Department of Mathematics, UBC

Tue 14 Nov 2017, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

A Fast Sweeping Method for Eikonal Equations on Implicit Surfaces

ESB 4133 (PIMS Lounge)
Tue 14 Nov 2017, 12:30pm1:30pm
Abstract
Eikonal equation is a fundamental nonlinear PDE that find vast applications. One particular example is to compute geodesic distance on a curved surface through solving an eikonal equation defined on the surface (surface eikonal equations). However, there are only very few literatures on solving surface eikonal equations numerically, due to the complication from the surface geometry. In this talk, we present a simple and efficient numerical algorithm to solve surface eikonal
equations on general implicit surfaces.
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UBC & Univ. Basel

Tue 14 Nov 2017, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

Conformal metrics on \mathbb{R}^n with arbitrary total Qcurvature

ESB 2012
Tue 14 Nov 2017, 3:30pm4:30pm
Abstract
I will talk about the existence of solution to the Qcurvature problem
\begin{align}\label{1}
(\Delta)^\frac n2 u=Qe^{nu}\quad\text{in }\mathbb{R}^n,\quad \kappa:=\int_{\mathbb{R}^n}Qe^{nu}dx<\infty,
\end{align}
where Q is a nonnegative function and n>2. Geometrically, if u is a solution to \eqref{1} then Q is the Qcurvature of the conformal metric g_u = e^{2u}dx^2 (dx^2 is the Euclidean metric on \mathbb{R}^n), and \kappa is the total Qcurvature of g_u.
Under certain assumptions on Q around origin and at infinity, we prove the existence of solution to \eqref{1} for every \kappa > 0.
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University of Puget Sound

Tue 14 Nov 2017, 4:00pm
ESB 4127

Authoring Open Textbooks with PreTeXt

ESB 4127
Tue 14 Nov 2017, 4:00pm5:00pm
Details
PreTeXt is a new markup language for describing structured scholary documents, such as research articles and textbooks. It was designed originally to meet the demands of communicating mathematics, but has now been used to author books on computer science, physics, music theory, and composition (writing). It is the basis for the mobile edition of UBC's CLP calculus text. A key feature of PreTeXt is highfidelity conversions to print, PDF, online (HTML), Jupyter notebooks, and soon EPUB.
After an introduction, I will demonstrate some of the more interesting extra capabilities of the online versions, including embedded live Sage code and WeBWorK automated homework problems. Recent advances in producing Jupyter notebooks will also be demonstrated.
Project website: mathbook.pugetsound.edu
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UBC

Wed 15 Nov 2017, 2:00pm
Mathematical Biology Seminar
PIMS Videoconference room

Coupling Mechanical Tension and GTPase Signaling to Generate Cell and Tissue Dynamics

PIMS Videoconference room
Wed 15 Nov 2017, 2:00pm2:45pm
Abstract
Regulators of the actin cytoskeleton such Rho GTPases can modulate forces developed in cells by promoting actomyosin contraction. At the same time, through mechanosensing, tension is known to affect the activity of Rho GTPases.
What happens when these effects act in concert? Using a minimal model (1 GTPase coupled to a KelvinVoigt element), we show that twoway feedback between signaling (“RhoA”) and mechanical tension (stretching) leads to a spectrum of cell behaviors, including contracted or relaxed cells, and cells that oscillate between these extremes. When such “model cells” are connected to one another in a row or in a 2D sheet (“epithelium”), we observe waves of contraction/relaxation and GTPase activity sweeping through the tissue. The minimal model lends itself to full bifurcation analysis, and suggests a mechanism that explains behavior observed in the context of development and collective cell behavior.
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University of Washington

Wed 15 Nov 2017, 3:00pm
Probability Seminar
ESB 2012

The Conformal Continuum Random Tree

ESB 2012
Wed 15 Nov 2017, 3:00pm4:00pm
Abstract
I will begin with a gentle introduction to "conformal welding" from the probabilistic viewpoint, which is at the heart of Scott Sheffields "quantum zipper" as well as Malliavin's and his coauthors work on Brownian measures on the group of circle homeomorphisms. Then I will describe a conformal welding problem involving to the CRT, discuss the existence of its solution (joint work with Peter Lin), and describe how it arises as the limit of certain dessin d'enfants.
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Wayne State University

Wed 15 Nov 2017, 3:15pm
Topology and related seminars
ESB 4133

Tensortriangulated number theory

ESB 4133
Wed 15 Nov 2017, 3:15pm4:15pm
Abstract
In the 1970s, work of Adams, Baird, Bousfield, and Ravenel gave a description of the orders of the KU[1/2]local stable homotopy groups of spheres as the denominators of special values of the Riemann zetafunction. Meanwhile, Lichtenbaum conjectured a formula, ultimately proven 30 years later as a consequence of the Iwasawa main theorem and the norm residue theorem, relating the orders of the algebraic Kgroups of totally real number rings to special values of their Dedekind zetafunctions. In this talk I will describe two general approaches, an analytic approach and an algebraic approach, to a general kind of number theory that arises in any tensor triangulated category: this is a general framework for the above results and gneralizations of them, and which aims to describe the orders of Bousfieldlocalized stable homotopy groups of finite spectra in terms of special values of Lfunctions. Then I'll show off some new results in this framework, in particular, a "universal" description of the KUlocal homotopy groups of the Moore spectrum S/p in terms of Lvalues, and as a consequence, a proof of a certain (infinite) family of cases of Leopoldt's conjecture, by counting orders of homotopy groups.
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Université de Montréal

Fri 17 Nov 2017, 11:00am
Number Theory Seminar
GEOG 101

A geometric generalization of the square sieve and applications to cyclic covers

GEOG 101
Fri 17 Nov 2017, 11:00am12:00pm
Abstract
We study a generalization of the quadratic sieve to a geometric setting. We apply this to counting points of bounded height on an lcyclic cover over the rational function field and we consider a question of Serre. In addition to the geometric quadratic sieve, we use Fourier analysis over function fields, deep results of Deligne and Katz about cancellation of mixed character sums over finite fields, and a bound on the number of points of bounded height due to Browning and Vishe.
This is joint work with A. Bucur, A. C. Cojocaru, and L. B. Pierce.
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UBC

Fri 17 Nov 2017, 3:00pm
SPECIAL
Department Colloquium
ESB 2012

PIMSUBC Distinguished Colloquium: The role of random models in compressed sensing and matrix completion

ESB 2012
Fri 17 Nov 2017, 3:00pm4:00pm
Abstract
Random models lead to a precise and comprehensive theory of compressed sensing and matrix completion. The number of random linear measurements needed to recover a sparse signal, or a lowrank matrix, or, more generally, a structured signal, are now well understood. This is appealing in practice since it helps to determine the pros and cons of different models and gives a benchmark for success. Nevertheless, a practitioner with a fixed data set will wonder: Can they apply theory based on randomness? Is there any hope to get the same guarantees? We discuss these questions in compressed sensing and matrix completion, which, surprisingly, seem to have divergent answers.
Yaniv Plan is the 2016 winner of the PIMS UBC Math Sciences Prize.
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Seminar Information Pages

Note for Attendees
Light refreshments will be served at 2:45pm in ESB 4133, the PIMS Lounge before this colloquium.