BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Gal Binyamini DTSTART:20251202T200000Z DTEND:20251202T210000Z DTSTAMP:20260419T151622Z UID:BC-MIT/28 DESCRIPTION:Title: Unlikely intersections with Bessel functions and Laguerre polynomials I\nby Gal Binyamini as part of BC-MIT number theory seminar\n\nLecture hel d in Maloney 560 at Boston College.\n\nAbstract\nSeveral problems in arith metic geometry identify a class of "special points" and seek to describe t he set of special points satisfying a given system of algebraic equations. Two classical examples are the Manin-Mumford conjecture concerning torsio n points in abelian varieties\, and the Andre-Oort conjecture concerning C M points in Shimura varieties. We propose a new variation on this theme\, where the role of special points is played by the zeros of special functio ns such as the Bessel function\, or of classical orthogonal polynomials. T he Bessel function problem is related to a conjecture of Fuglede in harmon ic analysis from 1974\, and the orthogonal polynomial problem to a conject ure of Stieltjes from 1890.\n\nIn the first talk we will recall the Manin- Mumford conjecture and introduce the Bessel function and orthogonal polyno mial analogs. We will sketch the proof of classical Manin-Mumford using o- minimality and how it can be adapted to obtain various results in this new context. This naturally leads to the more "exotic" o-minimal structure of multisummable functions\, as opposed to the structure R_{an\,exp} used in classical applications.\nIn the second talk we will discuss new functiona l transcendence results that are needed to complete the argument: a varian t of the Ax-Schanuel theorem for the special functions appearing in this c ontext. This naturally leads to the study of differential Galois groups fo r irregular-singular systems\, as opposed to the regular-singular systems used in classical applications.\n\nAll the results are based on joint work with Avner Kiro and some also with Gady Kozma.\n LOCATION:https://researchseminars.org/talk/BC-MIT/28/ END:VEVENT END:VCALENDAR