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SUMMARY:Raymond Puzio
DTSTART:20261104T190000Z
DTEND:20261104T203000Z
DTSTAMP:20261109T050834Z
UID:Category_Theory/116
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Category_The
 ory/116/">Gaussians\, Groups\, and Renormalization.</a>\nby Raymond Puzio 
 as part of New York City Category Theory Seminar\n\nLecture held in Room 4
 214.03 in The Graduate Center\, CUNY.\n\nAbstract\nAbstract: Gaussian (a.k
 .a. normal) probability distributions are ubiquitous. One reason for this 
 is the fact that the set of Gaussian distributions is closed under multipl
 e operations---subspace restriction\, fiberwise integration\, disjoint mul
 tiplication\, pointwise multiplication\, convolution. Also\, as Heisenberg
  and Dirac realized in the early days of quantum mechanics\, the Gaussian 
 distribution may be characterized uniquely as the fixed point of a group a
 ction. In this talk\, we will show how the aforementioned operations on di
 stributions correspond to operations on groups. This provides a systematic
 \, functorial\, and generalizable approach to deriving and understanding p
 roperties of Gaussian distributions.\n<br><br>\nMy interest in this topic 
 comes from a joint project with Sam McCrosson on renormalization in quantu
 m field theory. We used this group-theoretic approach to Gaussian distribu
 tions to derive the renormalization flow from the path integral. After a q
 uick but self-contained introduction to renormalization\, I will give an o
 verview of this project as a practical application of the ideas presented 
 here.\n
LOCATION:https://researchseminars.org/talk/Category_Theory/116/
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