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SUMMARY:Statistics for random representations of Lie algebras [MPIM]
DTSTART:20251202T153000Z
DTEND:20251202T163000Z
DTSTAMP:20260417T223600Z
UID:indico-event-959@math-events.uni-bonn.de
DESCRIPTION:Speakers: Caner Nazaroglu (Universität zu Köln)\n\nNumber th
 eory lunch seminar\nHow does a typical finite-dimensional representation o
 f a complex Lie algebra look like? In this talk\, we address this question
  for the infinite family $\\mathfrak{sl}_{r+1}(\\mathbb{C})$ with $r \\geq
  2$. Specifically\, we derive the asymptotic statistical properties of a r
 epresentation sampled uniformly from all representations with a given larg
 e dimension. This naturally extends similar studies on integer partitions 
 with methods inspired from statistical mechanics. The multivariable genera
 lization we consider contains some new features compared to integer partit
 ions\, which have been studied from a large range of points of view from c
 ombinatorics to modularity. In the talk\, we will review those aspects fam
 iliar from integer partitions\, describe the physics inspired approach to 
 the problem\, and finally detail our results for the general case. This is
  joint work with Walter Bridges and Kathrin Bringmann.\n \n\nhttps://math
 -events.uni-bonn.de/event/959/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/959/
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