Mathematics Dept.
  Events
UBC Zoology
Wed 1 Mar 2017, 3:00pm
Probability Seminar
ESB 2012
Fixation Probability when Selection Occurs in Both Haploid and Diploid phases
ESB 2012
Wed 1 Mar 2017, 3:00pm-4:00pm

Abstract

Joint work with Kazuhiro Bessho. Classical population genetic theory generally assumes either a fully haploid or fully diploid life cycle. However, many
organisms exhibit more complex life cycles, with both free-living haploid and diploid stages. Here we ask what the probability of fixation is for selected alleles in organisms with selection acting on both haploid and diploid phases of a sexual life cycle,  based on both a Moran model and a Wright–Fisher model. Applying a branching process approximation, we obtain  an accurate fixation probability assuming that the population is large and the net effect of the mutation is beneficial. We also find the diffusion approximation for the fixation probability, which is accurate even in small populations and for deleterious alleles, as long as selection is weak. These fixation probabilities from branching process and diffusion approximations are similar when selection is weak for beneficial mutations that are not fully recessive. In many cases, particularly when one phase predominates, the fixation probability differs substantially for haploid-diploid organisms compared to either fully haploid or diploid species.
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Roger Donaldson
Adjunct Professor, UBC Mathematics and CEO Midvale Applied Mathematics
Wed 1 Mar 2017, 3:00pm
Institute of Applied Mathematics / PIMS Seminars and PDF Colloquiums
Michael Smith Labs, Room 101
The Promising Future of Mathematics in Industry
Michael Smith Labs, Room 101
Wed 1 Mar 2017, 3:00pm-4:00pm

Abstract

The diversity of mathematics and roles of mathematicians in industry has expanded greatly over the last decade.   The first part of this talk is a survey of work that I have done as an applied mathematician working in industry.  Areas include modeling groundwater flow for soil remediation, image editing, content-based image search, and machine learning for searching large satellite images.

The second part of this talk will focus on a particular use of mathematics in indexing high dimensional floating-point vectors using a search engine intended for text.  The result is a database search method that can combine "fuzzy" data, such as image textures or audio recordings, with text-based data such as document titles or descriptive keywords in an infrastructure easy for a software engineer to build and maintain.

The ultimate purpose of this talk is to highlight areas of mathematics of particular use to my work in industry, and hence of particular interest to future industrial practitioners.

Note for Attendees

This is a talk in the new BC Data Colloquium. 

Convene beforehand for PIMS tea in the PIMS lounge at 14:45

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Paris 7
Thu 2 Mar 2017, 3:30pm
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
Questions on modulo p representations of reductive p-adic groups.
ESB 4127
Thu 2 Mar 2017, 3:30pm-5:00pm

Abstract

Our work  on  modulo p  smooth representations of reductive p-adic groups (classification of irreducible admissible representations, functoriality properties,Satake homomorphisms, with Abe, Henniart, Herzig, Ollivier), raises questions for which a kind of answer is required if we want to venture further.   
This talk is part of the PIMS focus semester on the mod p Langlands program.
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University of California, San Diego
Fri 3 Mar 2017, 3:00pm SPECIAL
Department Colloquium
ESB2012
PIMS-UBC Distinguished Colloquium--Sequences: random, structured or something in between
ESB2012
Fri 3 Mar 2017, 3:00pm-4:00pm

Abstract

There are many fundamental problems concerning sequences that arise in many areas of mathematics and computation.  Typical problems include finding or avoiding patterns;
testing or validating various `random-like’ behavior; analyzing or comparing different statistics, etc. In this talk, we will examine various notions of regularity or irregularity for  sequences and mention numerous open problems.

Note for Attendees

Refreshments will be served in ESB 4133 from 2:45pm-3:00pm.
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Donghai Pan
Stanford University
Mon 6 Mar 2017, 3:00pm
Algebraic Geometry Seminar
MATX 1102
Galois cyclic covers of the projective line and pencils of Fermat hypersurfaces
MATX 1102
Mon 6 Mar 2017, 3:00pm-4:00pm

Abstract

Classically, there are two objects that are particularly interesting to algebraic geometers: hyperelliptic curves and quadrics. The connection between these two seemingly unrelated objects was first revealed by M. Reid, which roughly says that there’s a correspondence between hyperelliptic curves and pencil of quadrics. I’ll give a brief review of Reid’s work and then describe a higher degree generalization of the correspondence.
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Lei Zhang
University of Florida
Tue 7 Mar 2017, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Local mass concentration and a priori estimate for singular rank 2 Toda systems
ESB 2012
Tue 7 Mar 2017, 3:30pm-4:30pm

