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 Events
Oregon State University
Wed 28 Sep 2016, 3:00pm
Probability Seminar
ESB 2012
Some probability theory that arises from worrying about Navier-Stokes and other quasilinear equations
ESB 2012
Wed 28 Sep 2016, 3:00pm-4:00pm

Abstract

The success of probability theory in the analysis of linear, or even certain semi-linear,  parabolic and elliptic pde’s is well documented.  In spite of various attempts to find a stochastic foothold for the analysis of Navier-Stokes equations and related quasilinear equations, the problem remains a substantial challenge.  That said, the quest can lead to new stochastic structures and problems that relate to modern probability in fundamental ways.  In this talk I will try to indicate this with a few explicit examples largely stemming from the Lejan-Sznitman multiplicative cascade/branching random walk  framework for Navier-Stokes equations. 
 
This talk is  primarily based on recent joint work with Radu Dascaliuc, Nicholas Michalowski, and Enrique Thomann with partial support from the National Science Foundation. 
 
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University of Illinois, Urbana–Champaign
Wed 28 Sep 2016, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
An equivariant motivic slice filtration
ESB 4133 (PIMS Lounge)
Wed 28 Sep 2016, 3:15pm-4:15pm

Abstract

Mixing Voevodsky's filtration in motivic homotopy and Dugger's in C_2-equivariant homotopy theory leads to an interesting filtration on the C_2-equivariant motivic homotopy category. In this talk, I'll introduce these slice filtrations and talk about some joint work with P. A. Ostvaer, where we compute the resulting zero slice of the equivariant motivic sphere spectrum.


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UBC Math
Fri 30 Sep 2016, 3:00pm
Department Colloquium
ESB 2012
UBC Mathematics and PIMS Faculty Award Colloquium -- On the local Langlands conjectures
ESB 2012
Fri 30 Sep 2016, 3:00pm-4:00pm

Abstract

The Langlands program, initiated in the 1960s, is a set of conjectures predicting a unification of number theory and the representation theory of groups. More precisely, the Langlands correspondence provides a way to interpret results in number theory in terms of group theory, and vice versa.

In this talk we sketch a few aspects of the local Langlands correspondence using elementary examples. We then comment on some questions raised by the emerging "mod p" Langlands program.
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Jessica Bosch
Department of Computer Science, UBC
Tue 4 Oct 2016, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Fast Iterative Solvers for Cahn-Hilliard Problems
ESB 4133 (PIMS Lounge)
Tue 4 Oct 2016, 12:30pm-1:30pm

Abstract

The Cahn-Hilliard equation models the motion of interfaces between several phases. The underlying energy functional includes a potential for which different types were proposed in the literature. We consider smooth and nonsmooth potentials with a focus on the latter. In the nonsmooth case, we apply a function space-based algorithm, which combines a Moreau-Yosida regularization technique with a semismooth Newton method. We apply classical finite element methods to discretize the problems in space. At the heart of our method lies the solution of large and sparse fully discrete systems of linear equations. Block preconditioners using effective Schur complement approximations are presented. For the smooth systems, we derive optimal preconditioners, which are proven to be robust with respect to crucial model parameters. Further, we prove that the use of the same preconditioners give poor approximations for the nonsmooth formulations. The preconditioners we present for the nonsmooth problems incorporate the regularization terms. Extensive numerical experiments show an outstanding behavior of our developed preconditioners. Our strategy applies to different Cahn-Hilliard problems including phase separation and coarsening processes, image inpainting, and two-phase flows. 
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University of California at Irvine
Tue 4 Oct 2016, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
On the first eigenvalue estimate for sub-Laplacian and Kohn Laplacian and Rigidity Theorems on pseudo-Hermitian CR manifolds
ESB 2012
Tue 4 Oct 2016, 3:30pm-4:30pm

Abstract

 In this talk, I will present  a CR-version of Lichnerowicz--Obata type theorem in a closed pseudo-Hermitian CR manifolds. It includes the lower bound estimates for the first positive eigenvalue for the both sub-Laplacian and Kohn Laplacian. I will also provide Obata type theorem associated to the sub-Laplacian and Kohn Laplacian on a closed pseudo-Hermitian manifold. As an application, we give some rigidity theorem when lower bound of eigenvalue is achieved. This is based on a joint work with X. Wang and a joint work with Duong N. Son and Wang. I will also talk about some ongoing work in this topic.
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Santiago Salazar
UBC
Tue 4 Oct 2016, 4:00pm
Discrete Math Seminar
ESB 4127
Forbidden Berge hypergraphs
ESB 4127
Tue 4 Oct 2016, 4:00pm-5:00pm

Abstract

 
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