Toric and Tropical Techniques in Symplectic Field Theory

June 24 - June 28, 2024

The techniques of symplectic and tropical geometry have given us important tools for both constructing and computing modern invariants of Kähler manifolds and symplectic manifolds that are related to holomorphic curves. These approaches are crucial for analysing the A-side in homological mirror symmetry. They also have connections to invariants in low-dimensional topology and knot theory, such as the one furnished by gauge theory. Notable examples of such techniques are as follows.

  • Gromov-Witten invariants (of symplectic manifolds) that count closed curves; open Gromov-Witten invariants (of pairs formed by a symplectic manifold and a Lagrangian submanifold) that count curves with boundary on the Lagrangian submanifold. Tropical geometry provides important tools for computing these invariants.
  • Symplectic Field Theory (SFT) is a large framework for analogous counts in the setting when either the symplectic or Lagrangian submanifolds are non-compact with cylindrical ends. There are neck-stretching formulae that relate Gromov-Witten invariants to SFT counts.
  • Techniques for understanding deformations, degenerations, and wall-crossing phenomena of (open) Gromov-Witten invariants, which occur when the symplectic or complex data changes, can be approached by using both SFT and tropical techniques. Understanding such deformations is essential for computation of the invariants.
  • Various types of refinements of the above invariants have recently been suggested, e.g. via enumeration of tropical curves, upgrades to values in the Skein-module from low-dimensional topology, and counts defined for singular manifolds by using SFT.

 

The main aim of the workshop is to enable researchers that study these invariants from the sides of SFT and tropical geometry to gather and present the latest developments, including applications in homological mirror symmetry and low-dimensional topology. The purpose is to provide a forum that would facilitate new perspectives, scopes, and connections between these theories and their applications.

Seminars Scroll to the next upcoming seminar

  • TBA June 24 10:00 - 11:00

    TBA

  • Umut Varolgünes: TBA June 24 11:15 - 12:15

    Umut Varolgünes: TBA

  • Jean-Yves Welschinger: TBA June 24 13:30 - 14:30

    Jean-Yves Welschinger: TBA

  • Jake Salomon: TBA June 25 09:30 - 10:30

    Jake Salomon: TBA

  • Erwan Brugallé: TBA June 25 11:00 - 12:00

    Erwan Brugallé: TBA

  • TBA June 25 13:30 - 14:30

    TBA

  • TBA June 25 15:00 - 16:00

    TBA

  • Sushmita Venugopalan: TBA June 25 15:00 - 16:00

    Sushmita Venugopalan: TBA

  • TBA June 26 09:30 - 10:30

    TBA

  • TBA June 26 11:00 - 12:00

    TBA

  • TBA June 26 13:30 - 14:30

    TBA

  • TBA June 27 09:30 - 10:30

    TBA

  • TBA June 27 11:00 - 12:00

    TBA

  • Kyler Siegel: TBA June 27 13:30 - 14:30

    Kyler Siegel: TBA

  • TBA June 27 15:00 - 16:00

    TBA

Participants

Name University Country Arrival and Departure
Mohammed
Abouzaid
University: Stanford University City: United States Arrival and Departure: -
Santiago
Achig Andrango
University: Uppsala University City: Sweden Arrival and Departure: -
Hülya
Argüz
University: University of Georgia City: United States Arrival and Departure: -
Thomas
Blomme
University: University of Geneva City: Switzerland Arrival and Departure: -
Pierrick
Bousseau
University: University of Georgia City: United States Arrival and Departure: -
Erwan
Brugallé
University: Nantes Université City: France Arrival and Departure: -
Francesca
Carocci
University: University of Geneva City: Switzerland Arrival and Departure: -
Georgios
Dimitroglou Rizell
University: Uppsala University City: Sweden Arrival and Departure: -
Luís
Diogo
University: Uppsala University City: Sweden Arrival and Departure: -
Yakov
Eliashberg
University: Stanford University City: United States Arrival and Departure: -
Sergey
Finashin
University: Middle East Technical University City: Turkey Arrival and Departure: -
Sheel
Ganatra
University: University of Southern California City: USA Arrival and Departure: -
Penka
Georgieva
University: Sorbonne Université City: France Arrival and Departure: -
Richard
Hind
University: University of Notre Dame City: United States Arrival and Departure: -
Michael
Hutchings
University: University of California, Berkeley City: United States Arrival and Departure: -
Ilia
Itenberg
University: Sorbonne University City: France Arrival and Departure: -
Viatcheslav
Kharlamov
University: Université de Strasbourg City: France Arrival and Departure: -
Lionel
Lang
University: University of Gävle City: Sweden Arrival and Departure: -
Noémie
Legout
University: Chalmers Universitet City: Sweden Arrival and Departure: -
Conan Nai Chung
Leung
University: The Chinese University of Hong Kong City: Hong Kong Arrival and Departure: -
Diego
Matessi
University: University of Milan City: Italy Arrival and Departure: -
Grigory
Mikhalkin
University: University of Geneva City: Switzerland Arrival and Departure: -
John
Pardon
University: Simons Center for Geometry and Physics City: United States Arrival and Departure: -
Dhruv
Ranganathan
University: University of Cambridge City: United Kingdom Arrival and Departure: -
Johannes
Rau
University: Universidad de los Andes, Bogot City: Colombia Arrival and Departure: -
Helge
Ruddat
University: University of Stavanger City: Norway Arrival and Departure: -
Felix
Schlenk
University: Université de Neuchâtel City: Switzerland Arrival and Departure: -
Boris
Shaprio
University: Stockholm University City: Sweden Arrival and Departure: -
Vivek
Shende
University: University of Southern Denmark City: Denmark Arrival and Departure: -
Mikhail
Shkolnikov
University: International Center for Mathematical Sciences City: Bulgaria Arrival and Departure: -
Jake
Solomon
University: Hebrew University City: Israel Arrival and Departure: -
Kyler
Siegel
University: University of Southern California City: United States Arrival and Departure: -
Alex
Takeda
University: Uppsala University City: Sweden Arrival and Departure: -
Sara
Tukachinsky
University: Tel Aviv University City: Israel Arrival and Departure: -
Umut
Varolgüneş
University: Koc University City: Turkey Arrival and Departure: -
Jean-Yves
Welschinger
University: CNRS, Université Lyon 1 City: France Arrival and Departure: -
Sushmita
Venugopalan
University: Institute of Mathematical Sciences, CIT Campus Taramani Chennai City: India Arrival and Departure: -
Renato
Vianna
University: Universidade de São Paulo City: Brazil Arrival and Departure: -
Oleg
Viro
University: Stony Brook University City: United States Arrival and Departure: -
Chris
Woodward
University: Rutgers City: United States Arrival and Departure: -
Weiwei
Wu
University: Zhejiang University City: China Arrival and Departure: -