Motivic and topological multiple zeta functions and Euler-type reflexion formulas
Speaker: Lê Quý Thường (VNU University of Science in Hanoi)

Time: Saturday, January 8, 2022, 2:30pm-4:30pm, GMT+7 – Hanoi time

Abstract: We introduce a new product of two formal series with coefficients in distinct Grothendieck rings of algebraic varieties, which preserves the integrability and commutes with the limit of rational series. In the same context, we define a motivic multiple zeta function with respect to an ordered family of regular functions, which is integrable and connects closely to Denef-Loeser’s motivic zeta functions. We will present an explicit formula for the motivic double zeta functions using resolution of singularities. A version of the Euler-type reflexion formula for motivic double zeta functions will be also given, and by taking its limit the motivic Thom-Sebastiani theorem will be recovered. We also discuss the so-called topological multiple zeta functions and an Euler-type reflexion formula for them. First half of the talk is a joint work with Nguyen Hong Duc.

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