BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jonathan Pila DTSTART:20251202T213000Z DTEND:20251202T223000Z DTSTAMP:20260419T152924Z UID:BC-MIT/27 DESCRIPTION:Title: Unlikely intersections with Bessel functions and Laguerre polynomials II\nby Jonathan Pila as part of BC-MIT number theory seminar\n\nLecture he ld in Maloney 560 at Boston College.\n\nAbstract\nSeveral problems in arit hmetic geometry identify a class of "special points" and seek to describe the set of special points satisfying a given system of algebraic equations . Two classical examples are the Manin-Mumford conjecture concerning torsi on points in abelian varieties\, and the Andre-Oort conjecture concerning CM 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 functi ons such as the Bessel function\, or of classical orthogonal polynomials. The Bessel function problem is related to a conjecture of Fuglede in harmo nic analysis from 1974\, and the orthogonal polynomial problem to a conjec ture of Stieltjes from 1890.\n\nIn the first talk we will recall the Manin -Mumford conjecture and introduce the Bessel function and orthogonal polyn omial 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 ne w context. This naturally leads to the more "exotic" o-minimal structure o f multisummable functions\, as opposed to the structure R_{an\,exp} used i n classical applications.\nIn the second talk we will discuss new function al transcendence results that are needed to complete the argument: a varia nt of the Ax-Schanuel theorem for the special functions appearing in this context. This naturally leads to the study of differential Galois groups f or irregular-singular systems\, as opposed to the regular-singular systems used in classical applications.\n\nAll the results are based on joint wor k with Avner Kiro and some also with Gady Kozma.\n LOCATION:https://researchseminars.org/talk/BC-MIT/27/ END:VEVENT END:VCALENDAR