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McGill University
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Mon 8 Apr 2013, 3:00pm
Harmonic Analysis Seminar
Math 126
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Conformal invariants from nodal sets
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Math 126
Mon 8 Apr 2013, 3:00pm-4:00pm
Abstract
We study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators, which include the Yamabe and Paneitz operators. We give several applications to curvature prescription problems. We establish a version in conformal geometry of Courant's Nodal Domain Theorem. We also show that on any manifold of dimension n >=3, there exist many metrics for which our invariants are nontrivial. We prove that the Yamabe operator can have an arbitrarily large number of negative eigenvalues on any manifold of dimension n >=3. We obtain similar results for some higher order GJMS operators on some Einstein and Heisenberg manifolds. This is joint work with Yaiza Canzani, Rod Gover and Raphael Ponge.
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University of Notre Dame
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Mon 8 Apr 2013, 3:10pm
Algebraic Geometry Seminar
ESB 4133
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Paving Hessenberg Varieties by Affines
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ESB 4133
Mon 8 Apr 2013, 3:10pm-4:10pm
Abstract
Hessenberg varieties are closed subvarieties of the full flag variety. Examples of Hessenberg varieties include both Springer fibers and the flag variety. In this talk we will show that Hessenberg varieties corresponding to nilpotent elements which are regular in a Levi factor of the Lie algebra are paved by affines. We then provide a partial reduction from paving Hessenberg varieties for arbitrary elements to paving those corresponding to nilpotent elements, generalizing results of Tymoczko.
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UBC
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Mon 8 Apr 2013, 4:10pm
Algebraic Geometry Seminar
ESB 4133
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Cohomology of Springer Fibres and Springer's Weyl group action via localization
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ESB 4133
Mon 8 Apr 2013, 4:10pm-4:40pm
Abstract
I will apply Martha Precup's theorem on affine pavings to describe the equivariant cohomology algebras of (regular) Springer fibres in terms of certain Weyl group orbits. This will also yield a simple description of Springer's representation of W on the cohomology of the above Springer fibres.
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Chalmers University of Technology
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Wed 10 Apr 2013, 3:00pm
Probability Seminar / Symbolic Dynamics and Ergodic Theory Seminar
ESB 2012
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The many faces of the T T-inverse process
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ESB 2012
Wed 10 Apr 2013, 3:00pm-4:00pm
Abstract
The T T-inverse process or equivalently "random walk in random scenery" is a family of stationary processes that exhibits an amazing amount of behavior. Each random walk yields such a process and as you vary the random walk, you obtain essentially all possible ergodic theoretic behaviors. There is also a phase transition that arises which we can only partially prove. I will give an overview of this area which contains work both old and (somewhat) new.
This work is done jointly with a number of people including Frank den Hollander, Mike Keane and Sebastien Blachere.
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Thu 11 Apr 2013, 9:00am
SPECIAL
One Time Event
Graduate Student Center, Room 203
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Doctoral Exam
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Graduate Student Center, Room 203
Thu 11 Apr 2013, 9:00am-11:30am
Details
Let E and f be an Eisenstein series and a cusp form, respectively, of the same weight k 2 and of the same level N, both eigenfunctions of the Hecke operators, and both normalized so that a1 = 1. The main result we seek is
that when E and f are congruent mod a prime p (which may be a prime ideal lying over a rational prime p > 2), the algebraic parts of the special values L(E; ; j) and L(f; ; j) satisfy congruences mod the same prime. On the way to proving the congruence result, we construct the modular symbol attached to an Eisenstein series.
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UBC
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Thu 11 Apr 2013, 3:30pm
Number Theory Seminar
room MATH 126
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Forms in many variables over the primes
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room MATH 126
Thu 11 Apr 2013, 3:30pm-4:30pm
Abstract
We study the number of solutions of diophantine equations f(x1,...,xn)=v when the variables xi are restricted to primes. It has been established by Birch and Schmidt that one has the expected number of integer solutions if f is a homogeneous integral polymomial of sufficiently large rank with respect to its degree. We show that the same phenomenon holds when the variables are restricted to primes, extending the results of Hua for diagonal forms. We illustrate some of the ideas on quadratic forms and discuss some elements of the proof of the general case.
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