Research Seminars @ Illinois

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Tailored for undergraduate researchers, this calendar is a curated list of research seminars at the University of Illinois. Explore the diverse world of research and expand your knowledge through engaging sessions designed to inspire and enlighten.

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GGT seminar: Links in 3-manifolds which behave like the prime numbers

Event Type: Seminar/Symposium
Sponsor: Groups, Geometry, and Topology Seminar
Location: 347 Altgeld Hall
Date: May 8, 2025 11:00 am - 12:00 pm
Speaker: Nadav Gropper (Haifa / Penn)
Views: 81
Originating Calendar: Groups, Geometry, and Topology Calendar; Arithmetic topology, also known as the "knots and primes" analogy, studies connections and analogies between low dimensional topology and number theory. In low dimensional topology, McMullen constructed a sequence of knots linked in a "Chebotarev way", and it may be seen as an analogue of the set of all prime numbers. In my talk, I will outline the above and discuss an ongoing joint work with Jun Ueki and Yi Wang, in which we use this notion to provide a topological version of Nuekirch-Uchida theorem. In other words, we construct a profinite group of a 3-manifold relative to the link, which is the "absolute Galois group" of the manifold. We show that such a group determines the manifold. In our arguments we study analogies of fundamental number theoretic concepts such as Hilbert ramification theory and L-functions for links.

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