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Seminars for the week of October 25, 2010
Colloquium
Thursday, 3:35, in VinH 16Professor Bryden Cais
of University of Wisconsin, Madison
will speak on
"Galois representations and their families" The study of systems of polynomial equations with rational
coefficients has its origins in the mathematics of ancient Greece, and lies at the very heart of
algebraic number theory and arithmetic geometry. Rather than studying one equation at a time, it
is far more fruitful to study the set of all solutions to all equations at once: this set has an
enormous wealth of structure, which is encoded by its group of symmetries, the absolute Galois
group. This group is extremely complicated and full of mysteries, so to glimpse its inner workings
we are led to study its continuous representations. Over the real or complex numbers, any such
representation necessarily has finite image, and unfortunately much of the structure of the
Galois group is lost. There is however a remarkable substitute for the real and complex numbers
as coefficients: the field of p-adic numbers (for a prime p). In dramatic contrast,representations
of the Galois group over the p-adic numbers rarely have finite image and their study is full of
riches: indeed, p-adic Galois representations have played a pivotal role in some of the most
spectacular advances in modern number theory,including the recent proofs of Fermat's Last Theorem,
the Shimura-Taniyama Conjecture, and Serre's Conjecture. A key feature of p-adic Galois representations
(in no way shared by real or complex valued representations) underlying these achievements is the fact
that they can be deformed in continuous families.
In this talk, I will survey the exciting world of p-adic Galois representations and the groundbreaking
work of H. Hida from the 1980's which first proved the existence of certain interesting families of them.
I will then outline a new and purely geometric approach to Hida's work via recent progress in p-adic
Hodge theory.
Monday, 25 Oct 2010
Junior Colloquium:
at 12:20 in VinH 570
-
... Will not meet this week
Topology Seminar:
at 3:30 in VinH 203A
-
Professor Alexander A. Voronov
will speak on "Quantum deformations: Smoothness theorem"
Dynamical Systems Seminar:
at 3:35 in VinH 570
-
... Will not meet this week
Student Seminar in Symplectic Geometry:
at 4:30 in VinH 203B
-
Ching-Hao Chang
will speak on "Isotopy of nodal curves - a continuation"
Tuesday, 26 Oct 2010
Student Combinatorics Seminar:
at 11:15 in VinH 570
-
Nathan Williams
will speak on "Title: to be announced"
IMA Postdoc Seminar:
at 11:15 in LindH 305
-
Oscar E. Fernandez (1st year Postdoc)
will speak on "Simulating nonholonomic mechanics using variational integrators through Hamiltonization"
Math Physics Seminar:
at 12:25 in VinH 570
-
Rob Thompson
will speak on "Introduction to equivariant moving frames"
Differential Geometry/Symplectic Topology:
at 1:30 in VinH 570
-
... Will not meet this week
Student MFM Seminar:
at 2:30 in VinH 570
-
... Will not meet this week
Arithmetic Applications of p-Adic Cohomology Seminar:
at 3:40 in VinH 570
-
Professor Steven Sperber
will speak on "Estimating the degree of the L-function associated with exponential sums"
Wednesday, 27 Oct 2010
Climate Change:
at 11:15 in VinH 570
-
Professor Richard McGehee
will speak on "An introduction to energy balance models"
Working Seminar on Langlands Functoriality:
at 1:25 in VinH 20
-
Mr. Xin Shen
will speak on "Representations and local factors-unitary groups"
Student Seminar in Symplectic Geometry:
at 3:30 in VinH 570
-
Xu Wang
will speak on "Seidel's long exact sequence"
PDE Seminar:
at 3:35 in VinH 206
-
Professor Herbert Koch
from (University of Bonn)
will speak on "Parabolic equations with rough initial data"
Thursday, 28 Oct 2010
Math Club Seminar:
at 12:10 in VinH 120
-
Kara Maki
from IMA
will speak on "Title: to be announced"
Differential Geometry/Symplectic Topology:
at 1:30 in VinH 570
-
Professor Ovidiu Munteanu
from Columbia University
will speak on "Gradient Ricci Solitons"
Colloquium:
at 3:30 in VinH 16
-
Professor Bryden Cais
from University of Wisconsin, Madison
will speak on "Galois representations and their families"
Friday, 29 Oct 2010
Graduate Student Forum Seminar:
at 12:20 in VinH 16
-
... Will not meet this week
Industrial Problems Seminar:
at 1:25 in VinH 16
-
Irina Rish
from Computational Biology Center, IBM
will speak on "Predictive modeling of mental states from fMRI data"
Lie Theory Seminar:
at 1:30 in VinH 311
-
Professor Dihua Jiang
will speak on "Eisenstein series and L-functions"
Probability Seminar:
at 2:30 in VinH 207
-
Professor Bert Fristedt
will speak on "The descent sets of one-dependent random sequences"
Special Algebraic Representation Theory Seminar:
at 2:30 in VinH 203A
-
Professor Shigeo Koshitani
from Chiba University, Japan
will speak on "Scott modules in representation theory of finite groups"
Special Scientific Computation Seminar:
at 3:30 in Walter Library 402
-
Professor Mitch Luskin
will speak on "Development and analysis of atomistic-to-continuum coupling methods"
Combinatorics Seminar:
at 3:35 in VinH 570
-
Professor June Huh
from University of Illinois, Urbana Champaign
will speak on "Milnor numbers of projective hypersurfaces and the chromatic polynomial of graphs"
Automorphic Forms and Number Theory:
at 3:35 in VinH 301
-
Professor Paul Garrett
will speak on "Colin de Verdiere's proof - a continuation"
Practitioners' Financial Mathematics Seminar:
at 5:30 in VinH 16
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Christopher Prouty
from Cargill
will speak on "Commodities"
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