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##### Events
University of Washington
Thu 1 Mar 2012, 3:00pm
Number Theory Seminar
Room WMAX 216 (PIMS - UBC Campus)
Some computations of the Riemann zeta function
Room WMAX 216 (PIMS - UBC Campus)
Thu 1 Mar 2012, 3:00pm-3:50pm

#### Abstract

I'll give a historical overview of computations of the zeta function on the critical line and then describe some recent computations from the past year or so. Mostly this will focus on an implementation of Ghaith Hiary's O(t1/3) method for computing ζ(1/2+it) and some computations that Hiary and I have run using it. Highlights will include the 1032nd zero, values of |ζ(1/2+it)| larger than 14000, and some record observations of irregularities in the distribution of zeros.

#### Note for Attendees

Refreshments will be served between the two talks.
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The Chinese University of Hong Kong
Thu 1 Mar 2012, 3:45pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
WMAX 110 (PIMS)
Specialized Seminar: Mathematical Analysis of Localized Patterns in Reaction-Diffusion Systems
WMAX 110 (PIMS)
Thu 1 Mar 2012, 3:45pm-4:45pm

#### Abstract

Abstract: I will describe some mathematical issues related to the analysis of localized patterns (spikes and interfaces) in reaction diffusion systems. For spikes, the analysis of the spectrum of various classes of nonlocal eigenvalue problems (NLEP) is essential.  I will discuss some new and interesting NLEPs arising in cross diffusion systems and crime models. For interfaces, a nonlocal geometric problem involving mean curvature and Newtonian potential is derived and analyzed. Our goal is to give mathematically rigorous proofs of existence and stability of various classes of patterns that have been observed in experiments and simulations in the physics literature. Our further goal is to predict the existence of some new patterns which have not yet been found in experiments.  (Joint works with T. Kolokolnikov, X. Ren, M. Ward, and M. Winter.)

#### Note for Attendees

Refreshments will be served in the PIMS Lounge from 3:30-3:45 p.m.
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Djun Kim
UBC
Thu 1 Mar 2012, 4:00pm
Mathematical Education
MATH 126
Teaching Seminar: Knowledge, assumptions and problem solving behaviours for teaching
MATH 126
Thu 1 Mar 2012, 4:00pm-5:00pm

#### Abstract

This week Djun Kim will conduct the discussion. We will study the section titled "Knowledge, assumptions and problem solving behaviours for teaching". This section is composed of four papers:

• From concept images to pedagogic structure for a mathematical topic (pdf)
• Promoting effective mathematical practices in students: insights from problem solving research (pdf)
• When students don't apply the knowledge you think they have, rethink your assumptions about transfer (pdf)
• How do mathematicians learn to teach? Implications from research on teachers and teaching for graduate student professional development (pdf)

Please see the Seminar's wiki page available at: http://wiki.ubc.ca/Sandbox:Math_Teaching_Seminar
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University of Calgary/University of Washington
Thu 1 Mar 2012, 4:10pm
Number Theory Seminar
Room WMAX 216 (PIMS - UBC Campus)
Room WMAX 216 (PIMS - UBC Campus)
Thu 1 Mar 2012, 4:10pm-5:00pm

#### Abstract

The study of numerical stability of algorithms for computing with polynomials and matrices over archimedian fields like R and C constitutes an entire branch of numerical analysis. The analogous problems over Qp have received far less attention. In this talk I will outline some number theoretic questions in which these problems arise, and describe joint work with Xavier Caruso in which we propose a general methodology for approaching them in practice.
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The Chinese University of Hong Kong
Fri 2 Mar 2012, 3:00pm SPECIAL
Department Colloquium
MATX 1100
On Toda Systems: Classification and Applications
MATX 1100
Fri 2 Mar 2012, 3:00pm-4:00pm

#### Abstract

It is well-known that the self dual non-Abelian Chern-Simons gauge equations coupled with a Schrodinger matter field can be reduced to Toda systems with Cartan matrix of rank r and singular sources. In this talk, using purely PDE methods, we give a complete classification of SU(n+1) Toda system with a single source. Then we apply this classification result to construct non-topological solutions for the SU(3) Chern-Simons system and obtain sharp estimates for the blow-up rates of SU(3) Toda system on a surface. (Joint work with Ao, CS Lin and D. Ye.)

