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SUMMARY:Changes in arithmetic properties of rational points of some curves
  with respect to field extensions [MPIM]
DTSTART:20260625T130000Z
DTEND:20260625T140000Z
DTSTAMP:20260623T225400Z
UID:indico-event-1422@math-events.uni-bonn.de
DESCRIPTION:Speakers: Sun Woo Park (MPIM)\n\nMPI-Oberseminar\nFinding solu
 tions of a polynomial equation $f(x\,y) = 0$ over the rational numbers $\\
 mathbb{Q}$ (such as Fermat's last theorem) has been one of the key classic
 al problems in number theory. A related question is to ask whether the num
 ber of solutions (or other arithmetic properties) changes if we find solut
 ions to the same equation over an extension field\, such as $\\mathbb{Q}(i
 )$ or $\\mathbb{Q}(\\sqrt{5})$. We will discuss some of the quantitative c
 haracterizations of changes in arithmetic properties of solutions to these
  polynomial equations. If time allows\, we will discuss how such character
 izations hint at a possible interplay among arithmetic statistics of ratio
 nal points on curves\, stochastic properties of Markov operators\, and top
 ological properties of Hurwitz spaces. The talk is based on joint works wi
 th Daniel Keliher\, Stevan Gajovic\, and Wanlin Li\, as well as some other
  works of mine. \n\nhttps://math-events.uni-bonn.de/event/1422/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1422/
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