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##### Events
Quest
Mon 27 Mar 2017, 3:00pm
Algebraic Geometry Seminar
MATX 1102
Betti tables of graded systems of ideals
MATX 1102
Mon 27 Mar 2017, 3:00pm-4:00pm

#### 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 Boij-Soederberg decompositions.
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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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Rice
Tue 4 Apr 2017, 3:00pm
Algebraic Geometry Seminar
MATX 1102
TBA
MATX 1102
Tue 4 Apr 2017, 3:00pm-4:00pm

#### Abstract

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Columbia University
Tue 4 Apr 2017, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012 (PIMS)
Regularity of the Gauss curvature flow
ESB 2012 (PIMS)
Tue 4 Apr 2017, 3:30pm-4:30pm

#### Abstract

We will discuss about the regularity of the Gauss curvature flow: the optimal $C^{1,\frac{1}{n-1}}$ regularity of degenerate solutions with flat sides and the interior $C^{\infty}$ regularity of strictly convex solutions.
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Purdue University
Wed 5 Apr 2017, 3:00pm
Probability Seminar
ESB 2012
Littlewood-Paley Estimates for Lévy Processes
ESB 2012
Wed 5 Apr 2017, 3:00pm-4:00pm

#### Abstract

L^p inequalities for certain Littlewood-Paley functionals arising from  Lévy processes will be discussed. These are motivated by applications to the L^p boundedness of Fourier multiples which give L^p regularity of solutions to some non-local operators, including the fractional Laplacian.  Non-local operates have been extensively studied in recent years by researchers in analysis, probability and PDE.  The relevant Fourier multiples have been studied using the deep sharp martingale transform inequalities of Burkholder.  The proofs here, although not sharp, are completely elementary and use nothing more than Itô’s formula and arguments similar to those for the classical case of the Laplacian.
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McMaster University
Wed 5 Apr 2017, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Group actions on homology 3-spheres
ESB 4133 (PIMS Lounge)
Wed 5 Apr 2017, 3:15pm-4:15pm

#### Abstract

I will discuss finite group actions on integral or rational homology 3-spheres. The main examples for this talk are the Brieskorn integral homology 3-spheres M(p,q,r) arising from isolated singularities, which bound smooth 4-manifolds with definite intersection forms. In addition, there are special infinite families of Brieskorn homology 3-spheres which can be realized as boundaries of smooth contractible 4-manifolds. We ask whether the free periodic actions on Brieskorn spheres extend to smooth actions with isolated fixed points on one of these associated 4-manifolds.
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U.C. Santa Barbara
Tue 11 Apr 2017, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Min-max minimal hypersurfaces with free boundary
ESB 2012
Tue 11 Apr 2017, 3:30pm-4:30pm

#### Abstract

I will present a joint work with Martin Li. Minimal surfaces with free boundary are natural critical points of the area functional in compact smooth manifolds with boundary. In this talk, I will describe a general existence theory for minimal surfaces with free boundary. In particular, I will show the existence of a smooth embedded minimal hypersurface with free boundary in any compact smooth Euclidean domain. The minimal surfaces with free boundary were constructed using the min-max method. I will explain the basic ideas behind the min-max theory as well as our new contributions.
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UBC
Wed 12 Apr 2017, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
TBA
ESB 4133 (PIMS Lounge)
Wed 12 Apr 2017, 3:15pm-4:15pm

#### Abstract

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UBC
Wed 19 Apr 2017, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
TBA
ESB 4133 (PIMS Lounge)
Wed 19 Apr 2017, 3:15pm-4:15pm

#### Abstract

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Ecole Normale Supérieure de Lyon
Thu 27 Apr 2017, 3:30pm
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
TBA
ESB 4127
Thu 27 Apr 2017, 3:30pm-5:00pm

#### Abstract

TBA

(This talk is part of the PIMS focus semester on the mod p Langlands program).
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MIT
Wed 3 May 2017, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
TBA
ESB 4133 (PIMS Lounge)
Wed 3 May 2017, 3:15pm-4:15pm

#### Abstract

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Université de Montpellier, France
Fri 12 May 2017, 1:00pm
Diff. Geom, Math. Phys., PDE Seminar
Time and Location TBA
Prescribing the curvature of hyperbolic convex bodies
Time and Location TBA
Fri 12 May 2017, 1:00pm-2:00pm

#### Abstract

The Gauss curvature of a convex body can be seen as a measure on the unit sphere (with some properties). For such a measure $\mu$, Alexandrov problem consists in proving the existence of a convex body whose curvature measure is $\mu$. In the Euclidean space, this problem is equivalent to an optimal transport problem on the sphere.

In this talk I will consider Alexandrov problem for convex bodies of the hyperbolic space. After defining the curvature measure, I will explain how to relate this problem to a non linear Kantorovich problem on the sphere and how to solve it.

Joint work with J\’er\^ome Bertrand.
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Pierre Colmez, Wieslawa Niziol, and others
Mon 15 May 2017, 11:00am
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
Week of May 15 - Lectures on p-adic geometry (details TBA)
Mon 15 May 2017, 11:00am-1:00pm

#### Abstract

During the week of May 15 through May 19 there will be lectures by several visitors as part of the PIMS focus period on Representations in Arithmetic, on the topics in p-adic geometry related to Scholze's work on perfectoid spaces. This listing is a placeholder until there's a specific schedule set for the talks.

The talks by Colmez and Niziol will have the following title and abstract:
Title: "p-adic etale cohomology of p-adic symmetric spaces"
Abstract: "We will present different ways to compute the p-adi etale cohomology
of layers of the Drinfeld tower, and give applications to the p-adic local Langlands correspondence".

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University of Toronto
Thu 25 May 2017, 3:30pm
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
TBA
ESB 4127
Thu 25 May 2017, 3:30pm-4:30pm

#### Abstract

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Syvia Serfaty
Courant Institute, NYU
Fri 1 Dec 2017, 3:00pm SPECIAL
Department Colloquium
ESB 2012
PIMS-UBC Distinguished Colloquium--TBA
ESB 2012
Fri 1 Dec 2017, 3:00pm-4:00pm

#### Abstract

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Umberto Zannier
SNS, Pisa
Fri 2 Mar 2018, 3:00pm SPECIAL
Department Colloquium
ESB2012
PIMS-UBC Distinguished Colloquium--TBA
ESB2012
Fri 2 Mar 2018, 3:00pm-4:00pm

#### Note for Attendees

Refreshments will be served in ESB 4133 from 2:45 p.m.-3:00 p.m.
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