#### Note for Attendees

Tea and cookies will be served from 2:45-3:00 p.m.
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Microsoft and MIT
Mon 5 Mar 2012, 11:00am
Probability Seminar
MATH 126
Directed random polymers and Macdonald processes
MATH 126
Mon 5 Mar 2012, 11:00am-12:00pm

#### Abstract

The goal of the talk is to survey recent progress in understanding
statistics of certain exactly solvable growth models, particle systems,
directed polymers in one space dimension, and stochastic PDEs. A
remarkable connection to representation theory and integrable systems is
at the heart of Macdonald processes, which provide an overarching theory
for this solvability. This is based off of joint work with Alexei Borodin.

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UBC
Mon 5 Mar 2012, 3:10pm
Algebraic Geometry Seminar
WMAX 110
Counting Hyperelliptic curves on Abelian Surfaces with Quasimodular Forms
WMAX 110
Mon 5 Mar 2012, 3:10pm-4:10pm

#### Abstract

In this talk we will present a formula to count the number of hyperelliptic curves on a polarized Abelian surface, up to translation.  This formula is obtained using orbifold Gromov-Witten theory, the crepant resolution conjection and the Yau-Zaslow formula to related hyperelliptic curves to rational curves on the Kummer surface Km(A). We will show how this formula can be described in terms of certain generating functions studied by P. A. MacMahon, which turn out to be quasimodular forms.

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Christoph Ortner
University of Warwick
Mon 5 Mar 2012, 4:00pm SPECIAL
Department Colloquium
MATX 1100
From atomistic to continuum descriptions of crystalline solids
MATX 1100
Mon 5 Mar 2012, 4:00pm-5:00pm

#### Abstract

Multi-scale modelling has become a paradigm that transcends most scientific disciplines. A key challenge that arises in many scientific problems is the connection between discrete atomistic and continuum descriptions of matter.  The Cauchy-Born rule postulates such a connection for crystal elasticity, which seems almost naive at first glance. Nevertheless, the Cauchy-Born model has been found to provide an accurate description of crystal elasticity even at the sub-grain scale.  In this talk, I will derive the Cauchy-Born model from a formal perspective and then present rigorous approximation results for 0T statics and dynamics. New ideas that have arisen from my work on this problem include a novel localisation mechanism, an atomistic notion of stress, and a surprising symmetry of certain multi-lattices.
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Christoph Ortner
University of Warwick
Tue 6 Mar 2012, 12:30pm SPECIAL
Scientific Computation and Applied & Industrial Mathematics
WMAX 110
Construction and (in-)consistency of atomistic-to-continuum coupling methods
WMAX 110
Tue 6 Mar 2012, 12:30pm-1:30pm

#### Abstract

Continuum mechanics models generally have an astonishing range of validity. For example, nonlinear elasticity can accurately describe the elastic behaviour of crystals even at the sub-grain scale (see talk on Monday). However, crystal defects such as cracks and dislocations are difficult to model quantitatively within CM. By coupling atomistic models of defects with continuum models of elastic far fields one can, in principle, obtain models with near-atomistic accuracy at significantly reduced computational cost. That said, various pitfalls must be overcome in the construction of efficient and reliable coupling mechanisms. In this talk, I will take a numerical
analysis approach to this problem  and analyze a sequence of coupling mechanisms in terms of their accuracy relative to their computational cost, which requires a thorough understanding of the consistency errors committed in the coupled models.
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UBC
Tue 6 Mar 2012, 2:00pm
Stochastic Dynamics Working Group
IAM Lounge
The Probability Density Function of the Positive Occupation Time of Brownian Motion with Two-Valued Drift
IAM Lounge
Tue 6 Mar 2012, 2:00pm-3:00pm

#### Abstract

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UBC
Tue 6 Mar 2012, 3:30pm
Algebraic Groups and Related Structures
MATX 1101
A few words on cohomological invariants
MATX 1101
Tue 6 Mar 2012, 3:30pm-4:30pm

#### Abstract

We will review the foundations on the Cohomology of k(t) and it's various completions. By doing so we will be able to define the notion of unramified elements, and we'll see how these fit on the  calculation of Inv_k(C_2,C_2).
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UBC
Tue 6 Mar 2012, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
WMAX 110 (PIMS)
Local dynamics near unstable branches of NLS solitons
WMAX 110 (PIMS)
Tue 6 Mar 2012, 3:30pm-4:30pm

#### Abstract

TBA
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Yu-Ting Chen
UBC
Wed 7 Mar 2012, 3:00pm
Probability Seminar
WMAX 110
Sharp Benefit-to-Cost Rules for the Evolution of Cooperation on Regular Graphs
WMAX 110
Wed 7 Mar 2012, 3:00pm-4:00pm

#### Abstract

We study two of the simple rules on finite graphs under the death-birth updating and the imitation updating discovered by Ohtsuki, Hauert, Lieberman, and
Nowak [\emph{Nature} {\bf 441} (2006) 502-505]. Each rule specifies a payoff-ratio cutoff point for the magnitude of fixation probabilities of the underlying
evolutionary game between cooperators and defectors. We view the Markov chains associated with the two updating mechanisms as voter model perturbations. Then
we present a first-order approximation for fixation probabilities of general voter model perturbations on finite graphs subject to small perturbation in terms of
the voter model fixation probabilities. In the context of regular graphs, we obtain algebraically explicit first-order approximations for the fixation
probabilities of cooperators distributed as certain uniform distributions. These approximations lead to a rigorous proof that both of the rules of Ohtsuki et al. are valid and are sharp.


