Mirror Symmetry for Character Varieties and Field Theory by Sergey Galkin

Explore an in-depth lecture on mirror symmetry for character varieties and field theory, presented by Sergey Galkin at the International Centre for Theoretical Sciences. Delve into the construction of mirrors for moduli spaces of SU(2) character varieties on Riemann surfaces, using mirrors for projective threespaces as building blocks. Discover how this construction allows for rapid computation of periods across all genera and leads to the creation of oscillatory integrals satisfying the gluing axiom of topological field theory. Examine the relationship between the mirror construction and a conjecture on decomposing derived categories of coherent sheaves on moduli spaces of stable rank 2 bundles. Throughout the lecture, encounter key concepts such as the Ginzberg-Landau model, 3-valent graphs, classical periods, random walks on lattices, Newton polytopes, homological mirror symmetry, and quantum periods. Gain insights into the mathematical foundations and implications of this research, including its connections to singularity theory, algebraic geometry, and topological field theory.

Date/Time: Wednesday, March 4, pm
Mirror symmetry for character varieties and field theory
"Ginzberg Landau model" - Singularity theory of functions
Basic building block
3-valent graph gamma with n leaves
Classical Periods
Theorem - K gamma, c depends on gamma,c only up to homotopy: Proof
Theorem
Random walk on the lattice
Newton Polytops of Wgamma, c
Important piece
Need 3 pieces of data
Graphs
Different Variations
Narasimhan Seshadri
Expectation
Homological mirror symmetry - Related Categories
Quantum period of fundamental counts
VHS - Quantum period of F
TUY - Flat sheet of vector spaces over Mg,n
Manon
Mu r Crit PointsW are among displaceable
Our Conjecture
Samotion-type decomposition