BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Christopher Williams (Warwick) DTSTART:20201119T140000Z DTEND:20201119T150000Z DTSTAMP:20260423T040008Z UID:UCDANT/3 DESCRIPTION:Title: p -adic L-functions in higher dimensions\nby Christopher Williams (Warwi ck) as part of Dublin Algebra and Number Theory Seminar\n\n\nAbstract\nThe re are lots of theorems and conjectures relating special values of complex analytic L-functions to arithmetic data\; for example\, celebrated exampl es include the class number formula and the BSD conjecture. These conjectu res predict a surprising (complex) bridge between the fields of analysis a nd arithmetic. However\, these conjectures are extremely difficult to prov e. Most recent progress has come from instead trying to build analogous $p $-adic bridges\, constructing a $p$-adic version of the $L$-function and r elating it to $p$-adic arithmetic data via "Iwasawa main conjectures". Fro m the $p$-adic bridge\, one can deduce special cases of the complex bridge \; this strategy has\, for example\, led to the current state-of-the-art r esults towards the BSD conjecture.\n\nEssential in this strategy is the co nstruction of a $p$-adic L-function. In this talk I will give an introduct ion to $p$-adic L-functions\, focusing first on the $p$-adic analogue of t he Riemann zeta function (the case of ${\\rm GL}_1$)\, then describing wha t one expects in a more general setting. At the end of the talk I will sta te some recent results from joint work with Daniel Barrera and Mladen Dimi trov on the construction of $p$-adic L-functions for certain automorphic r epresentations of ${\\rm GL}_{2n}$.\n\nPasscode: The 3-digit prime numerat or of Riemann zeta at -11\n LOCATION:https://researchseminars.org/talk/UCDANT/3/ END:VEVENT END:VCALENDAR