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Galo Higuera Rojo
UBC
Wed 7 Mar 2012, 3:00pm
Topology and related seminars
WMAX 216 (PIMS)
Spaces of homomorphisms and commuting matrices
WMAX 216 (PIMS)
Wed 7 Mar 2012, 3:00pm-4:00pm

#### Abstract

Given a lie group G and a finitely generated group P we can give a topology to the set of group homomorphisms Hom(P,G) as a subset of G^k. There has
been an increasing interest in understanding these spaces, and particularly their connected components,  for their relevance in bundle theory. In particular when P=Z^k the space Hom(Z^k,G) is identified with the set of commuting k-tuples in G. We will present some of the generalities of these spaces and a possible systematic approach to their study. Then we will use that approach applied to the particular case when G=O(n), the group of orthogonal matrices, and compute the number of components of Hom(Z^k,O(n)).

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Vivek Goyal
Electrical Engineering and Computer Science, MIT
Wed 7 Mar 2012, 4:00pm SPECIAL
Department Colloquium
WMAX 110 (PIMS)
Bayesian Analysis of Compressed Sensing under Replica Symmetry
WMAX 110 (PIMS)
Wed 7 Mar 2012, 4:00pm-5:00pm

#### Abstract

Compressed sensing has brought the use of sparsity- and compressibility-based signal models to the forefront of data acquisition and inverse problems.  The well-known analyses of compressed sensing are indirect and hold pointwise over the possible signals of interest.  Inspired by the conservatism of these analyses, we developed a Bayesian analysis framework.  Under the assumption of replica symmetry, we prove convergence in distribution as problem size grows of the joint marginal of one variable of interest and its estimate to the joint distribution in a simple scalar equivalent problem.  This gives a simple mechanism for asymptotically-exact performance predictions that applies to a large class of estimators applied to a large class of problems.  For example, it shows that l1-regularized least squares estimation typically performs much better than predicted by previous analyses.  It can also be applied to l0-regularized least squares and various other estimators.  Taken together, these analyses are significantly more optimistic than the traditional analyses.

Compressed sensing is far from the only reason to look at inverse problems with linear forward models.  I will also present a cross section of work in magnetic resonance imaging where we have exploited sparsity-based regularization.  This includes excitation design, GRAPPA kernel calibration, and image reconstruction.

Biography:

Vivek Goyal received the B.S. degree in mathematics and the B.S.E. degree in electrical engineering from the University of Iowa, where he received the John Briggs Memorial Award for the top undergraduate across all colleges.  He received the M.S. and Ph.D. degrees in electrical engineering from the University of California, Berkeley, where he received the Eliahu Jury Award for outstanding achievement in systems, communications, control, or signal processing.

His previous positions include Member of Technical Staff in the Mathematics of Communications Research Department of Bell Laboratories, Lucent Technologies; and Senior Research Engineer for Digital Fountain, Inc., Fremont, CA.  His research interests include source coding theory, quantization, sampling, and computational imaging.

Professor Goyal was awarded the IEEE Signal Processing Society Magazine Award and an NSF CAREER Award.  He served on the IEEE Signal Processing Society’s Image and Multiple Dimensional Signal Processing Technical Committee, is a permanent Co-chair of the SPIE Wavelets and Sparsity conference series, and is a TPC Co-Chair of the IEEE International Conference on Image Processing 2016.  He is a co-author of a forthcoming textbook available for download at FourierAndWavelets.org, and he will present tutorials on teaching signal processing at IEEE ICASSP 2012 and ICIP 2012.

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Andrew Morrison
Thu 8 Mar 2012, 12:30pm SPECIAL
Doctoral Exam
Thu 8 Mar 2012, 12:30pm-3:00pm

#### Details

Title: Computing Motivic Donaldson-Thomas Invariants

This thesis develops a method (dimensional reduction) to compute motivic Donaldson-Thomas invariants. The method is then employed to compute these invariants in several different cases.

