BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sean Eberhard (Cambridge University) DTSTART:20210304T143000Z DTEND:20210304T160000Z DTSTAMP:20260423T024456Z UID:NumTheory/9 DESCRIPTION:Title: Irreducibility of the characteristic polynomial of a random integer matr ix\nby Sean Eberhard (Cambridge University) as part of CRM-CICMA Québ ec Vermont Seminar Series\n\nLecture held in En ligne/Web.\n\nAbstract\nCo nsider a random polynomial with integer coefficients. A natural conjecture is that the polynomial is irreducible with high probability and its Galoi s group is S_n. This question has been studied for various models of rando m polynomial. The usual two models are the "bounded degree model"\, in whi ch the degree is constant and the coefficients are large\, and the "bounde d height model"\, in which the coefficients are drawn uniformly from a fix ed interval and the degree becomes large. We will study a variant of the b ounded height model: take a large n x n matrix with independent +-1 entrie s and take its characteristic polynomial. To study this question we will c ombine ideas from the bounded height model with random matrix theory over a finite field. The method we use is dependent on both the extended Rieman n hypothesis and the classification of finite simple groups.\n LOCATION:https://researchseminars.org/talk/NumTheory/9/ END:VEVENT END:VCALENDAR