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Enumerative Geometry via Homological Algebra
If you have a question about this talk, please contact Tyler Kelly.
(Note: Special Day and Seminar Room)
I will discuss how homological algebra (matrix factorizations and derived categories) can be used to (virtually) count curves on algebraic varieties. This is based on joint work in progress with I. Ciocan-Fontanine, J. Guéré, B. Kim, and M. Shoemaker. In summary, we have constructed a cohomological field theory which descends from a Fourier-Mukai transform. This provides an algebraic construction of curve-counting invariants for GIT quotients of affine space together with a function/superpotential. As special cases, we recover Gromov-Witten theory and R-spin/FJRW theory.
This talk is part of the Algebraic Geometry Seminar series.
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