#### Note for Attendees

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Yale University
Thu 8 Mar 2012, 3:00pm
Number Theory Seminar
Room WMAX 216 (PIMS - UBC Campus)
Distribution of values of irrational quadratic forms at integral points
Room WMAX 216 (PIMS - UBC Campus)
Thu 8 Mar 2012, 3:00pm-3:50pm

#### Abstract

I will talk about various asymptotic results related to the title.
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Vivek Goyal
Electrical Engineering and Computer Science, MIT
Thu 8 Mar 2012, 3:00pm SPECIAL
WMAX 110 (PIMS)
Mathematical Signal Processing Seminar: Compressive Depth Acquisition Cameras: Principles, Algorithms, and Demonstrations
WMAX 110 (PIMS)
Thu 8 Mar 2012, 3:00pm-4:00pm

#### Details

LIDAR systems and time-of-flight cameras use time elapsed from transmitting a pulse and receiving a reflected response, along with scanning by the illumination source or a 2D sensor array, to acquire depth maps.  We introduce a method for compressive acquisition of scene depth with high spatial and range resolution using a single, omnidirectional, time-resolved photodetector and no scanning components.  This opens up possibilities for accurate and high-resolution 3D sensing using compact and mobile devices.

In contrast to compressive photography, the information of interest -- scene depths -- is nonlinearly mixed in the measured data.  To overcome this aspect of the inverse problem, the depth map reconstruction relies on parametric signal modeling of the impulse response of piecewise-planar scenes.  Through the use of parametric deconvolution, we achieve much finer depth resolution than dictated by the illumination pulse width and detector bandwidth alone.  Spatial resolution in our framework is rooted in patterned illumination or patterned reception followed by decoupling the inverse problems of range estimation and spatial resolution recovery during computational processing.

Our compressive depth acquisition camera (CoDAC) framework is an example of broader research themes of exploiting time resolution in optical imaging and identifying and exploiting structure in inverse problems.

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Michael Lindstrom and Thomas Wong
UBC
Thu 8 Mar 2012, 4:00pm
Mathematical Education
MATH 126
TAAP Seminar: Learning Objectives for the Qualifying Exam
MATH 126
Thu 8 Mar 2012, 4:00pm-5:00pm

#### Abstract

This session will discuss what are learning objectives precisely and how to create effective ones using the Qualifying Exam for practice. Coffee, tea and cookies will be provided by the MGC and there will be a board games event just after this session.
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Hung Phan Minh
PIMS/UBC-O
Fri 9 Mar 2012, 12:00pm
PIMS Seminars and PDF Colloquiums
WMAX 216
Restricted Normal Cones: Basic Properties and Applications
WMAX 216
Fri 9 Mar 2012, 12:00pm-1:00pm

#### Abstract

In this talk, I introduce the restricted normal cone, which is a novel generalization of the Mordukhovich (also known as basic or limiting) normal cone. Basic properties are presented. In the case of subspaces, we make a connection to the Friedrichs angle between the subspaces.  Restricted normal cones are useful in extending work by Lewis, Luke and Malick on the method of alternating projections for two (possibly nonconvex) sets.

Based on joint work with: Heinz Bauschke (UBC Kelowna), Russell Luke (Goettingen, Germany), and Shawn Wang (UBC Kelowna).
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Yale University
Fri 9 Mar 2012, 3:00pm
Department Colloquium
MATX 1100. PIMS/UBC Distinguished Colloquium
Homogeneous dynamics and number theory
MATX 1100. PIMS/UBC Distinguished Colloquium
Fri 9 Mar 2012, 3:00pm-4:00pm

#### Abstract

Homogeneous dynamics is another name for the theory of flows on homogeneous spaces, or homogeneous flows. The study of homogeoeus flows has been attracting considerable attention for the last 40-50 years. During the last three decades, it has been realized that some problems in number theory and, in particular in Diophantine approximation, can be solved using mathods from the theory of homogeneous flows. The purpose of the talk is to give examples of interactions between number theory and homogeneous dynamics; mostly only formulations will be given, but there will be also very brief description of some proofs.

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Ohio State University
Mon 12 Mar 2012, 3:10pm
Algebraic Geometry Seminar
WMAX 110
Rigid curves on moduli spaces of stable rational curves and arithmetic breaks
WMAX 110
Mon 12 Mar 2012, 3:10pm-4:10pm

#### Abstract

The Mori cone of curves of the Grothendieck-Knudsen moduli space of stable rational curves with n markings, is conjecturally generated by the one-dimensional strata (the so-called F-curves). A result of Keel and McKernan states that a hypothetical counterexample must come from rigid curves that intersect the interior. In this talk I will show several ways of constructing rigid curves. In all the examples a reduction mod p argument shows that the classes of the rigid curves that we construct can be decomposed as sums of F-curves. This is joint work with Jenia Tevelev.
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Rensselaer Polytechnic Institute
Mon 12 Mar 2012, 4:00pm SPECIAL
Department Colloquium
MATX 1100
MATX 1100
Mon 12 Mar 2012, 4:00pm-5:00pm

#### Abstract

Radar imaging is a technology that has been developed, very successfully, within the engineering community during the last 50 years.  Radar systems on satellites now make beautiful images of regions of our earth and of other planets such as Venus.  One of the key components of this impressive technology is mathematics, and many of the open problems are mathematical ones.