Abstract

 A Toda system is a nonlinear second order elliptic system with exponential nonlinearity. It is very commonly observed in physics and has many ties with algebraic geometry. From analytic viewpoints it is challenging since the solutions do not have symmetry, maximum principles cannot be applied and the structures of global solutions are incredibly complicated. In this joint work with Chang-shou Lin, Juncheng Wei and Wen Yang, we use a unified approach to discuss all rank two singular Toda systems. First for local systems we prove that all weak limits of mass concentration belong to a very small finite set. Then for systems defined on compact Riemann surface we establish some new estimates. Our approach is a combination of delicate blowup analysis and fundamental tools from algebraic geometry. 
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University of Washington
Wed 8 Mar 2017, 3:00pm
Probability Seminar
ESB 2012
The tree of geodesics can have finitely many ends
ESB 2012
Wed 8 Mar 2017, 3:00pm-4:00pm

Abstract

 The study of infinite geodesics in first passage percolation have received a lot of attention since the work of Hoffman [`05] and [08], Damron and Hanson [`14] and more recently Ahlberg and Hoffman [`16]. In this talk we discuss further advances in this topic presenting a family of measures for which it is possible to completely characterize the set of infinite geodesics. This is joint work with Christopher Hoffman.
 
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UBC
Wed 8 Mar 2017, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Nilpotent n-tuples in SU(2)
ESB 4133 (PIMS Lounge)
Wed 8 Mar 2017, 3:15pm-4:15pm

Abstract

A classical approach to understanding spaces of homomorphisms is to describe its connected components. We mainly focus in the spaces Hom(N_{n,q},SU(2)), where N_{n,q} denotes the free q-nilpotent group on n-generators. We show that the connected components arising from non-commuting q-nilpotent n-tuples in SU(2) are homeomorphic to RP^3 and we give the exact number of these. We prove it by showing a seemingly unknown result about SU(2) that states: all non-abelian nilpotent subgroups are conjugated to the quaternion group Q_8 or to the generalized quaternion groups Q_{2^q}, of order 2^q. Some applications of this result are the stable homotopy type of Hom(N_{n,q},SU(2)); a homotopy description of the classifying spaces B(q,SU(2)) of transitionally q-nilpotent principal SU(2)-bundles, and its derived versions for SO(3) and U(2). If time permits I'll also show some cohomology calculations for the spaces B(r,Q_{2^q}) for low values of r.

This is joint work with Omar Antolín Camarena.
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Stanford
Thu 9 Mar 2017, 3:30pm
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
A Satake homomorphism for the mod p derived Hecke algebra
ESB 4127
Thu 9 Mar 2017, 3:30pm-5:00pm

Abstract


Recently, Venkatesh introduced a global version of the derived Hecke algebra to explain extra endomorphisms on the cohomology of arithmetic manifolds: the crucial local construction is a derived version of the spherical Hecke algebra of a reductive p-adic group.
Working with p-torsion coefficients, we will describe a Satake homomorphism for the derived spherical Hecke algebra of a p-adic group. This allows us to understand its structure well enough to attack some global questions, which are work in progress.


(This talk is part of the
PIMS focus semester on the mod p Langlands program).
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Dave Fracchia
Centre for Digital Media
Fri 10 Mar 2017, 12:00pm
PIMS Seminars and PDF Colloquiums
SFU Harbour Centre Campus in Downtown Vancouver, Room 1530
PIMS Lunchbox Lecture Series: The Mathematics of Game Design
SFU Harbour Centre Campus in Downtown Vancouver, Room 1530
Fri 10 Mar 2017, 12:00pm-1:00pm

Abstract

Mathematics is integral to every aspect of game development including character and level creation, movement, player input, NPC behaviour, physics simulations, and real-time rendering. Fortunately for game designers, most of this computation is conveniently supplied by software developers and/or handled by existing game engines. However, when designing a game, lots of systems and mechanics are dependent on numbers such as weapons ranges, jump heights, experience points, damage, rewards, currency, etc., many of which can have complex inter-relationships. Although much of the math may be basic, a good understanding of the underlying equations as well as the fields of logic, probability, and statistics can be incredibly beneficial to a designer, especially when it comes to game design and balancing. This lecture will give an overview of how even the most basic knowledge of these fields can benefit a game designer.

