04.06.2024 (Tuesday)

Pedagogical Introduction to Geometric Langlands and its Generalizations via Gauge and String Theory, 2 of 4

Colloquium Mengchwan Tan (NUS, Singapore)

at:
11:00 Other
room LIMS, Royal Institution
abstract:

TITLE: An introduction to Geometric Langlands Duality: from Faraday to Montonen-Olive to Hitchin to Kapustin-Witten ABS: As the first two of a four-part Bragg Lecture Series, we will furnish a pedestrian introduction to geometric Langlands duality via its manifestation in physical gauge theory. To this end, we will first explain what the arithmetic Langlands duality is, and its geometric version. Then, we will cover the underlying physics and math ideas starting with Faraday and electromagnetism, on to Montonen-Olive and the Langlands duality of electric-magnetic charges, then to Hitchin and the mirror symmetry of his moduli spaces, and finally, to Kapustin-Witten and S-duality of 4d N=4 topological gauge theory.