This lecture will explain, from first principles, some of the basics of radar and the mathematics involved in producing high-resolution radar images.

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Harvey Mudd College
Tue 13 Mar 2012, 11:30am
IBLC 261
An Introduction to Surface Tension (Or Why Raindrops are Spherical)
IBLC 261
Tue 13 Mar 2012, 11:30am-12:30pm

#### Abstract

A common misconception is that raindrops take the form of teardrops. In fact,
they tend to be nearly spherical due to surface tension forces. This is an example
of how at small scales fluid the tendency of molecules to adhere to each other
is the dominate effect driving a fluid's motion. In this talk we will explain
how surface tension arises from intermolecular forces. We will also examine some
examples of the behavior that can occur at small scales due to the balance between
fluid-fluid and fluid-solid forces, with applications as varied as understanding
how detergents help clean clothes to the design of fuel tanks in zero gravity
environments.
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Rensselaer Polytechnic Institute
Tue 13 Mar 2012, 12:30pm SPECIAL
Scientific Computation and Applied & Industrial Mathematics
WMAX 110 (PIMS)
Multistatic Radar Imaging of Moving Targets
WMAX 110 (PIMS)
Tue 13 Mar 2012, 12:30pm-1:30pm

#### Abstract

This talk explores the spatial, temporal, and spectral attributes of radar data and the associated target information.  We see that existing signal-processing approaches combine these attributes, two at a time, to form images.

The question of combining all three attributes arises in the problem of using fixed, distributed sensors to image multiple moving targets.  This talk explains how a comprehensive theory can be developed that incorporates sensor positions and the (possibly different) waveforms transmitted by the various transmitters.   The theory leads to a formula for producing an image and a formula for the imaging point-spread function.   Included are plots of the point-spread function for various geometries and waveforms.
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Brown University
Tue 13 Mar 2012, 2:00pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
WMAX 110 (PIMS)
Elliptic equations in convex wedges with irregular coefficients
WMAX 110 (PIMS)
Tue 13 Mar 2012, 2:00pm-3:00pm

#### Abstract

I will present a recent result on the $W^2_p$-solvability of elliptic equations in convex wedge domains or in convex polygonal domains with discontinuous coefficients. A corresponding result for parabolic equations in polyhedrons with time-irregular coefficients will also be discussed.
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University of Washingon
Tue 13 Mar 2012, 3:30pm
Algebraic Groups and Related Structures
MaTX 1102
Piecewise Laurent polynomials and (operational) equivariant K-theory of toric varieties
MaTX 1102
Tue 13 Mar 2012, 3:30pm-4:30pm

#### Abstract

For a smooth compact toric variety X, the equivariant cohomology of X is identified with the ring of piecewise polynomials on the associated fan.  For singular toric varieties, this correspondence breaks down: the equivariant cohomology ring is not well understood.  However, Payne identified the ring of piecewise polynomials with the operational equivariant Chow cohomology of X; this agrees with the usual equivariant cohomology when X is smooth.  It turns out that a similar story holds for K-theory: when X is smooth and compact, the equivariant K-theory of algebraic vector bundles on X can be identified with the ring of "piecewise Laurent polynomials" on the associated fan.  So, what is this ring for a general toric variety?  In this talk, I will describe joint work with Sam Payne: for an arbitrary toric variety X, we identify the ring of piecewise Laurent polynomials on the fan with the operational equivariant K-theory of X.  The proof requires us to develop some foundational aspects of operational K-theory, as well as the usual equivariant K-theory of coherent sheaves.  Our point of view leads to the curious result that the abstract operational theory is tractable and computable on varieties where the usual K-theory (of algebraic vector bundles) is completely unknown.
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Betsy Strovall
Tue 13 Mar 2012, 4:00pm SPECIAL
Department Colloquium
MATH 105
Counteracting flatness with affine arclength measure
MATH 105
Tue 13 Mar 2012, 4:00pm-5:00pm

