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 Events
Stanford
Mon 29 Sep 2014, 3:30pm
CRG Geometry and Physics Seminar
ESB 2012
Stabilization of discriminants in the Grothendieck ring
ESB 2012
Mon 29 Sep 2014, 3:30pm-4:30pm

Abstract

We consider the ``limiting behavior'' of {\em discriminants}, by which we mean informally the closure of the locus in some parameter space of some type of object where the objects have certain singularities. We focus on the space of partially labeled points on a variety X, and linear systems on X. These are connected --- we use the first to understand the second. We describe their classes in the "ring of motives", as the number of points gets large, or as the line bundle gets very positive. They stabilize in an appropriate sense, and their stabilization can be described in terms of the motivic zeta values. The results extend parallel results in both arithmetic and topology. I will also
present a conjecture (on ``motivic stabilization of symmetric powers'') suggested by our work. Although it is true in important cases, Daniel Litt has shown that it contradicts other hoped-for statements. This is joint work with Melanie Wood. 

Note for Attendees

 Note the unusual place, ESB 2012, and the unusual time, 3:30-4:30pm.
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Chen Greif
Computer Sciences, UBC
Tue 30 Sep 2014, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Null-Space Based Block Preconditioners for Saddle-Point Systems with a Maximally Rank-Deficient Leading Block
ESB 4133 (PIMS Lounge)
Tue 30 Sep 2014, 12:30pm-1:30pm

Abstract

We consider nonsingular saddle-point matrices whose (1,1) block is maximally rank deficient, and show that the inverse in this case has unique mathematical properties. We then develop a class of indefinite block preconditioners that rely on approximating the null space of the leading block. Under certain conditions, even though the preconditioned matrix is a product of two indefinite matrices, the conjugate gradient method can be applied and is rapidly convergent. Spectral properties of the preconditioners are observed, which are validated by numerical experiments.

This is joint work with Ron Estrin.

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University of Minnesota
Tue 30 Sep 2014, 2:30pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
ESB 4127
Geometry of shrinking Ricci solitons
ESB 4127
Tue 30 Sep 2014, 2:30pm-3:30pm

Abstract

This talk concerns the geometry of shrinking Ricci solitons, a class of self-similar solutions to the Ricci flows. We plan to provide some general background results and explain a recent work with Ovidiu Munteanu on the curvature estimates of four dimensional solitons.

Note for Attendees

 Please note unusual time and room.
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Universite de Cergy-Pontoise
Tue 30 Sep 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Stationary Kirchhoff systems in closed manifolds
ESB 2012
Tue 30 Sep 2014, 3:30pm-4:30pm

Abstract

 We investigate various issues for stationary Kirchhoff systems in closed manifolds, such as the questions of existence, non-existence and compactness of solutions to the equations.
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Hong Kong University of Science and Technology
Wed 1 Oct 2014, 3:00pm
Probability Seminar
ESB 2012
Solving the high-dimensional Markowitz Optimization Problem: a tale of sparse solutions
ESB 2012
Wed 1 Oct 2014, 3:00pm-4:00pm

Abstract

We consider the high-dimensional Markowitz optimization problem. A new approach combining sparse regression and estimation of optimal returns based on random matrix theory is proposed to solve the problem. We prove that under some sparsity assumptions on the underlying optimal portfolio, our novel approach asymptotically yields the theoretical optimal return, and in the meanwhile satisfies the risk constraint. To the best of our knowledge, this is the first method that can achieve these two goals simultaneously in the high-dimensional setting. We further conduct simulation and empirical studies to compare our method with some benchmark methods, including the equally weighted portfolio, the bootstrap-corrected method by Bai et al. (2009) and the covariance-shrinkage method by Ledoit and Wolf (2004). The results demonstrate substantial advantage of our method, which attains high level of returns while keeping the risk well controlled by the given constraint.

Based on joint work with Mengmeng Ao and Yingying Li.

 
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UBC
Wed 1 Oct 2014, 3:15pm
Topology and related seminars
ESB 4133 (may move to Thursday)
The Status of the Farrell-Jones conjecture
ESB 4133 (may move to Thursday)
Wed 1 Oct 2014, 3:15pm-4:15pm

Abstract

In the beginning of this talk I will use the Farrell-Jones conjecture to express the K-theory of R[Z^2] in Terms of the K-theory of R. Geometric conditions on a Group that imply the conjecture will be mentioned . The class of Groups for which the conjecture is known is quite large I will define it and mention some interesting open cases.
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Université Pierre et Marie Curie
Thu 2 Oct 2014, 3:30pm
Number Theory Seminar
room MATH 126
Points of small height on abelian varieties over function fields
room MATH 126
Thu 2 Oct 2014, 3:30pm-4:30pm

Abstract

An old conjecture of Lang (for elliptic curves) generalized by Silverman, asserts that the Néron-Tate height of a rational point of an abelian variety defined over a number field can be bounded below linearly in terms of the Faltings height of the underlying abelian variety. We shall explore the function field analogue of this problem.
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Université Paris-Sud
Thu 2 Oct 2014, 4:00pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
ESB 4133 (PIMS lounge)
Large Time behavior for the cubic Szego évolution
ESB 4133 (PIMS lounge)
Thu 2 Oct 2014, 4:00pm-5:00pm

Abstract

The cubic Szegö equation is an Hamiltonian evolution on periodic functions with nonnegative Fourier modes, arising as a normal form for the large time behavior of a nonlinear wave equation on the circle. It defines a flow on every Sobolev space with enough regularity. In this talk, I will give the main arguments for the proof of the following theorem. The trajectories of the cubic Szegö equation are almost periodic in the Sobolev energy space, but
are generically unbounded in every more regular Sobolev space.This is a joint work with Sandrine Grellier and Zaher Hani.

Note for Attendees

 Please note unusual time and room.
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UBC
Fri 3 Oct 2014, 3:00pm
Department Colloquium
MATH ANNEX 1100
Recent developments for Ricci flow on non-compact manifolds.
MATH ANNEX 1100
Fri 3 Oct 2014, 3:00pm-4:00pm

Abstract

The Ricci flow is one of the most important equations in geometric analysis, and has been used to solve deep problems in topology and geometry. Through a system of local parabolic PDE's, the flow governs the evolution of a Riemannian metric tensor in space, and it's general theory is fundamentally based on the assumption that the metric is complete with bounded sectional curvatures. I will give an overview of the general theory, then discuss the problem of flowing unbounded curvature metrics on non-compact manifolds. I will then discuss recent results for U(n) invariant Kahler metrics on C^n, and connections to Yau's uniformization conjecture. The talk is based in part on joint work with L.F. Tam and K.F Li.

Note for Attendees

Refreshments will be served at 2:45pm in the Math Lounge area, MATH 125 before the colloquium.
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