Logic Seminar - Floris Vermeulen
| Dates: | 6 May 2026 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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Speaker: Floris Vermeulen (University of Münster)
Title: Kontsevich-Zagier in valued fields
Abstract: A period is a real number which is the measure of a semialgebraic set defined over the rationals. The ring of periods was formally introduced by Kontsevich and Zagier in 2001, and remains a rather mysterious object. Kontsevich and Zagier conjectured that every equality between periods can already be deduced from simple integration rules such as additivity, change of variables, and the fundamental theorem of calculus. While this conjecture remains completely open, a p-adic analogue was proven by Cluckers-Halupczok. In joint work with Mathias Stout, we use motivic integration and h-minimality to prove a general version of the Kontsevich-Zagier conjecture in henselian valued fields.
In this talk I will introduce periods in the reals and discuss the p-adic analogue due to Cluckers-Halupczok. Afterwards I will introduce motivic integration and discuss the period conjecture in this generality. Time permitting, I will give some ideas of the proof.
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Frank Adams 1
Alan Turing Building
Manchester
