Periods in Mirror Symmetry

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Periods in Mirror Symmetry

 20 - 23 Sep 2022

ICMS, Bayes Centre, Edinburgh

 Enquiries

Scientific Organisers:

  • Mohammed Abouzaid, Columbia University
  • Sheel Ganatra, University of Southern California
  • Hiroshi Iritani, Kyoto University
  • Tony Pantev, University of Pennsylvania
  • Nick Sheridan, University of Edinburgh

About:

While the relationship between periods and mirror symmetry has been studied for some time, it has been receiving new inputs in recent years from diverse fields such as homological mirror symmetry, tropical geometry, string theory, and (noncommutative) topological K-theory. The workshop brought together experts from these fields bringing complementary expertise to a topic of mutual interest, which is ripe for collaboration. The prospect of bringing Kontsevich’s powerful homological mirror symmetry conjecture to bear on the study of periods is particularly timely, in view of the rapid developments in HMS in recent years. One concrete objective motivating the workshop was to establish the connection between HMS and periods, by proving that the topological K-theory of the Fukaya category corresponds to the Gamma integral structure. The recently-developed string-theoretic understanding of the Gamma integral structure may play an important role here.

Resources

Programme:

Tuesday 20 September
Registration and Refreshments
Welcome and Housekeeping
Johannes Walcher, Heidelberg University Lecture series: Extended Mirror Symmetry
Bohan Fang, Peking University (ONLINE) Gamma II conjecture and HMS for toric Fanos
Lunch / Discussions
Minhyong Kim, ICMS Some preliminary comments on path integrals and L-functions
Sergey Galkin, PUC-Rio (ONLINE) Periods of Graph Potentials in Mirror Symmetry for Character Varieties - towards a fully extended Donaldson-Floer TQFT in 4d
Refreshments
Tony Yue Yu, California Institute of Technology (ONLINE) Mini-course: Non-archimedean Quantum K-theory and Gromov-Witten invariants
Welcome Reception, hosted at ICMS
Wednesday 21 September
Johannes Walcher, Heidelberg University Lecture series: Extended Mirror Symmetry
Refreshments
Fumihiko Sanda, Gakushuin University Mirror symmetry of Fano manifolds via toric degenerations
Mauricio Romo, Tsinghua University Some instances of noncommutative resolutions in GLSMs
Lunch / Discussions
Chiu-Chu Melissa Liu, Columbia University (ONLINE) Open/closed correspondence and mirror symmetry
Bernd Siebert, The University of Texas at Austin Enumerative period integrals of Landau–Ginzburg models via wall structures
Refreshments
Tony Yue Yu, California Institute of Technology (ONLINE) Mini-course: Non-archimedean Quantum K-theory and Gromov-Witten invariants
Thursday 22 September
Johannes Walcher, Heidelberg University Lecture series: Extended Mirror Symmetry
Refreshments
Vasily Golyshev, IITP (ONLINE) On the Deligne and Birch-Swinnerton-Dyer periods
Albrecht Klemm, Hausdorff Institut for Mathematics, University Bonn Calabi-Yau periods, Modularity and Arithmetic Geometry
Lunch / Discussions
Matt Kerr, Washington University in St. Louis Picard-Fuchs equations and motivic Gamma functions
Giulia Gugiatti, ICTP Hypergeometric partial twists
Refreshments
Tony Yue Yu, California Institute of Technology (ONLINE) Mini-course: Non-archimedean Quantum K-theory and Gromov-Witten invariants
Workshop Dinner, hosted at South Hall Complex 19.00 arrival drinks (Kirkland room), 19.30 dinner (South Hall)
Friday 23 September
Johanna Knapp, University of Melbourne (ONLINE) GLSMs, partition functions, and genus-0 invariants for hybrid models
Refreshments
Ursula Whitcher, Mathematical Reviews (AMS) Combinatorial pencils and Hasse-Witt invariants
Hiroshi Iritani, Kyoto University Approaches to the gamma conjecture
Collaboration / End of Workshop Boxed lunches available to-go