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SUMMARY:Jonathan Chapman (University of Warwick)
DTSTART:20250520T173000Z
DTEND:20250520T175500Z
DTSTAMP:20260423T041811Z
UID:CANT2025/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2025/19/
 ">Counting commuting integer matrices</a>\nby Jonathan Chapman (University
  of Warwick) as part of Combinatorial and additive number theory (CANT 202
 5)\n\nLecture held in CUNY Graduate Center - Science Center (4th floor).\n
 \nAbstract\nConsider the set of pairs of $d\\times d$ matrices $(A\,B)$ wh
 ose entries are all integers with absolute value at most $N$. We call $(A\
 ,B)$ a \\emph{commuting pair} if $AB=BA$. Browning\, Sawin\, and Wang rece
 ntly showed that the number of commuting pairs is at most $O_d(N^{d^2 + 2 
 - \\frac{2}{d +1}})$. They further conjectured that the lower bound $\\Ome
 ga_d(N^{d^2 + 1})$\, which comes from letting $A$ or $B$ be a multiple of 
 the identity matrix\, should be sharp. In this talk\, I will discuss progr
 ess on the cases $d=2$ and $d=3$\, where we show that this conjecture hold
 s. I will also demonstrate how our approach relates counting commuting pai
 rs of matrices to the study of restricted divisor correlations in number t
 heory.\\\\\nJoint work with Akshat Mudgal (University of Warwick)\n
LOCATION:https://researchseminars.org/talk/CANT2025/19/
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