#### Abstract

Abstract:  There are many operators in harmonic analysis for which the
curvature of some underlying manifold plays a significant role.  We
will discuss recent efforts to establish uniform estimates for such
operators by compensating for degeneracies of curvature with an
appropriate measure.  We will focus on the case when the underlying
manifolds are polynomial curves.
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Macalester College
Wed 14 Mar 2012, 12:00pm
Mathematical Education
LSK 462
Lunch Series on Teaching and Learning: Flipping a math class: How I learned to stop worrying and abandon in-class
LSK 462
Wed 14 Mar 2012, 12:00pm-1:00pm

#### Abstract

I will discuss recent pedagogical efforts which involve moving lecture-based elements of courses to a pre-class online format. These efforts aim to encourage students' mental effort outside of class and to leverage in-class meeting time to meet particular learning goals. The course design is built upon three technological tools. First, the LiveScribe pen enables pre-recording of lecture material. Second, Google Moderator is an online environment that aggregates and sorts user-submitted questions. Finally, PRS clickers facilitate a dialogue about material during class meeting time, and facilitate ongoing student assessment, feedback, and metacognitive reflective practice. Through a course design case study and some demonstrations, we will explore pedagogical and technical aspects of this learning ecosystem. I will leave ample time for discussion and questions.
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UC Berkeley
Wed 14 Mar 2012, 3:00pm SPECIAL
Probability Seminar
WMAX 110
Stochastic Models of Social and Economic Networks
WMAX 110
Wed 14 Mar 2012, 3:00pm-4:00pm

#### Abstract

I will discuss a few examples of analysis of stochastic models of social and economic behaviors on networks. The models presented are coming from statistics, computer science, marketing, learning and network games.
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Universitat Autònoma de Barcelona
Wed 14 Mar 2012, 3:00pm
Topology and related seminars
WMAX 216 (PIMS)
Cohomology of Kac-Moody groups over finite fields
WMAX 216 (PIMS)
Wed 14 Mar 2012, 3:00pm-4:00pm

#### Abstract

I will talk on work in progress (with Albert Ruiz) on Kac-Moody groups over finite fields from a topological point of view, including some explicit cohomological computations (at non-characteristic primes) as well as some (conjectural) general properties.

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U.C. Berkeley
Thu 15 Mar 2012, 1:00pm SPECIAL
Department Colloquium
MATH 100
Non-linear Invariance and Applications
MATH 100
Thu 15 Mar 2012, 1:00pm-2:00pm

#### Abstract

Over the last decade, generalization of the central limit theorem titled Non-Linear Invariance Principles, have played a major role in the theory of approximation algorithms in computer science and in the theory of voting schemes in theoretical economics.  The talk will provide a broad overview of non-linear invariance, Gaussian geometry and their connection to hardness of approximation and social choice theory.
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Wesleyan University
Thu 15 Mar 2012, 3:00pm
Number Theory Seminar
Room ASB 10900 (IRMACS - SFU Campus)
A characterization of almost universal ternary inhomogeneous quadratic forms
Room ASB 10900 (IRMACS - SFU Campus)
Thu 15 Mar 2012, 3:00pm-3:50pm

#### Abstract

A fundamental question in the study of integral quadratic forms is the representation problem which asks for an effective determination of the set of integers represented by a given quadratic form. A slightly different, but equally interesting problem, is the representation problem for inhomogeneous quadratic forms. In this talk, we will discuss a characterization of positive definite almost universal ternary inhomogeneous quadratic forms which satisfy some mild arithmetic conditions. Using these general results, we will then characterize almost universal ternary sums of polygonal numbers.

#### Note for Attendees

Refreshments will be served between the two talks.
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Katya Yurasovskaya
UBC
Thu 15 Mar 2012, 4:00pm
Mathematical Education
MATH 126
Teaching Seminar: Proving theorems
MATH 126
Thu 15 Mar 2012, 4:00pm-5:00pm

#### Abstract

This week Katya Yurasovskaya will conduct the discussion. We will study the section titled "Proving theorems". This section is composed of five papers:

• Overcoming students' difficulties in learning to understand and construct proofs (pdf)
• Mathematical induction: cognitive and instructional considerations (pdf)
• Proving starting from informal notions of symmetry and transformations (pdf)
• Teaching and learning group theory (pdf)
• Teaching for understanding: a case of students' learning to use the uniqueness theorem as a tool in differential equations (pdf)

Please see the Seminar's wiki page available at: http://wiki.ubc.ca/Sandbox:Math_Teaching_Seminar
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Jan de Gier
University of Melbourne
Thu 15 Mar 2012, 4:00pm
Discrete Math Seminar
WMAX 216
The critical surface adsorption for self-avoiding walks on the honeycomb lattice is $1+\sqrt{2}$
WMAX 216
Thu 15 Mar 2012, 4:00pm-5:00pm

#### Abstract

In 2010 Duminil-Copin and Smirnov (DCS) proved rigorously that the
growth constant for self-avoiding walks on the honeycomb lattice is
equal to $\sqrt{2+\sqrt{2}}$, a value conjectured by Nienhuis in 1982.
One of the main ingredients in DCS's proof is a finite lattice
identity for generating functions obtained from a discretely
holomorphic observable. I will discuss an extension of their proof to
include boundary weights, and hence a method for establishing the
critical fugacity for the adsorption transition for self avoiding
walks.