 

Note for Attendees

Please register, as space is limited: https://www.pims.math.ca/industrial-event/170310-pvlldf
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University of Grenoble
Fri 10 Mar 2017, 3:00pm SPECIAL
Department Colloquium
ESB 2012
PIMS-UBC Distinguished Colloquium:-Automorphism groups in algebraic geometry
ESB 2012
Fri 10 Mar 2017, 3:00pm-4:00pm

Abstract

The talk will first present some classical results on the automorphisms of complex projective curves (or alternatively, of compact Riemann surfaces). We will then discuss the automorphism groups of projective algebraic varieties of higher dimensions; in particular, their "connected part" (which can be arbitrary) and their "discrete part" (of which little is known).

Note for Attendees

Refreshments will be served in ESB 4133 from 2:45pm-3:00pm.
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MIT
Mon 13 Mar 2017, 3:00pm SPECIAL
Institute of Applied Mathematics
ESB 2012
Multifidelity and Surrogate Modeling for 'Data to Decisions' in Engineering Systems
ESB 2012
Mon 13 Mar 2017, 3:00pm-4:00pm

Abstract

 

Note for Attendees

A reception precedes the talk in ESB 4133 (the PIMS lounge). This is part of the IAM/PIMS distinguished colloquium series. 
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University of Grenoble
Mon 13 Mar 2017, 3:00pm
Algebraic Geometry Seminar
MATX 1102
Algebraic group actions on normal varieties
MATX 1102
Mon 13 Mar 2017, 3:00pm-4:00pm

Abstract

Let G be a connected algebraic k-group acting on a normal k-variety, where k is a field. We will show that X is covered by open G-stable quasi-projective subvarieties; moreover, any such subvariety admits an equivariant embedding into the projectivization of a G-linearized vector bundle on an abelian variety A, where A is a quotient of G. This generalizes a classical result of Sumihiro for actions of smooth connected algebraic groups.
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Iain Moyles
Mathematics Applications Consortium for Science, University of Limerick
Tue 14 Mar 2017, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
The formation of Liesegang Rings
ESB 4133 (PIMS Lounge)
Tue 14 Mar 2017, 12:30pm-1:30pm

Abstract

Many chemical systems exhibit a regular pattern of precipitate bands known as Liesegang rings in tribute to the chemist Raphael E. Liesegang who demonstrated them using a reaction of silver nitrate and potassium dichromate. A variety of theories have been studied to try and understand how these patterns develop and one of the most seminal papers on the topic was a mathematical model developed by Keller and Rubinow using a supersaturation framework. This model predicted the formation of primary and secondary bands using heuristic arguments and assumptions about the underlying equations. In this talk we present the Keller-Rubinow model from a formal asymptotic perspective and discuss the dynamics and formation of the primary precipitation band. Furthermore we show that secondary bands are infeasible under the model as posed thus necessitating the development of a new model. We will provide preliminary insights into such a new model and its resolution towards secondary bands.
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Nassif Ghoussoub
UBC Math
Tue 14 Mar 2017, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
Optimal Mass transport as a natural extension of classical mechanics to the manifold of probability measures II
ESB 2012
Tue 14 Mar 2017, 3:30pm-4:30pm

Abstract

This is part II of the February 28 talk. Original abstract: I will describe how deterministic and stochastic dynamic optimal mass transports are to Mean Field Games what the classical calculus of variations offers to classical mechanics.

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Gabriela Cohen Freue
UBC Statistics
Wed 15 Mar 2017, 1:45pm
Mathematical Biology Seminar
PIMS video conference room
PENSE: a penalized robust estimator for complex sparse regression models
UBC Math
Wed 15 Mar 2017, 3:00pm
Probability Seminar
ESB 2012
Finite-order correlation length of the |\varphi|^4 spin model in four dimensions
ESB 2012
Wed 15 Mar 2017, 3:00pm-4:00pm

Abstract

The correlation length of order p for the |\varphi|^4 spin model (a continuous-spin version of the O(n) model) is a normalization of the p-th moment of its two-point function. We will outline the proof (based on a renormalisation group method of Bauerschmidt, Brydges, and Slade) that, in the upper-critical dimension 4, this quantity undergoes mean-field scaling with a logarithmic correction as the critical point for this model is approached from above (for sufficiently weak coupling). Via a supersymmetric integral representation, this result also extends to the weakly self-avoiding walk with a contact attraction, for which the correlation length of order p is closely related to the mean p-th displacement of the walk. This is joint work with Roland Bauerschmidt, Gordon Slade, and Alexandre Tomberg.
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University of Düsseldorf
Wed 15 Mar 2017, 3:00pm
Algebraic Geometry Seminar
MATH 126
Singularities and counting points
MATH 126
Wed 15 Mar 2017, 3:00pm-4:00pm

