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SUMMARY:Dennis Davenport (Howard University)
DTSTART:20260915T180000Z
DTEND:20260915T190000Z
DTSTAMP:20260930T004145Z
UID:AI-CoNT/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AI-CoNT/1/">
 Riordan Arrays\, Pseudo-Involutions\, and AI-Assisted Mathematical Discove
 ry</a>\nby Dennis Davenport (Howard University) as part of AI\, Combinator
 ics and Number Theory Seminar\n\n\nAbstract\nThe Riordan group is a group 
 of infinite lower triangular matrices that are defined by\ntwo generating 
 functions\, $g$ and $f$. The $k^{\\mathrm{th}}$ column of each matrix has 
 a generating function related\nto $gf^k$. There are many applications of R
 iordan arrays\, among other things they can be used to\ncount combinatoria
 l objects and to prove combinatorial identities\n\nIn this talk\, I will i
 ntroduce Riordan arrays and discuss recent joint work with Dewayne Dixon a
 nd\nMoussa Doumbia on pseudo-involutions. In the Appell subgroup\, the pse
 udo-involution condition\nreduces to the simple identity\n\\[\ng(z)g(-z)=1
 \,\n\\]\nwhich leads to a useful classification and several interesting in
 teger sequences. I will also discuss\nhow artificial intelligence can assi
 st mathematical discovery by helping generate examples\, identify\npattern
 s\, and suggest conjectures\, while exact computation and proof remain ess
 ential.\n
LOCATION:https://researchseminars.org/talk/AI-CoNT/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matilde Lalín (Université de Montréal)
DTSTART:20260929T180000Z
DTEND:20260929T190000Z
DTSTAMP:20260930T004145Z
UID:AI-CoNT/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AI-CoNT/2/">
 The arithmetic of Boyd’s Mahler measure conjectures: from data analysis 
 to machine learning</a>\nby Matilde Lalín (Université de Montréal) as p
 art of AI\, Combinatorics and Number Theory Seminar\n\n\nAbstract\nThe Mah
 ler measure is an invariant of multivariable rational functions defined by
  averaging\n$\\log |P|$ over the unit torus. Boyd conjectured that\, for\n
 \\[\nx+y+\\frac{1}{x}+\\frac{1}{y}+k\,\n\\]\nits Mahler measure is a ratio
 nal multiple $r_k L'(E_k\,0)$\, where $E_k$ is an associated\nelliptic cur
 ve. We study the arithmetic of the factors $r_k$ using a dataset of the fi
 rst\n250\,000 values of $k$\, combining large-scale statistical analysis w
 ith transformer-based\nexperiments. We observe several striking patterns i
 n their size and $p$-adic behavior\,\nand find that the neural networks re
 cover substantial arithmetic structure from the data\,\nand perhaps a bit 
 more. This is joint work with Alberto Alfarano\, Pablo Bianucci\, and\nBer
 end Ringeling.\n
LOCATION:https://researchseminars.org/talk/AI-CoNT/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Katherine Stange (University of Colorado\, Boulder)
DTSTART:20261027T180000Z
DTEND:20261027T190000Z
DTSTAMP:20260930T004145Z
UID:AI-CoNT/3
DESCRIPTION:by Katherine Stange (University of Colorado\, Boulder) as part
  of AI\, Combinatorics and Number Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AI-CoNT/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Roe (MIT)
DTSTART:20261110T190000Z
DTEND:20261110T200000Z
DTSTAMP:20260930T004145Z
UID:AI-CoNT/4
DESCRIPTION:by David Roe (MIT) as part of AI\, Combinatorics and Number Th
 eory Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AI-CoNT/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Sutherland (MIT)
DTSTART:20261124T190000Z
DTEND:20261124T200000Z
DTSTAMP:20260930T004145Z
UID:AI-CoNT/5
DESCRIPTION:by Andrew Sutherland (MIT) as part of AI\, Combinatorics and N
 umber Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AI-CoNT/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seewoo Lee (EPFL)
DTSTART:20261013T180000Z
DTEND:20261013T190000Z
DTSTAMP:20260930T004145Z
UID:AI-CoNT/6
DESCRIPTION:by Seewoo Lee (EPFL) as part of AI\, Combinatorics and Number 
 Theory Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AI-CoNT/6/
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