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Marie Graff
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, 12:30pm-1:30pm

#### 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 time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton-type iteration. Instead of a grid-based discrete representation, the unknown wave speed is projected to a particular finite-dimensional 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 Tikhonov-type 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
MATX 1118
Intro to inquiry based learning (continued discussion from last week)
MATX 1118
Wed 29 Mar 2017, 12:00pm-1:00pm

#### 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, 3:00pm-4:00pm

#### Abstract

Let be an isotropic, sub-gaussian m by n matrix. We prove that the process Z_x = ||A x||_2 – m^(.5) ||x||_2 has sub-gaussian increments. Using this, we show that for any bounded set T in R^n, the deviation of Ax2 around its mean is uniformly bounded by the Gaussian complexity of T.  In other words, we give a simple sufficient condition for a random sub-Gaussian 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, 3:15pm-4:15pm

#### Abstract

A group is left-orderable 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 order-preserving homeomorphisms. A group being circularly orderable has a slightly trickier algebraic definition than left-orderability, but in the countable case boils down, as expected, to the existence of a orientation-preserving action by homeomorphisms on the circle.

The set of all left-orderings 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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Humboldt-Universität 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, 3:30pm-4:30pm

#### Abstract

Let F be a finite extension field of {\mathbb Q}_p. Let {\mathcal H} be the pro-p-Iwahori-Hecke 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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Alejandra Herrera
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, 3:00pm-4:00pm

#### 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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Utah
Mon 3 Apr 2017, 3:00pm SPECIAL
Institute of Applied Mathematics
ESB 2012
Extending the Theory of Composites to Other Areas of Science
ESB 2012
Mon 3 Apr 2017, 3:00pm-4:00pm

#### Note for Attendees

Reception precedes the talk in ESB 4133 (the PIMS lounge). This is in the IAM/PIMS distinguished colloquium series.
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