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SUMMARY:Tomer Schlank (Hebrew University of Jerusalem)
DTSTART:20230426T190000Z
DTEND:20230426T200000Z
DTSTAMP:20260422T185047Z
UID:HarvardNT/83
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HarvardNT/83
 /">Knots Invariants and Arithmetic Statistics</a>\nby Tomer Schlank (Hebre
 w University of Jerusalem) as part of Harvard number theory seminar\n\nLec
 ture held in Room 507 in the Science Center.\n\nAbstract\nThe Grothendieck
  school introduced étale topology to attach algebraic-topological invaria
 nts such as cohomology to varieties and schemes. Although the original mot
 ivations came from studying varieties over fields\, interesting phenomena 
 such as Artin–Verdier duality also arise when considering the spectra of
  integer rings in number fields and related schemes. A deep insight\, due 
 to B. Mazur\, is that through the lens of étale topology\, spectra of int
 eger rings behave as $3$-dimensional manifolds while prime ideals correspo
 nd to knots in these manifolds. This knots and primes analogy provides a d
 ictionary between knot theory and number theory\, giving some surprising a
 nalogies. For example\, this theory relates the linking number to the Lege
 ndre symbol and the Alexander polynomial to Iwasawa theory.  In this talk\
 , we shall start by describing some of the classical ideas in this theory.
  I shall then proceed by describing how via this theory\, giving a random 
 model on knots and links can be used to predict the statistical behavior o
 f arithmetic functions. This is joint work with Ariel Davis.\n
LOCATION:https://researchseminars.org/talk/HarvardNT/83/
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