Curve counts, representation theory, and 3d mirror symmetry

Hunter Dinkins (Northeastern)

22-Sep-2022, 18:50-19:50 (18 months ago)

Abstract: The last two decades have seen great success in studying representation theoretic objects through geometric techniques. One small part of this story involves Nakajima quiver varieties, curve counting, and a mysterious string-theoretic duality. More specifically, curve counting in Nakajima varieties turns out to be governed by certain q-difference equations that, after a nontrivial amount of work, can be seen to coincide with the some well-known equations from representation theory. Moreover, these curve counts are expected to possess deep nontrivial symmetries that have only been understood in very specific examples. I will provide an overview of the main concepts and results related to these ideas, discuss my own contributions, and mention some future directions.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( video )


Geometry, Physics, and Representation Theory Seminar

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