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SUMMARY:Chromatic congruences and Bernoulli numbers - Irakli Patchkoria (U
 niversity of Aberdeen)
DTSTART:20240617T101500Z
DTEND:20240617T111500Z
UID:TALK217381@talks.cam.ac.uk
DESCRIPTION:For every n and a fixed prime p\, we construct a new congruenc
 e for the orbifold Euler characteristic of a group which we call the chrom
 atic congruence at the height n. Here the word &ldquo\;chromatic&rdquo\; r
 efers to the chromatic stable homotopy theory\, though to understand this 
 talk no background in stable homotopy theory is required. The p-adic limit
  of these congruences when n tends to infinity recovers the well-known Bro
 wn-Quillen congruence. We apply these results to mapping class groups and 
 using Harer-Zagier we get an infinite family of congruences for Bernoulli 
 numbers. At the end we will see that these congruences in particular recov
 er classical congruences for Bernoulli numbers due to Kummer\, Voronoi\, C
 arlitz and Cohen.
LOCATION:External
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