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08 Jul, 2020 · 17:00 al 08 Jul, 2020 · 18:00 Sala Virtual Da Vinci

Seminario de Geometría: «The Kapustin-Witten equations»

Rafe Mazzeo

Conferencias, seminarios, divulgación científica

Seminario (virtual) de Geometría, impartido por Rafe Mazzeo (Stanford University).

Abstract: One of the new four-dimensional gauge theories is a set of equations discovered by Kapustin and Witten in 2005. This theory involves a boundary condition which in turn involves a knot K in a 3-manifold. A later conjecture by Gaiotto and Witten states that a sequence of numerical counts of elements of the moduli space of solutions determines the Jones polynomial of the knot.
While this remains open, quite a lot has been discovered. I will briefly survey these developments, including the basic structural and regularity theory of these equations, which was joint work with Witten, and a fairly complete resolution of this problem in the dimensionally reduced case, on the product of a Riemann surface and a half-line, which was joint work with S. He.



8 de julio

17:00 - 18:00