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DTSTART;TZID=America/Toronto:20261110T100000
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URL:https://uwaterloo.ca/pure-mathematics/events/number-theory-seminar-sour
 abhashis-das-prime-gaps-arithmetic
SUMMARY:Number Theory Seminar | Sourabhashis Das | Prime Gaps in Arithmetic
 \nProgressions Are Graphic
CLASS:PUBLIC
DESCRIPTION:SOURABHASHIS DAS (UNIVERSITY OF LETHBRIDGE)\n\n_Prime Gaps in A
 rithmetic Progressions Are Graphic_ \n\nA sequence of positive integers is
  called _graphic_ if it arises as\nthe degree sequence of a simple graph. 
 In this talk\, we explore a\nsurprising connection between this classical 
 graph-theoretic notion\nand the distribution of primes. \nLet us call a si
 mple graph on \\(n \\geq 2\\) vertices a _prime gap\ngraph_ if its vertex 
 degrees are \\(1\\) and the first \\(n-1\\) prime\ngaps. Growing out of an
  empirical observation by Toroczkai\, he and his\ncollaborators establishe
 d that a prime gap graph exists for every\nsufficiently large \\(n\\)\, an
 d for every \\(n \\geq 2\\) under the Riemann\nHypothesis\, and that an in
 finite sequence of such prime gap graphs can\nbe generated via the degree-
 preserving growth process---the first\nnaturally occurring infinite sequen
 ce of positive integers identified\nas graphic. \nIn this talk\, we extend
  these results to prime gaps in arithmetic\nprogressions. Specifically\, w
 e show that the gap sequences formed by\nconsecutive primes in a fixed pro
 gression \\(a \\pmod{q}\\)\, with\n\\(\\gcd(a\,q)=1\\)\, are likewise grap
 hic. The analytical tools required\nstem from Heath-Brown's work on boundi
 ng moments of large prime gaps.\nWe demonstrate these tools in the context
  of primes in arithmetic\nprogressions and explain how they drive our proo
 f. \nThis is joint work with Keshav Aggarwal and is a work in progress. \n
 MC 5501
DTSTAMP:20261101T083158Z
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