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SUMMARY:An overview of arithmetic statistics [Lecture]
DTSTART:20260119T090000Z
DTEND:20260119T094500Z
DTSTAMP:20260308T044100Z
UID:indico-event-1012@math-events.uni-bonn.de
DESCRIPTION:Speakers: Peter Koymans\n\nIn this talk\, I will give a broad 
 overview of recent developments in arithmetic statistics\, highlighting se
 veral directions from my own research. A central theme is understanding ho
 w fundamental arithmetic invariants\, such as ranks of elliptic curves\, c
 lass numbers\, and the solubility of Diophantine equations\, vary across f
 amilies. I will discuss (1) the construction of abelian varieties of presc
 ribed rank and its connection to Hilbert’s tenth problem\, (2) the solub
 ility of the negative Pell equation x^2 - dy^2 = -1\, (3) the distribution
  of ranks of elliptic curves\, including the problem of determining the pr
 oportion of integers representable as sums of two rational cubes\, and (4)
  statistical properties of class numbers.\n\nhttps://math-events.uni-bonn.
 de/event/1012/
LOCATION:Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/1012/
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