (National Taiwan University, Taiwan)

# Chia-Fu Yu (Academia Sinica, Taiwan)