BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alireza Salehi Golsefidy (UCSD) DTSTART:20201015T210000Z DTEND:20201015T220000Z DTSTAMP:20260423T040330Z UID:JNTS/2 DESCRIPTION:Title: Spe ctral gap in perfect algebraic groups over prime fields\nby Alireza Sa lehi Golsefidy (UCSD) as part of Columbia CUNY NYU number theory seminar\n \n\nAbstract\nSuppose $G$ is a connected algebraic $\\Bbb Q$-group which i s perfect\; that means $G=[G\,G].$ Let $H$ be the largest semisimple quoti ent of $G.$ We show that a family of Cayley graphs of $G(F_p)$ is a family of expander graphs if and only if their quotients as Cayley graphs of $H( F_p)$ form a family of expanders. This work extends a result of Lindenstra uss and Varju where they prove a similar statement for the group of specia l affine transformations. In combination with a result of Breuillard and G amburd\, one gets new families of finite groups with strong uniform expans ion. \n\n\\vskip 4pt\nIn the talk after defining the relevant terms\, we d iscuss the method developed by Bourgain and Gamburd for studying random wa lks in finite groups. Roughly this method says in the absence of large app roximate subgroups in a group $G$\, a random walk in $G$ has spectral gap if it can gain an initial entropy and has a Diophantine property. Next in the talk it will be explain why in our problem we only need to prove the n eeded Diophantine property. I will present how certain exponential cancell ations\, uniform convexity of $\\Cal L^p$-spaces\, and a type of hypercont ractivity inequality can help us obtain such a Diophantine property. \n\n\ \vskip 4pt\n\nThis is joint work with Srivatsa Srinivas.\n LOCATION:https://researchseminars.org/talk/JNTS/2/ END:VEVENT END:VCALENDAR