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2017 POSTECH Math Colloquium 



Arithmetic ChernSimons theory 

The ChernSimons theory is a gauge theory which is a version of (2+1)dimensional TQFT (topological quantum field theory). It provided a useful framework and tools to understand the topology of knots in a 3manifold, for example, the Jones polynomial of knots. The arithmetic ChernSimons theory, initiated by Minhyong Kim, is an arithmetic analogue of the ChernSimons theory, which is expected to attack the number theory problem (Galois theory problem, Lfunctions, Iwasawa theory, and etc) guided by physics (quantum field theory) and topology principles and techniques appearing in the ChernSimons theory. In this talk, we will briefly explain the analogy between primes in a number field and knots in a 3manifold, and define the arithmetic ChernSimons action. Then we will provide arithmetic applications to a certain Galois embedding problem based on an explicit computation of the arithmetic ChernSimons action. This is a joint work with HeeJoong Chung, Dohyeong Kim, Minhyong Kim, and Hwajong Yoo. 







