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SUMMARY:Frank Calegari (University of Chicago)
DTSTART:20220927T203000Z
DTEND:20220927T213000Z
DTSTAMP:20260423T125226Z
UID:MITNT/55
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/55/">T
 he arithmetic of power series</a>\nby Frank Calegari (University of Chicag
 o) as part of MIT number theory seminar\n\nLecture held in Room 2-143 in t
 he Simons Building (building 2).\n\nAbstract\nAbstract: A function of a co
 mplex variable $P(z)$ which is holomorphic around $z=0$ has a power series
  expansion $P(z)=\\sum a_n z^n$. Suppose that the $a_n$ are all integers: 
 what restrictions does that place on the function $P(z)$? We explore the r
 elationship between this problem to questions in complex analysis\, number
  theory\, and to Klein’s famous observation that not all finite index su
 bgroups of $\\mathrm{SL}_2(\\mathbf{Z})$ are determined by congruence cond
 itions. This talk is based on joint work with Vesselin Dimitrov and Yunqin
 g Tang.\n
LOCATION:https://researchseminars.org/talk/MITNT/55/
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