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SUMMARY:A geometric approach to Gauss composition with applications to pro
 per surfaces in the 4-ball [MPIM]
DTSTART:20241209T130000Z
DTEND:20241209T140000Z
DTSTAMP:20260415T094800Z
UID:indico-event-123@math-events.uni-bonn.de
DESCRIPTION:Speakers: Peter Feller (ETH Zürich)\n\nhttps://www.mpim-bonn.
 mpg.de/node/13779\nIn Disquisitiones Arithmeticae\, motivated by the probl
 em of characterizing which integers are representable as x^2+ny^2\, Gauss 
 described a composition law that turns primitive integral binary quadratic
  forms of a fixed discriminant D into a group. For this integral binary qu
 adratic forms – expressions of the form ax^2+bxy+cy^2 – are considered
  up to linear coordinate changes in the variables x and y.We discuss a new
  perspective on Gauss composition\, which relates to Bhargava's celebrated
  cube law. Our perspective grew out of a problem in 3.5-dimensional topolo
 gy: we tackle the problem of distinguishing Seifert surfaces in the 4-bal
 l\, and use our new perspective to provide robust constructions of pairs o
 f Seifert surfaces that are not isotopic in the 4-ball. This puts recent e
 xamples of Hayden-Kim-Miller-Sundberg-Park concerning a question of Living
 ston into a more general framework.Based on joint work with Menny Aka\, Al
 ison Beth Miller\, and Andreas Wieser.\nNo knowledge on Gauss composition 
 will be presupposed.\n\nhttps://math-events.uni-bonn.de/event/123/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/123/
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