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Seminars for the week of October 16, 2006
Colloquium
Thursday, 3:30, in VinH 16Professor Jordan Ellenberg
of University of Wisconsin
will speak on
"Local-global principles for representations of quadratic forms"
We discuss an application of ergodic theory to a classical problem of number theory. The problem of representing integers by quadratic forms has a long history. Starting with Lagrange's theorem that every nonnetative integer is the sum of four squares. More generally, give two quadratic lattices $Q'$ and $Q$, of ranks $m$ and $n$, one can ask whether $Q'$ can be embedded into $Q$. More precisely, one asks if the existence of embeddings over $R$ and over $Z_p$ for every $p$ implies the existence of an embedding over $Z$. Previously a statement of this kind was known when $n$ is at least $2m+3$. We show that in fact a local-to-global theorem holds whenever $n>=m+7$. The key idea is to relate the problem to a question about actions of p-adic groups, and then apply a version of Ratner's theorem to show, very loosely, that representations of $Q'$ by forms in the genus of $Q$ are equidistributed over the genus of $Q$. We also include some general discussion about orbits of integral points on homogeneous spaces, and their relation with adelic quotients and cohomology groups. (joint work with A. Venkatesh). If people want to look at the paper,it's on the arXiv at: http://front.math.ucdavis.edu/math.NT/0604232
Monday, 16 Oct 2006
- Professor Scot Adams will speak on "Mathematicians got it all - a continuation"
- ... Will not meet this week
- ... Will not meet this week
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Financial Mathematics:
at 3:30 in VinH 6
-
Dynamical Systems Seminar:
at 3:35 in VinH 570
-
Real Analysis [In memory of Gene Fabes]::
at 4:40 in VinH 6
Tuesday, 17 Oct 2006
- Anders Nedergaard Jensen from Aarhus University will speak on "Tropical varieties"
- Professor Steven Damelin from Georgia Southern University will speak on "Kernel methods in computer vision, integration, approximation, random matrices and data methods"
- ... Will not meet this week
- Josef Dorfmeister will speak on "Some symplectic topology"
- ... Will not meet this week
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IMA Postdoc Seminar:
at 11:15 in Lind Hall 409
-
Applied Math and Numerical Analysis:
at 11:15 in VinH 1
-
Algebraic Geometry:
at 1:25 in Vincent Hall 301
-
Jr. Colloquium:
at 3:35 in VinH 16
-
Student Seminar on Algebraic Geometry, Geometry and Topology:
at 4:40 in VinH 570
Wednesday, 18 Oct 2006
- Professor Zhonggang Zeng from Northeastern Illinois University will speak on "A numerical approach toward approximate algebraic computation"
- Professor Nicolai Krylov will speak on "Parabolic equaitons with VMO coefficients in Sobolev spaces with mixed norms"
-
Algebraic Geometry and Applications:
at 11:15 in Lind Hall 409
-
PDE:
at 3:35 in VinH 570
Thursday, 19 Oct 2006
- ... Will not meet this week
- Dr. Calin Chindris will speak on "Quivers and cluster algebras"
- Professor Jiaping Wang will speak on "Kahler manifolds with positive spectrum"
- Professor Jordan Ellenberg from University of Wisconsin will speak on "Local-global principles for representations of quadratic forms"
- ... Will not meet this week
-
Topology:
at 10:10 in 570 VinH
-
Algebraic Representation Theory:
at 11:15 in VinH 570
-
Differential Geometry/Symplectic Topology:
at 1:25 in VinH 570
-
Colloquium:
at 3:35 in VinH 16
-
Informal Mathematical Biology:
at 5:30 in VinH 570
Friday, 20 Oct 2006
- Jae Lew from Eaton Corporation will speak on "Control Theory: Real World Application"
- ... Will not meet this week
- Sen-Peng Eu will speak on "Enumeration of parking functions by leading terms"
- ... Will not meet this week. (Midwest Probability Conference at Northwestern)
- ... Will not meet this week
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Industrial Problems Seminar:
at 1:25 in VinH 6
-
Student Combinatorics:
at 2:30 in VinH 570
-
Combinatorics:
at 3:35 in VinH 570
-
Probability:
at 3:35 in VinH 206
-
Automorphic Forms and Number Theory:
at 4:40 in VinH 364
Professor Gennadyi Chistyakov, University of Bielefeld, Germany will visit the Mathematics Department October 12-23, 2006. His visit is partially sponsored by the Visitors Program. During his stay, his office will be Vincent Hall 239: you can reach him by phone at (612) 624- 4813. OFTEN
