Quest

Mon 27 Mar 2017, 3:00pm
Algebraic Geometry Seminar
MATX 1102

CANCELED

MATX 1102
Mon 27 Mar 2017, 3:00pm4:00pm
Abstract
Several patterns emerge in collections of Betti tables associated to the powers of a fixed ideal. For example, Wheildon and others demonstrated that the shapes of the nonzero entires of these tables eventually stabilize when the fixed ideal has generators of the same degree. In this talk, I will discuss patterns in the graded Betti numbers of these and other graded systems of ideals. In particular, I will describe ways in which the Betti tables may stabilize, and how different types of stabilization are reflected in the corresponding BoijSoederberg decompositions.
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Department of Earth, Ocean and Atmospheric Sciences, UBC

Tue 28 Mar 2017, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

Adaptive Eigenspace method for inverse scattering problems in the frequency domain

ESB 4133 (PIMS Lounge)
Tue 28 Mar 2017, 12:30pm1:30pm
Abstract
A nonlinear optimization method is proposed for the solution of inverse scattering problems in the frequency domain, when the scattered field is governed by the Helmholtz equation. The timeharmonic inverse medium problem is formulated as a PDEconstrained optimization problem and solved by an inexact truncated Newtontype iteration. Instead of a gridbased discrete representation, the unknown wave speed is projected to a particular finitedimensional basis of
eigenfunctions, which is iteratively adapted during the optimization. Truncating the adaptive eigenspace (AE) basis at a (small and slowly increasing) finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard Tikhonovtype regularization. Both analytical and numerical evidence underpins the accuracy of the AE representation. Numerical experiments demonstrate the efficiency and robustness to missing or noisy data of the resulting adaptive eigenspace inversion (AEI) method.
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Wed 29 Mar 2017, 12:00pm
Math Education Research Reading
MATX 1118

Intro to inquiry based learning (continued discussion from last week)

MATX 1118
Wed 29 Mar 2017, 12:00pm1:00pm
Abstract
On Wed March 29th we'll continue the discussion from the previous week on simple ways to introduce inquiry based learning into a class. The article is "Turning Routine Exercises Into Activities that Teach Inquiry A Practical Guide" as before. Please bring a "routine" exercise or lecture example, as well as a more "inquiry based" version of the same example/exercise. The goal will be to discuss the challenges of turning routine exercises into inquiry based exercises.
Some questions for discussion:
Which kind of topics, examples or exercises lend themselves well to inquiry based learning?
What challenges did you encounter when trying to create your inquiry based exercise?
What challenges do you anticipate when implementing your inquiry based exercise in lecture or homework?
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UBC Math

Wed 29 Mar 2017, 3:00pm
Probability Seminar
ESB 2012

A simple tool for bounding the deviation of random matrices on geometric sets

ESB 2012
Wed 29 Mar 2017, 3:00pm4:00pm
Abstract
Let A be an isotropic, subgaussian m by n matrix. We prove that the process Z_x = A x_2 – m^(.5) x_2 has subgaussian increments. Using this, we show that for any bounded set T in R^n, the deviation of ∥Ax∥2 around its mean is uniformly bounded by the Gaussian complexity of T. In other words, we give a simple sufficient condition for a random subGaussian matrix to be well conditioned when restricted to a subset of R^n. We also prove a local version of this theorem, which allows for unbounded sets. These theorems have various applications, such as a general theory of compressed sensing. We discuss some applications and point to open (probabilistic) questions that remain.
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University of Manitoba

Wed 29 Mar 2017, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)

The spaces of left and circular orderings of a group

ESB 4133 (PIMS Lounge)
Wed 29 Mar 2017, 3:15pm4:15pm
Abstract
A group is leftorderable if it has a strict total ordering that is invariant under multiplication from the left. For countable groups, this is equivalent to acting on the real line by orderpreserving homeomorphisms. A group being circularly orderable has a slightly trickier algebraic definition than leftorderability, but in the countable case boils down, as expected, to the existence of a orientationpreserving action by homeomorphisms on the circle.
The set of all leftorderings of a group forms a topological space, and similarly, so does the set of all circular orderings. I will provide an introduction to these spaces, and discuss recent progress towards understanding the structure of groups whose spaces of circular orderings are “degenerate”, in the sense that they consist simply of a finite set of points with the discrete topology. This is joint work with Cristobal Rivas and Kathryn Mann.
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HumboldtUniversität zu Berlin

Thu 30 Mar 2017, 3:30pm
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127

Supersingular Hecke modules for GL_n(F) and (\psi,Gamma)modules

ESB 4127
Thu 30 Mar 2017, 3:30pm4:30pm
Abstract
Let F be a finite extension field of {\mathbb Q}_p. Let {\mathcal H} be the propIwahoriHecke algebra for {\rm GL}_n(F), with coefficients in the residue field k of {\mathcal O}_F (or a finite extension of it). We are going to discuss an exact functor D from the category of supersingular {\mathcal H}modules to the category of (\psi,\Gamma)modules over k((X)). The latter category generalizes in a straightforward way the one defined and studied by Colmez in the case F={\mathbb Q}_p; in particular, it admits an exact functor to the category of (\varphi,\Gamma)modules, and hence to that of Galois representations. Our main result today is that the functor D is almost fully faithful, i.e. it is fully faithful when restricted to the category of supersingular {\mathcal H}modules satisfying a very mild additional assumption.
(This talk is part of the PIMS focus semester on the mod p Langlands program).
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UBC Math

Fri 31 Mar 2017, 3:00pm
Department Colloquium
Math Annex 1100

Graduate Research Award  Fluorescence microscopy, cell surface receptor proteins and mathematical modeling: a collage

Math Annex 1100
Fri 31 Mar 2017, 3:00pm4:00pm
Abstract
Fluorescence microscopy allows experimental biologists to obtain quantitative data about different cellular processes. This data is then an important part of mathematical models to further understand the biological system. In this talk I will focus on two fluorescence techniques and their application to cell adhesion and immune activation. Cell adhesion to the extracellular matrix is fundamental for shape and stability of multicellular organisms. Experimentally, these adhesions can be observed using fluorescence recovery after photobleaching (FRAP). We built an ODE model to analyze changes in collected FRAP data under different mutations, and by fitting the model, identified necessary conditions for stable adhesions. In the second part, immune cell activation is believed to be triggered by clustering of membrane receptors. Experimentally this system requires lower and more precise fluorescence labelling, obtained using stochastic optical reconstruction microscopy (STORM). STORM uses photoswitchable fluorophores to achieve resolutions at or below 20nm, with the down side of possibly observing a given fluorophore multiple times in the process. We are developing a mathematical model to estimate the number of fluorophores present in the experiment. We apply a Markov chain model to describe the temporal dynamics, and a Gaussian mixture model for the spatial information. This approach will enhance a microscopy technique that is already widely used in biological applications, and will allow more precise analysis of receptor cluster formation and its effects on immune cell signaling.
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