Abstract

Given a variety X defined over Z, there are two problems which a priori seem to not have a lot to do with each other:

1. Describe the singularities of the complex variety X(C)

2. Fix a prime p and describe how the cardinality of X(Z/p^rZ) depends on r.

A surprising result from the 80s concerning the second problem is that the Poincaré series of X - a formal power series having the above cardinalities as coefficients - is a rational function.

In this talk, I will explain this in more detail and I will present a new notion of stratifications which contributes to both problems: On the one hand, such a stratification specializes to a stratification of X(C) (which has stronger regularity properties than classical Whitney stratifications); on the other hand, using those stratifications, one obtains a (new) geometric proof of the rationality of Poincare series.

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Universität Heidelberg
Thu 16 Mar 2017, 3:30pm
Number Theory Seminar / PIMS Seminars and PDF Colloquiums
ESB 4127
WACH MODULES, REGULATOR MAPS AND epsilon-ISOMORPHISMS IN FAMILIES
ESB 4127
Thu 16 Mar 2017, 3:30pm-5:00pm

Abstract

In this talk on joint work with REBECCA BELLOVIN we discuss the “local ε-isomorphism” conjecture of Fukaya and Kato for (crystalline) families of G_{Q_p}-representations. This can be regarded as a local analogue of the global Iwasawa main conjecture for families, extending earlier work of Kato for rank one modules, of Benois and Berger for crystalline representations with respect to the cyclotomic extension as well as of Loeffler, Venjakob and Zerbes  for crystalline representations with respect to abelian p-adic Lie extensions of Q_p. Nakamura  has shown Kato’s conjecture for (ϕ,\Gamma)-modules over the Robba ring, which means in particular only after inverting p, for  rank one and trianguline families. The main ingredient of (the integrality part of) the proof consists of the construction of families of Wach modules generalizing work of Wach and Berger and following Kisin’s approach via a corresponding moduli space.

(This talk is part of the
PIMS focus semester on the mod p Langlands program).
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UBC Math
Fri 17 Mar 2017, 3:00pm
Department Colloquium
Math Annex 1100
Graduate Research Award - Large Sets Avoiding Patterns
Math Annex 1100
Fri 17 Mar 2017, 3:00pm-4:00pm

Abstract

What conditions must be placed on a set E \subset \mathbb{R}^n in order to guarantee that E contains certain finite arrangements of points? We will discuss some conditions on a set E that guarantee the existence of point configurations, and constructions of large sets E that avoid them. This work was completed jointly with Malabika Pramanik.

Note for Attendees

Refreshments will be served at 2:45 p.m. in MATH 125 before this colloquium.
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Curt Da Silva
Seismic Laboratory for Imaging and Modelling, UBC
Tue 21 Mar 2017, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
A level set, variable projection approach for convex composite
ESB 4133 (PIMS Lounge)
Tue 21 Mar 2017, 12:30pm-1:30pm

Abstract

Many useful and interesting optimization problems can be cast in a convex composite form min_x h(c(x)), where h is a non-smooth but convex function and c is a smooth nonlinear or linear mapping. The non-smoothness of the outer function prevents traditional methods such as the Gauss-Newton method from converging quickly, which is problematic for large scale problems. In this talk, we will explore level set methods, aka the SPGL1 'trick', for solving this class of problem 
when we can easily project on to the level sets of h(z). The resulting subproblems will be smooth and have simple constraints, which are amenable to smooth optimization methods such as LBFGS. We also use the variable projection technique, which gives us an alternate interpretation as computing the minimal distance between the level set of h and the image of our nonlinear mapping c. We will demonstrate the effectiveness of this technique on a number of convex and non-convex problems, including cosparsity-based compressed sensing for seismic data interpolation, audio signal declipping, robust tensor PCA/completion, and more. 
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UBC Math
Tue 21 Mar 2017, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012
On De Giorgi's Conjecture for Allen-Cahn and Free Boundary Problems
ESB 2012
Tue 21 Mar 2017, 3:30pm-4:30pm

