[Liste-CICMA] SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY (22/09/2016, Brandon Levin, Steve Lester)
Guillermo Martinez-Zalce
martinez at crm.umontreal.ca
Tue Sep 20 10:59:45 EDT 2016
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SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY
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DATE :
Le jeudi 22 septembre 2016 / Thursday, September 22, 2016
HEURE / TIME :
10 h 30 - 12 h / 10:30 a.m. - 12:00 p.m.
CONFERENCIER(S) / SPEAKER(S) :
Brandon Levin (Chicago)
TITRE / TITLE :
Weight elimination in Serre-type conjectures
LIEU / PLACE :
McGill University, Burnside Hall salle BH920
RESUME / ABSTRACT :
I will discuss recent results towards the weight part of Serre's conjecture for GL_n as formulated by Herzig. The conjecture predicts the set of weights where an odd n-dimensional mod p Galois representation will appear in cohomology (modular weights) in terms of the restriction of the representation to the decomposition group at p. We show that the set of modular weights is always contained in the predicted set in generic situations. This is joint work with Daniel Le and Bao V. Le Hung.
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DATE :
Le jeudi 22 septembre 2016 / Thursday, September 22, 2016
HEURE / TIME :
14 h - 15 h 30 / 2:00 p.m. - 3:30 p.m.
CONFERENCIER(S) / SPEAKER(S) :
Steve Lester (CICMA)
TITRE / TITLE :
Quantum Chaos and Arithmetic
LIEU / PLACE :
Concordia Bookstore, Library Building, 9th floor
RESUME / ABSTRACT :
In this talk I will discuss some problems in Quantum Chaos and describe results in arithmetic settings where more can be proved. Given a compact, smooth Riemannian manifold (M,g) a central problem in Quantum Chaos is to understand the behavior of eigenfunctions of the Laplace-Beltrami operator in the limit as the eigenvalue tends to infinity. The Quantum Ergodicity Theorem of Shnirelman, Colin de Vediere, and Zelditch asserts that if the geodesic flow on M is ergodic then the L^2 mass of almost all of the eigenfunctions equidistributes. I will discuss problems which go beyond the Quantum Ergodicity Theorem such as quantum unique ergodicity and small scale quantum ergodicity in the setting of arithmetic surfaces such as the torus and modular surface. I will also describe how these problems are related to lattice point estimates, representations of integers by quadratic forms, modular forms, and L-functions.
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Responsable(s) :
Henri Darmon (darmon at math.mcgill.ca)
Eyal Z. Goren (eyal.goren at mcgill.ca)
Chantal David (cdavid at mathstat.concordia.ca)
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http://www.dms.umontreal.ca/~qvnts/QVNTSinfo.html
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