We are excited to announce the TSVP Thematic Program "Duality in Geometry and Representation Theory". The program will run from July to August, 2027 (tentative).
Title: Duality in Geometry and Representation Theory
Theme of the Program: This thematic program focuses on duality phenomena appearing in geometry and representation theory. Duality is a universal phenomenon in mathematics, often inspired by ideas from mathematical physics, that reveals unexpected connection between two seemingly different theories. A prominent example is the “Langlands duality”, which originated in number theory but now connects to low-dimensional topology and enumerative geometry through a physical interpretation. Mirror symmetry, a duality between symplectic geometry and complex geometry, has been a central topic in mathematics over the past three decades, with recent applications to classical problems in birational geometry.
This program brings together experts from diverse fields, including representation theory, algebraic geometry, topology, and number theory to foster collaboration between these subjects at a time in which they are absorbing the above transformative advances, in order to promote interdisciplinary research towards future breakthroughs in all of them.
Program Coordinators
Yukinobu Toda (IPMU, University of Tokyo)
Ben Davison (University of Edinburgh)
Tasuki Kinjo (RIMS, Kyoto University)
Hyonjun Park (Korea Institute For Advanced Study)
Tentative Schedule
Week 1: Workshop on "Derived and non-commutative geometry and their applications".
Week 2-3: Research focus on Langlands duality and symplectic duality. We will bring together experts and early-career mathematicians working on Langlands duality and symplectic duality from various perspectives including number theory, topology and representation theory, to foster the exchange of ideas across different math communities. During these weeks, we also plan to organize outreach activities, including a public lecture by the organizers.
Week 4: Summer school for graduate students. We will have lecture course for graduate students by experts working on (1) Geometric Langlands duality, (2) Relative Langlands duality, (3) Symplectic duality, (4) Mirror symmetry.
We also plan to have exercise sessions by early-career mathematicians to help graduate students understand these topics.
Week 5: Closing conference on "Duality in Geometry and Representation Theory"