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Path Integrals and L-Functions

Introductory Workshop: Diophantine Geometry February 06, 2023 - February 10, 2023

February 09, 2023 (03:30 PM PST - 04:30 PM PST)
Speaker(s): Minhyong Kim (International Centre for Mathematical Sciences)
Location: MSRI: Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC

Path Integrals And L-Functions


In the 1960s, Barry Mazur noticed an analogy between knots and primes that led to a view of the main conjecture of Iwasawa theory in which the p-adic L-function plays the role of the Alexander polynomial. In the late 1980s, Edward Witten reconstructed the Jones polynomial as a path integral-in the sense of quantum field theory-associated to SU(2) Chern-Simons theory. This talk will review some of this history and present a weak arithmetic analogue of Witten’s formula. (This is joint work with Magnus Carlson, Hee-joong Chung, Dohyeong Kim, Jeehoon Park, and Hwajong Yoo.)

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Path Integrals And L-Functions

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