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TBA
Thu 15 Mar 2012, 4:10pm
Number Theory Seminar
Room ASB 10900 (IRMACS - SFU Campus)
Room ASB 10900 (IRMACS - SFU Campus)
Thu 15 Mar 2012, 4:10pm-5:00pm

#### Abstract

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Cindy Greenwood
UBC
Fri 16 Mar 2012, 1:00pm
Stochastic Dynamics Working Group
IAM Lounge
Properties of single stochastic neurons which are preserved in a coupled system of two neurons
IAM Lounge
Fri 16 Mar 2012, 1:00pm-2:00pm

#### Abstract

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UCLA
Fri 16 Mar 2012, 3:00pm
Department Colloquium
MATX 1100
The quasiconformal geometry of fractals
MATX 1100
Fri 16 Mar 2012, 3:00pm-4:00pm

#### Abstract

Many questions in analysis and geometry lead to problems of quasiconformal geometry on non-smooth or fractal spaces. For example, there is a close relation of this subject to the problem of characterizing fundamental groups of hyperbolic 3-orbifolds or to Thurston's characterization of rational functions with nite post-critical set. In recent years, the classical theory of quasiconformal maps between Euclidean spaces has been successfully extended to more general settings and powerful tools have become available. Fractal 2-spheres or Sierpinski carpets are typical spaces for which this deeper understanding of their quasiconformal geometry is particularly relevant and interesting. In my talk I will give a survey on some recent developments in this area.
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Stanford University
Tue 20 Mar 2012, 3:00pm
Topology and related seminars
ESB 4127
TBA
ESB 4127
Tue 20 Mar 2012, 3:00pm-4:00pm

#### Abstract

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UBC
Tue 20 Mar 2012, 3:30pm
Algebraic Groups and Related Structures
MATX 1102
A few words on cohomological invariants
MATX 1102
Tue 20 Mar 2012, 3:30pm-4:30pm

#### Abstract

TBA
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Tom Wong
UBC
Tue 20 Mar 2012, 4:00pm
Discrete Math Seminar
Math 126
Finding Geodesics on Polygonal Triangulations
Math 126
Tue 20 Mar 2012, 4:00pm-5:00pm

#### Abstract

Edge-flip distance between polygonal triangulations measures the degree of similarity between two rooted triangulations and has applications in balancing rooted binary trees. Currently, there are no known poly-time algorithm for computing edge-flip distances. However, the existence of matched edges makes computing geodesic distances more manageable. In this talk, we will describe a method of reducing the problem by partitioning it into smaller components. We will present some results related the asymptotic distribution of these components as they are central to determining the effectiveness of this method.
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UBC
Wed 21 Mar 2012, 3:00pm
Probability Seminar / Topology and related seminars
WMAX 110 (PIMS)
Distributional limits of Riemannian manifolds and graphs with sublinear genus growth
WMAX 110 (PIMS)
Wed 21 Mar 2012, 3:00pm-4:00pm

#### Abstract

Studying Gromov-Hausdorff limits of sequences of Riemannian manifolds (M_i) satisfying suitable conditions on their local geometry is an extremely fruitful idea. However, in the most interesting case that the diameter of M_i grows without bounds, one is forced to choose base points p_i\in M_i and consider limits of the pointed spaces (M_i,p_i) in the pointed Gromov-Hausdorff topology. The choice of the base points p_i influences enormously the obtained limits. Benjamini and Schramm introduced the notion of distributional limit of a sequence of graphs; this basically amounts to "choosing the base point by random". In this talk I will describe the distributional limits of sequences (M_i) of manifolds with uniformly pinched curvature and satisfying a certain condition of quasi-conformal nature. I will also explain how these results yield a modest extension of Benjamini's and Schramm's original result. This is joint work with Hossein Namazi and Pekka Pankka.
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Schuola Normale Superiore (Italy)
Thu 22 Mar 2012, 2:00pm
Algebraic Geometry Seminar
GEOG 147
The Nori correspondence
GEOG 147
Thu 22 Mar 2012, 2:00pm-3:00pm

