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SUMMARY:Joshua Males (University of Manitoba)
DTSTART:20230320T180000Z
DTEND:20230320T190000Z
DTSTAMP:20260423T021138Z
UID:NTC/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTC/11/">For
 gotten conjectures of Andrews for Nahm-type sums</a>\nby Joshua Males (Uni
 versity of Manitoba) as part of Lethbridge number theory and combinatorics
  seminar\n\nLecture held in University of Lethbridge: M1040 (Markin Hall).
 \n\nAbstract\nIn his famous '86 paper\, Andrews made several conjectures o
 n\nthe function $\\sigma(q)$ of Ramanujan\, including that it has\ncoeffic
 ients (which count certain partition-theoretic objects) whose\nsup grows i
 n absolute value\, and that it has infinitely many Fourier\ncoefficients t
 hat vanish. These conjectures were famously proved by\nAndrews-Dyson-Hicke
 rson in their '88 Invent. paper\, and the function\n$\\sigma$ has been rel
 ated to the arithmetic of $\\mathbb{Z}[\\sqrt{6}]$\nby Cohen (and extensio
 ns by Zwegers)\, and is an important first\nexample of quantum modular for
 ms introduced by Zagier.\n\nA closer inspection of Andrews' '86 paper reve
 als several more\nfunctions that have been a little left in the shadow of 
 their sibling\n$\\sigma$\, but which also exhibit extraordinary behaviour.
  In an\nongoing project with Folsom\, Rolen\, and Storzer\, we study the f
 unction\n$v_1(q)$ which is given by a Nahm-type sum and whose coefficients
 \ncount certain differences of partition-theoretic objects. We give\nexpla
 nations of four conjectures made by Andrews on $v_1$\, which\nrequire a bl
 end of novel and well-known techniques\, and reveal that\n$v_1$ should be 
 intimately linked to the arithmetic of the imaginary\nquadratic field $\\m
 athbb{Q}[\\sqrt{-3}]$.\n
LOCATION:https://researchseminars.org/talk/NTC/11/
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