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 Events
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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Western Washington University
Wed 5 Oct 2016, 3:00pm
Harmonic Analysis Seminar
Math 126
On probabilistic Strichartz estimates for the NLS
Math 126
Wed 5 Oct 2016, 3:00pm-4:00pm

Abstract

We will begin by briefly discussing the non-linear Schroedinger (NLS) equation and the corresponding classical Strichartz estimates. We will then introduce a so-called Wiener randomization of initial data and indicate how it leads to an improvement of the classical Strichartz estimates. As a toy application, we will show how, in contrast with the deterministic case, the energy-critical cubic NLS in four dimensions is almost surely well-posed with respect to randomized initial data below the energy space. This is a joint work with Tadahiro Oh (University of Edinburgh) and Oana Pocovnicu (Heriot-Watt University).
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UBC Computer Science and PIMS
Wed 5 Oct 2016, 3:00pm
Probability Seminar
ESB 2012
On longest paths and diameter in random Apollonian networks
ESB 2012
Wed 5 Oct 2016, 3:00pm-4:00pm

Abstract

Consider the following iterative construction of a random planar triangulation. Start with a triangle embedded in the plane. In each step, choose a bounded face uniformly at random, add a vertex inside that face and join it to the vertices of the face. After n – 3 steps, we obtain a random triangulated plane graph with n vertices, which is called a Random Apollonian Network (RAN). See http://www.math.cmu.edu/~ctsourak/ran.html for an example.

We prove that the diameter of a RAN is asymptotic to c log(n) in probability, where c ≈ 1.668 is the solution of an explicit equation. The proof adapts a technique of Broutin and Devroye for estimating the height of random trees.

We also prove that there exists a fixed s<1, such that eventually every self-avoiding walk in this graph has length less than n^s, which verifies a conjecture of Cooper and Frieze. Using a similar technique, we show that if r < d are fixed constants, then every r-ary subtree of a random d-ary recursive tree on n vertices has less than n^b vertices, for some b=b(d,r)<1.

Based on joint work with A. Collevecchio, E. Ebrahimzadeh, L. Farczadi, P. Gao, C. Sato, N. Wormald, and J. Zung.
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University of Southern California
Wed 5 Oct 2016, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
A new proof of the decomposition theorem
ESB 4133 (PIMS Lounge)
Wed 5 Oct 2016, 3:15pm-4:15pm

Abstract

In this talk, we will discuss a new proof of the decomposition theorem of Beilinson, Bernstein, Deligne and Gabber for semi-simple perverse sheaves of geometric origin on complex algebraic varieties. This proof follows from rather formal considerations of higher algebra, stable motivic homotopy theory and Grothendieck's six functors, avoiding both the positive-characteristic methods of the original proof, and the delicate analysis of degenerations of mixed Hodge structures involved in M. Saito's proof.
 
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