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DTSTAMP:20171027T110938Z
DTSTART;TZID=America/Los_Angeles:20171030T151000
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SUMMARY:Arithmetic Geometry and Number Theory RTG Seminar: On the Gross-Stark conjecture
UID:112964-ucb-events-calendar@berkeley.edu
ORGANIZER;CN="UC Berkeley Calendar Network":
LOCATION:891 Evans Hall
DESCRIPTION:Samit Dasgupta\, UCSC\n\n$Seminar\\\, Format$:\n\nThe seminar consists of two 50-minute talks\, a pre-talk (3:10-4:00) and an advanced talk (4:10-5:00)\, with a 10-minute break (4:00-4:10) between them. The advanced talk is a regular formal presentation about recent research results to general audiences in arithmetic geometry and number theory\; the pre-talk (3:10-4:00) is to introduce some prerequisites or background for the advanced talk to audiences consisting of graduate students.\n\n$Pre$-$talk$: Stark's conjectures (classical and $p$-adic)\n\nIn this talk we will state the classical Stark conjecture. Next we will qualitatively describe the two $p$-adic Stark conjectures (at $s=1$ and $s=0$)\, due to Serre-Solomon and Gross\, respectively. If time permits\, I will sketch "Ribet's Method"\, which is a technique to relate special values of L-functions to algebraic objects\, and will be employed in the second talk.\n\n$Advanced\\\, talk$: On the Gross-Stark conjecture\n\nIn 1980\, Gross conjectured a formula for the expected leading term at $s=0$ of the Deligne–Ribet $p$-adic $L$-function associated to a totally even character ψ of a totally real field $F$. The conjecture states that after scaling by $L(\\psi \\omega ^{-1}\, 0)$\, this value is equal to a $p$-adic regulator of units in the abelian extension of $F$ cut out by $\\psi \\omega ^{-1}$. In this talk we describe a proof of Gross's conjecture. This is joint work with Mahesh Kakde and Kevin Ventullo. If time permits\, we will briefly describe joint work with Michael Spiess on a refinement of Gross's conjecture that gives a formula for the characteristic polynomial of the regulator matrix. This refined conjecture is still open.
URL:http://events.berkeley.edu/index.php/calendar/sn/pubaff.html?event_ID=112964&view=preview
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