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DTSTART:20070311T020000
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DTSTAMP:20260219T221509
DTSTART;TZID=America/Detroit:20260225T160000
DTEND;TZID=America/Detroit:20260225T170000
SUMMARY:Workshop / Seminar:Topology seminar: Top-dimensional cohomology of the congruence subgroup Gamma_{0\,n}(p)
DESCRIPTION:Let Gamma_{0\,n}(p) be the congruence subgroup of level p of SL_n(Z) whose first column is congruent to (*\,0\,\dots\,0)^t \mod p. The cohomology of this subgroup has connections to problems in algebraic K-theory and number theory. Borel and Serre (1973) showed that the rational cohomology of Gamma_{0\,n}(p) vanishes above degree n(n+1)/2. \n\nWe prove that the top-dimensional rational cohomology group of Gamma_{0\,n}(p) vanishes for all p equal to 2\,3\,5\,7\,13 and when n is at least 3\, as well as for all primes p at most 6n-14. We also reprove the known non-vanishing result that this group is nonzero for n=2 for every prime p\, and we establish a new non-vanishing for n=3 for all primes p not equal to 2\,3\,5\,7\,13. \n\nIn this talk\, I will outline the ideas behind these results and briefly survey what is known about the top-dimensional cohomology of related congruence subgroups.
UID:143836-21894104@events.umich.edu
URL:https://events.umich.edu/event/143836
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 3866
CONTACT:
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DTSTAMP:20260324T085405
DTSTART;TZID=America/Detroit:20260225T160000
DTEND;TZID=America/Detroit:20260225T170000
SUMMARY:Meeting:Unpacking the News with U-M Faculty Experts
DESCRIPTION:Each session offers a space to pause\, sort out what’s happening\, and engage in thoughtful\, civil discussion with peers. Bring your questions\, your curiosity\, and your perspective—no preparation required.\n\nJosh Pasek is Professor of Communication & Media and Political Science\, Faculty Associate at the Center for Political Studies\, Institute for Social Research\, and Associate Director of the Michigan Institute for Data Science at the University of Michigan.
UID:143802-21894059@events.umich.edu
URL:https://events.umich.edu/event/143802
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Civic Engagement,Civic Learning,Culture,Education,Free,In Person,Media,Politics,Social Impact,Talk,Undergraduate
LOCATION:Michigan League - Room 4
CONTACT:
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