Abstract

 I will report recent progress in De Giorgi's type conjectures (and beyond) for Allen-Cahn equation and some free boundary problems in the whole space. 
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Kristina Nelson
UBC Math
Tue 21 Mar 2017, 4:00pm
Discrete Math Seminar
ESB 4127
Bounding the Size of Elliptic Curves on Subsets of F_p
ESB 4127
Tue 21 Mar 2017, 4:00pm-5:00pm

Abstract

We prove two related concentration inequalities concerning the points of elliptic curves contained within subsets of F_p^2. In particular we investigate the probability of a large difference between the portions of quadratic residues and non-residues in the image of f(S), where S is a subset of F_p and f is a cubic, or higher degree polynomial.
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Wed 22 Mar 2017, 12:00pm
Math Education Research Reading
MATH ANNEX 1118
Turning Routine Exercises Into Activities that Teach Inquiry: A Practical Guide
MATH ANNEX 1118
Wed 22 Mar 2017, 12:00pm-1:00pm

Abstract

On March 22nd, we'll be discussing the article entitled "Turning Routine Exercises Into Activities that Teach Inquiry: A Practical Guide". This is a great article for anyone interested in finding out more about inquiry based learning and how it can be easily implemented. This could be especially relevant for anyone teaching students who are still relatively new to proofs and mathematical thinking. 

Anyone interested is encouraged to attend. Snacks are provided. 
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IBM Professor of Mathematics and Theoretical Physics, Emeritus, Caltech
Wed 22 Mar 2017, 3:00pm SPECIAL
Department Colloquium
ESB 2012
Public Lecture -Tales of our Forefathers
ESB 2012
Wed 22 Mar 2017, 3:00pm-4:00pm

Abstract

This is not a mathematics talk but it is a talk for mathematicians. Too often, we think of historical mathematicians as only names assigned to theorems. With vignettes and anecdotes, I'll convince you they were also human beings and that, as the Chinese say, "May you live in interesting times" really is a curse. Among the mathematicians with vignettes in this talk are Euler, Weierstrass, Fejer, Banach, Kolmogorov, Weyl, Cotlar, Fourier, Paley, Hausdorff and Schur.

Note for Attendees

A light reception will be served in ESB 4133, PIMS Lounge, from 2:30pm - 3:00pm
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IBM Professor of Mathematics and Theoretical Physics, Emeritus, Caltech
Thu 23 Mar 2017, 3:00pm SPECIAL
Department Colloquium
ESB 2012 **Please note special day**
PIMS-UBC Distinguished Colloquium - Spectral Theory Sum Rules, Meromorphic Herglotz Functions and Large Deviations
ESB 2012 **Please note special day**
Thu 23 Mar 2017, 3:00pm-4:00pm

Abstract

After defining the spectral theory of orthogonal polynomials on the unit circle (OPUC) and real line (OPRL), I'll describe Verblunsky's version of Szego's theorem as a sum rule for OPUC and the Killip--Simon sum rule for OPRL and their spectral consequences. Next I'll explain the original proof of Killip--Simon using representation theorems for meromorphic Herglotz functions. Finally I'll focus on recent work of Gambo, Nagel and Rouault who obtain the sum rules using large deviations for random matrices.

Note for Attendees

A light reception will be hosted at PIMS, ESB 4133 from 2:30pm- 3:00pm.
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Université Paris 13
Thu 23 Mar 2017, 4:15pm
Number Theory Seminar
ESB 4127
Horizontal variation of the arithmetic of elliptic curves.
ESB 4127
Thu 23 Mar 2017, 4:15pm-5:15pm

Abstract

Let E be an elliptic curve over the rationals. Let K be an imaginary quadratic field and H_K the corresponding Hilbert class field. We discuss recent results on the arithmetic of E over H_K as K varies (joint with H. Hida and Y. Tian). 
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John Ma
UBC Math
Fri 24 Mar 2017, 3:00pm
Department Colloquium
Math Annex 1100
Graduate Research Award - Singularity of Lagrangian mean curvature flow
Math Annex 1100
Fri 24 Mar 2017, 3:00pm-4:00pm

Abstract

In this talk, I will discuss the formation of singularity in Lagrangian mean curvature flow and study the space of such singularity. The goal is to show a compactness result on the space of such singularity.

This is a joint work with Professor Jingyi Chen.

Note for Attendees

Refreshments will be served at 2:45 p.m. in MATH 125 before this colloquium.
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Quest
Mon 27 Mar 2017, 3:00pm
Algebraic Geometry Seminar
MATX 1102
CANCELED
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
Math Education Research Reading
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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