BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jishnu Ray (University of British Columbia) DTSTART:20200423T210000Z DTEND:20200423T220000Z DTSTAMP:20260423T041111Z UID:UCSD_NTS/1 DESCRIPTION:Title: Conjectures in Iwasawa Theory of Selmer groups and Iwasawa Algebras\n by Jishnu Ray (University of British Columbia) as part of UCSD number theo ry seminar\n\n\nAbstract\nThe Iwasawa Theory of Selmer groups provides a n atural way for p-adic approach to the celebrated Birch and Swinnerton Dyer conjecture. Over a non-commutative p-adic Lie extension\, the (dual) Selm er group becomes a module over a non-commutative Iwasawa algebra and its s tructure can be understood by analyzing “(left) reflexive ideals” in t he Iwasawa algebra. In this talk\, we will start by recalling several exis ting conjectures in Iwasawa Theory and then we will give an explicit ring- theoretic presentation\, by generators and relations\, of such Iwasawa alg ebras and sketch its implications in understanding the (two-sides) reflexi ve ideals. Generalizing Clozel’s work for SL(2)\, we will also show that such an explicit presentation of Iwasawa algebras can be obtained for a m uch wider class of p-adic Lie groups viz. uniform pro-p groups and the pro -p Iwahori of GL(n\,Z_p). Further\, if time permits\, I will also sketch s ome of my recent Iwasawa theoretic results joint with Sujatha Ramdorai.\n\ npretalk\n LOCATION:https://researchseminars.org/talk/UCSD_NTS/1/ END:VEVENT END:VCALENDAR