Conference on Number Theory, Geometry, Moonshine & Strings

  • Organized by
  • Quantrell Award winner Jeff Harvey, a physics professor, in the Gordon Center Monday, May 20, 2013, at the University of Chicago.    (Photo by Robert Kozloff)Jeffrey Harvey, Ph.D.Professor, University of Chicago
Date & Time

The recognition that Calabi-Yau manifolds are fundamental for string compactification initiated a synthesis of geometry and string theory in the 1980s. This reinvigorated enumerative geometry, reshaped Gromov-Witten theory, and precipitated the development of new fields such as Donaldson-Thomas theory, quantum cohomology and homological mirror symmetry. Contemporaneously, efforts to unravel the mysteries of monstrous moonshine produced new algebraic theories which elucidated the role of automorphic forms in string theory and facilitated further developments in these and other fields.

In this century, the connections between number theory, geometry and string theory have deepened, with developments in the theory of harmonic Maass forms, the appearance of mock modular forms in enumerative geometry and string theory, and new relationships between automorphic forms and arithmetic geometry. New forms of moonshine have illuminated new paths for exploration.

The Conference on Number Theory, Geometry, Moonshine & Strings is the first in a series of meetings that will bring together mathematicians and physicists to elucidate, synthesize, develop and disseminate these emerging relationships between number theory, geometry, moonshine and string theory. The first meeting will focus on exploring number theoretic and string theoretic aspects of some recently discovered half-integral weight forms of moonshine which exhibit connections to modularity of varieties and the Birch–Swinnerton-Dyer conjecture.

Agenda & Slides

Wednesday, September 6

  1. Eric Urban: The BSD Conjecture
  2. Michael Mertens: O’Nan Moonshine (PDF)
  3. David Morrison: The Number Theory of Elliptic Curves and the Physics of F-theory (PDF)
  4. Jens Funke: Kudla-Milson for Physicists
  5. Jan Brunier: Theta Lifts
  6. Public Lecture by Jeff Harvey: From Moonshine to Black Holes: Number Theory in Mathematics and Physics

Thursday, September 7

  1. Miranda Cheng: Class Number Moonshine
  2. Scott Carnahan: Generalized Moonshine
  3. John Duncan: The Shimura Correspondence and Moonshine
  4. Sarah Harrison: Strings, M5-branes and Skew-holomorphic Jacobi Forms
  5. Discussion

Friday, September 8

  1. Boris Pioline: Maass Forms and Mock Modular Forms in Physics (PDF)
  2. Larry Rolen: Maass Forms and Mock Modular Forms in Mathematics
  3. Greg Moore: Relations between the U-plane Integral of Donaldson-Witten Theory, Mock Modular Forms and Indefinite Theta Functions (PDF)
  4. Arnav Tripathy: BPS State Counting and Jumping Loci
  5. Minhyong Kim: Arithmetic Topological Quantum Field Theory? (PDF)
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