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Automorphic Structures in String Theory: March 4 – 8, 2019

 

ScheduleAttendee List

 
Organized by Terry Gannon, David Ginzburg, Axel Kleinschmidt, Stephen D. Miller, Daniel Persson, Boris Pioline
 
The purpose of this interdisciplinary workshop is to investigate connections between string theory, automorphic forms, mock modular forms, and beyond.
Automorphic representations are part of the basic language of the Langlands program, while at the same time playing a crucial role in understanding the structure of scattering amplitudes in string theory. Mock modular forms appear ubiquitously in studying quantum black holes and new moonshine phenomena. Investigations of string amplitudes have also given rise to new objects called “modular graph functions”, whose mathematical structure is only beginning to emerge. Higher-curvature corrections in string theory satisfy unconventional (“Poisson-type”) differential equations that call for a generalization of the notion of automorphic form that goes beyond the current mathematical framework. The workshop represents the kick-off event for a month-long program with the same title, and therefore aims to introduce the various topics and open questions, which can then be further discussed and fostered during the program. Since the participants will come from a wide range of different fields the workshop will combine research talks with longer introductory lectures by physicists for mathematicians, and vice versa. This may be viewed as a continuation of the workshops on “Automorphic forms, mock modular forms and string theory”, which ran at SCGP in the fall of 2016 and at BIRS in the fall of 2017.
 

This workshop is associated with the program Automorphic Structures in String Theory: March 4 – April 5, 2019

Talk Schedule


Time Title Speaker Location
9:30am Automorphic forms and representation theory Paul Garrett (Overview) SCGP 102
10:30am Coffee N/A SCGP Cafe
11:00am Automorphic forms and representation theory Paul Garrett (Overview) SCGP 102
12:00pm Lunch N/A SCGP Cafe
2:00pm Fourier coefficients of Langlands Eisenstein series on $GL(n)$ Dorian Goldfeld SCGP 102
2:40pm gamma-factors as distributions Freydoon Shahidi SCGP 102
3:20pm Coffee N/A SCGP Cafe
3:50pm Massive Automorphic Green’s Functions Marcus Berg SCGP 102
6:00pm Banquet N/A SCGP Cafe

Time Title Speaker Location
9:30am BPS-states and modular forms Shamit Kachru (Overview) SCGP 102
10:30am Coffee N/A SCGP Cafe
11:00am BPS-states and modular forms Shamit Kachru (Overview) SCGP 102
12:00pm Lunch N/A N/A
2:00pm   Sarah Harrison SCGP 102
2:40pm Topological field theories and modular integrals Jan Manschot SCGP 102
3:20pm Coffee N/A SCGP Cafe
3:50pm Modular and mock modular generating series in arithmetic geometry Stephen Kudla SCGP 102

Time Title Speaker Location
9:30am String theory and automorphic representations Henrik Gustafsson (Overview) SCGP 102
10:30am Coffee N/A SCGP Cafe
11:00am String theory and automorphic representations Henrik Gustafsson (Overview) SCGP 102
12:00pm Lunch N/A SCGP Cafe
2:00pm Fourier coefficients of automorphic forms, and applications to minimal and next-to-minimal representations Dmitry Gourevitch SCGP 102
2:40pm L-Functions and Unipotent Orbits Solomon Friedberg SCGP 102
3:20pm Coffee N/A SCGP Cafe
3:50pm Metaplectic Representations of Hecke algebras Siddhartha Sahi SCGP 102

Time Title Speaker Location
9:30am Multi-zeta values and modular graph functions Pierre Vanhove (Overview) SCGP 102
10:30am Coffee N/A SCGP Cafe
11:00am Multi-zeta values and modular graph functions Pierre Vanhove (Overview) SCGP 102
12:00pm Lunch N/A SCGP Cafe
2:00pm Open versus closed strings at one loop: From elliptic multiple zeta values to modular graph forms Oliver Schlotterer SCGP 102
2:40pm Solvable Lattice Models, Vertex Operators and Whittaker Functions Daniel Bump SCGP 102
3:20pm Coffee N/A SCGP Cafe
4:00pm Colloquium: Sphere packing, Fourier interpolation, and the Universal Optimality Theorem Stephen Miller SCGP 102

Time Title Speaker Location
9:30am
Superstrings on the SU(3) group manifold: beyond BPS
Anne Taormina SCGP 102
10:10am Coffee N/A SCGP Cafe
10:40am The symmetric space of type E10, and the action of the arithmetic Kac-Moody group Ralf Koehl SCGP 102
11:20am Some unexpected properties of maximal compact subalgebras of hyperbolic Kac-Moody algebras Hermann Nicolai SCGP 102
1:00Pm On Invariants shared by Geometry and Conformal Field Theory Katrin Wendland SCGP 313