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, 3:00pm4:00pm
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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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 CahnHilliard Problems

ESB 4133 (PIMS Lounge)
Tue 4 Oct 2016, 12:30pm1:30pm
Abstract
The CahnHilliard 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 spacebased algorithm, which combines a MoreauYosida 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 CahnHilliard problems including phase separation and coarsening processes, image inpainting, and twophase 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 subLaplacian and Kohn Laplacian and Rigidity Theorems on pseudoHermitian CR manifolds

ESB 2012
Tue 4 Oct 2016, 3:30pm4:30pm
Abstract
In this talk, I will present a CRversion of LichnerowiczObata type theorem in a closed pseudoHermitian CR manifolds. It includes the lower bound estimates for the first positive eigenvalue for the both subLaplacian and Kohn Laplacian. I will also provide Obata type theorem associated to the subLaplacian and Kohn Laplacian on a closed pseudoHermitian 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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UBC

Tue 4 Oct 2016, 4:00pm
Discrete Math Seminar
ESB 4127

Forbidden Berge hypergraphs

ESB 4127
Tue 4 Oct 2016, 4:00pm5:00pm
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, 3:00pm4:00pm
Abstract
We will begin by briefly discussing the nonlinear Schroedinger (NLS) equation and the corresponding classical Strichartz estimates. We will then introduce a socalled 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 energycritical cubic NLS in four dimensions is almost surely wellposed with respect to randomized initial data below the energy space. This is a joint work with Tadahiro Oh (University of Edinburgh) and Oana Pocovnicu (HeriotWatt 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, 3:00pm4:00pm
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 selfavoiding 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 rary subtree of a random dary 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, 3:15pm4:15pm
Abstract
In this talk, we will discuss a new proof of the decomposition theorem of Beilinson, Bernstein, Deligne and Gabber for semisimple 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 positivecharacteristic 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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