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SUMMARY:Hilbert 10 via additive combinatorics [Oberseminar Logik]
DTSTART:20250519T150000Z
DTEND:20250519T160000Z
DTSTAMP:20260416T073000Z
UID:indico-event-435@math-events.uni-bonn.de
DESCRIPTION:Speakers: Carlo Pagano (MPIM/Concordia)\n\nI will overview rec
 ent joint work with Peter Koymans\, where we introduced a new method to co
 nstruct elliptic curves over general number fields with positive but const
 rained rank. This comes in two flavors: either positive rank that is uncha
 nged under quadratic extensions (which we established in 2024) or rank exa
 ctly equal to 1 (ongoing work in progress). Our main idea is to combine 2-
 descent with additive combinatorics. With the first of these two cases\, w
 e were able to settle Hilbert's tenth problem in the negative for all fini
 tely generated infinite commutative rings. I will overview the reductions 
 of Hilbert tenth's problem to such an elliptic curve question\, and the ma
 in steps in our method. \n\nhttps://math-events.uni-bonn.de/event/435/
LOCATION:Endenicher Allee 60\, Nebengebäude/N0-003 - Seminarraum (Matheze
 ntrum)
URL:https://math-events.uni-bonn.de/event/435/
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