BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dennis Davenport (Howard University) DTSTART:20260915T180000Z DTEND:20260915T190000Z DTSTAMP:20261113T235223Z UID:AI-CoNT/1 DESCRIPTION:Title: Riordan Arrays\, Pseudo-Involutions\, and AI-Assisted Mathematical Discovery\nby Dennis Davenport (Howard University) as part of AI\, Com binatorics and Number Theory Seminar\n\n\nAbstract\nThe Riordan group is a group of infinite lower triangular matrices that are defined by\ntwo gene rating functions\, $g$ and $f$. The $k^{\\mathrm{th}}$ column of each matr ix has a generating function related\nto $gf^k$. There are many applicatio ns of Riordan arrays\, among other things they can be used to\ncount combi natorial objects and to prove combinatorial identities\n\nIn this talk\, I will introduce Riordan arrays and discuss recent joint work with Dewayne Dixon and\nMoussa Doumbia on pseudo-involutions. In the Appell subgroup\, the pseudo-involution condition\nreduces to the simple identity\n\\[\ng(z) g(-z)=1\,\n\\]\nwhich leads to a useful classification and several interes ting integer sequences. I will also discuss\nhow artificial intelligence c an assist mathematical discovery by helping generate examples\, identify\n patterns\, and suggest conjectures\, while exact computation and proof rem ain essential.\n LOCATION:https://master.researchseminars.org/talk/AI-CoNT/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Matilde Lalín (Université de Montréal) DTSTART:20260929T180000Z DTEND:20260929T190000Z DTSTAMP:20261113T235223Z UID:AI-CoNT/2 DESCRIPTION:Title: The arithmetic of Boyd’s Mahler measure conjectures: from data an alysis to machine learning\nby Matilde Lalín (Université de Montréa l) as part of AI\, Combinatorics and Number Theory Seminar\n\n\nAbstract\n The Mahler measure is an invariant of multivariable rational functions def ined 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 rational multiple $r_k L'(E_k\,0)$\, where $E_k$ is an associated\nellip tic curve. We study the arithmetic of the factors $r_k$ using a dataset of the first\n250\,000 values of $k$\, combining large-scale statistical ana lysis with transformer-based\nexperiments. We observe several striking pat terns in their size and $p$-adic behavior\,\nand find that the neural netw orks recover substantial arithmetic structure from the data\,\nand perhaps a bit more. This is joint work with Alberto Alfarano\, Pablo Bianucci\, a nd\nBerend Ringeling.\n LOCATION:https://master.researchseminars.org/talk/AI-CoNT/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Katherine Stange (University of Colorado\, Boulder) DTSTART:20261027T180000Z DTEND:20261027T190000Z DTSTAMP:20261113T235223Z UID:AI-CoNT/3 DESCRIPTION:Title: Illustrating Mathematics (now with AI)\nby Katherine Stange (Un iversity of Colorado\, Boulder) as part of AI\, Combinatorics and Number T heory Seminar\n\n\nAbstract\nI'll make a case for AI use in exploring math ematical research directions visually\, and demonstrate how accessible vis ual exploration has become. I'll draw on some of my own explorations in l attices\, algebraic numbers\, Kleinian groups\, Diophantine approximation\ , continued fractions and the like.\n LOCATION:https://master.researchseminars.org/talk/AI-CoNT/3/ END:VEVENT BEGIN:VEVENT SUMMARY:David Roe (MIT) DTSTART:20261110T190000Z DTEND:20261110T200000Z DTSTAMP:20261113T235223Z UID:AI-CoNT/4 DESCRIPTION:Title: Absolute Galois groups of 2-adic fields\, AI\, and formalization\nby David Roe (MIT) as part of AI\, Combinatorics and Number Theory Semi nar\n\n\nAbstract\nIn 1982\, Jannsen and Wingberg gave an explicit present ation for the absolute group of any $p$-adic field\, as long as $p \\ne 2$ . I will describe the journey to completing this result by giving present ations for $2$-adic fields. Along the way I will discuss my experiences w ith AI-generated solutions\, different methods for verification of propose d solutions\, auto-formalization in Lean and the Tau Ceti project\, which is rapidly expanding into a formal library spanning all of mathematics.\n LOCATION:https://master.researchseminars.org/talk/AI-CoNT/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Sutherland (MIT) DTSTART:20261124T190000Z DTEND:20261124T200000Z DTSTAMP:20261113T235223Z 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://master.researchseminars.org/talk/AI-CoNT/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Seewoo Lee (EPFL) DTSTART:20261013T180000Z DTEND:20261013T190000Z DTSTAMP:20261113T235223Z UID:AI-CoNT/6 DESCRIPTION:Title: Some practical tips on digesting AI proofs: informal and formal asp ects\nby Seewoo Lee (EPFL) as part of AI\, Combinatorics and Number Th eory Seminar\n\n\nAbstract\nIn this new era of proof abundance\, "digestio n" has become an important part of mathematics. As of October 2026\, LLM-g enerated proofs are still hard to read\, and making them accessible requir es considerable effort. On August 1\, OpenAI announced a result on the opt imal exponent for both the Cohn–Elkies linear programming bound and the Bourgain–Clozel–Kahane sign uncertainty principle. In this talk\, I wi ll share my experience digesting this result. We will also go through its formalization and how it can be improved.\n LOCATION:https://master.researchseminars.org/talk/AI-CoNT/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Ed Hirst (University of Campinas) DTSTART:20261208T190000Z DTEND:20261208T200000Z DTSTAMP:20261113T235223Z UID:AI-CoNT/7 DESCRIPTION:by Ed Hirst (University of Campinas) as part of AI\, Combinato rics and Number Theory Seminar\n\nAbstract: TBA\n LOCATION:https://master.researchseminars.org/talk/AI-CoNT/7/ END:VEVENT END:VCALENDAR