Time: April 11, 2025, 4:00 pm Place: Room 403, IMI - BAS Speaker: Felipe Espreafico Guelerman, Sorbonne Université - Paris Title: On Motivic and Arithmetic Donaldson-Thomas invariants Further information: https://icms.bg/category/icms-seminar/ Abstract. Aiming to understand the relation to other "refined invariants", and especially their possible interpretation in quantum theory, we explain how to obtain a quadratic, A1-version of Donaldson-Thomas invariants from the motivic refinements first introduced in Kontsevich-Soibelman. Following ideas from Behrend, Bryan and Szendroi, we provide predictions for these invariants in a few simple examples, mainly the computation of DT invariants of A3. Our main goal is to draw relationships with the literature, including works of Levine, Denef and Loser, Azouri, Pepin-Lehaulleur, Srinivas among others. We begin with a brief introduction to A1-enumerative geometry [...]
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A joint meeting of the ICMS Seminar and the "Algebra and Logic" Seminar will be held next Tuesday, with a talk by Georges Tomanov. The details are as follows. Tuesday, April 29-th, 2:00 pm, in room 403 of IMI-BAS. Georges Tomanov, Université Claude Bernard, Lyon 1. Group action on homogeneous spaces and applications in number theory Abstract:Many longstanding conjectures and problems in number theory can be reformulated in terms of group actions on homogeneous spaces. This reformulation allows them to be tackled using, alongside deep methods from algebra and algebraic geometry, powerful tools from ergodic theory and dynamical systems. An example of the effectiveness of this approach is Margulis's groundbreaking proof of the Oppenheim conjecture (formulated in 1929) concerning the values of quadratic forms at integer points. [...] |
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