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
Given two matrices A,B we say that A is a Berge hypergraph of B if there is a submatrix of B, say matrix D, and a row and column permutation of A, say matrix C, so that C<=D. Define Av(m,F) to be the set of all mrowed (0,1)matrices with no repeated columns and no Berge hypergraph F. Define Bh(m,F) to be the maximum, over all matrices A in Av(m,F), of the number of columns of A. We are interested in determining the asymptotic growth of Bh(m,F) for specific F. We show some techniques we can use to this end and mention the general results determined for F with 5 or fewer rows. We also show that if F is the vertexedge incidence matrix of a tree then bh(m,F) has a linear bound. When F is the vertexedge (s+t)x(st) incidence matrix of the bipartite graph K_{s,t} we show that finding Bh(m,F) relates to determining ex(m,K_r,K_{s,t} ), the maximum number of complete subgraphs K_r in a mvertex graph avoiding K_{s,t} as a subgraph. Recent papers by Alon and others have solved some cases.
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UBC

Wed 5 Oct 2016, 1:45pm
Mathematical Biology Seminar
PIMS (ESB 4th floor)

Hidden Patterns Revealed by Noise: semiarid vegetation patterns

PIMS (ESB 4th floor)
Wed 5 Oct 2016, 1:45pm2:45pm
Abstract
A deterministic model may sometimes seem to be a good description of the dynamics of an observed system but may have a longterm stable constant limit, whereas observations of the system itself show a noisy pattern. An example is semiarid vegetation patterns. Adding noise to the model may well reveal the pattern. In this talk I show some photos, talk about some math, and show some simulations. This is not a magic show.
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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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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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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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Harvard University, ENS

Fri 7 Oct 2016, 3:00pm
SPECIAL
Department Colloquium
ESB 2012

PIMSUBC Distinguished ColloquiumPropagation of chaos and irreversibility in gas dynamics

ESB 2012
Fri 7 Oct 2016, 3:00pm4:00pm
Abstract
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Seminar Information Pages

Note for Attendees
Refreshments (A light reception) are served in ESB 4133 from 2:30pm3:00pm before the colloquium.