#### Abstract

Let X be a variety over a field k, with a fixed rational point x_0 in X(k). Nori defined a profinite group scheme N(X,x_0), usually called Nori's fundamental group, with the property that homomorphisms N(X,x_0) to a fixed finite group scheme G correspond to G-torsors P --> X, with a fixed rational point in the inverse image of x_0 in P. If k is algebraically closed this coincides with Grothendieck's fundamental group, but is in general very different. Nori's main theorem is that if X is complete, the category of finite-dimensional representations of N(X,x_0) is equivalent to an abelian subcategory of the category of vector bundles on X, the category of essentially finite bundles.

After describing Nori's results, I will explain my work in collaboration with Niels Borne, from the University of Lille, in which we extend them by removing the dependence on the base point, substituting Nori's fundamental group with a gerbe (in characteristic 0 this had already been done by Deligne), and give a simpler definition of essentially finite bundle, and a more direct and general proof of the correspondence between representations and essentially finite bundles.

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Jielin Zhu
UBC
Fri 23 Mar 2012, 1:00pm
Stochastic Dynamics Working Group
IAM Lounge
Asymptotic analysis for noise induced early escape problem
IAM Lounge
Fri 23 Mar 2012, 1:00pm-2:00pm

#### Abstract

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Fri 23 Mar 2012, 3:00pm
Department Colloquium
MATX 1100
Local uniformization in positive characteristic
MATX 1100
Fri 23 Mar 2012, 3:00pm-4:00pm

#### Abstract

In 1965, Hironaka showed resolution of singularities for all algebraic varieties over fields of characteristic 0. Since then, the analogue in positive characteristic has remained an open problem. When one cannot solve a problem globally, one tries to solve it locally. Here this means getting rid of singularities one at a time. Since Zariski it is known that the local version of resolution of singularities, called local uniformization'', is of valuation theoretical nature. It was proved by Zariski in 1939 in the case of characteristic 0. Also for local uniformization, the positive characteristic case is still unsolved. The only known partial solutions so far are:

- resolution up to dimension 3 (Abhyankar; Cossart and Piltant)
- resolution by alteration (de Jong)
- local uniformization for Abhyankar places (Knaf & Kuhlmann)
- local uniformization by alteration with Galois extensions (Knaf &
Kuhlmann)
- inseparable local uniformization (Temkin)

Alteration takes an extension of the function field of the algebraic variety into the bargain. The version for local uniformization gives better information about the extension than can be deduced from de Jong's result, and the proof by Knaf and Kuhlmann is purely valuation theoretical. Temkin arrived at a complementary result which uses alteration by purely inseparable extensions.

In our talk we will discuss the various known results about local uniformization and how they relate to the structure theory of valued function fields. Can the complementary results of Knaf & Kuhlmann and Temkin be put together to avoid extensions of the function field altogether? To hear our opinion, you will have to wait until the end of our talk...
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Peter A. Malte
University of Augsburg
Tue 27 Mar 2012, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
WMAX 110
A multi-scale approach to reaction-diffusion processes in domains with microstructure
WMAX 110
Tue 27 Mar 2012, 12:30pm-1:30pm

#### Abstract

Reaction-diffusion processes occur in many materials with microstructure such as biological cells, steel or concrete. The main difficulty in modelling and simulating accurately such processes is to account for the fine microstructure of the material. One method of upscaling multi-scale problems, which has proven reliable for obtaining feasible macroscopic models, is the method of periodic homogenisation.

The talk will give an introduction to multi-scale modelling of chemical mechanisms in domains with microstructure as well as to the method of periodic homogenisation. Moreover, certain aspects particularly relevant in upscaling reaction-diffusion processes in biological cells will be discussed.

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UBC
Tue 27 Mar 2012, 3:30pm
Algebraic Groups and Related Structures
MATX 1102
On lifting fixed curves equivariantly
MATX 1102
Tue 27 Mar 2012, 3:30pm-4:30pm

#### Abstract

TBA
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Tyler Helmuth
UBC
Tue 27 Mar 2012, 4:00pm
Discrete Math Seminar
Math 126
Ising Model Observables and Non-Backtracking Walks
Math 126
Tue 27 Mar 2012, 4:00pm-5:00pm

#### Abstract

The Ising model is a discrete mathematical model for ferromagnetism. A classical argument shows that to study the Ising model on a finite graph G it is equivalent to study the generating function of even subgraphs of G. In the 60s Sherman showed that when G is planar this generating function can be rewritten as a generating function of closed non-backtracking walks on G, and recent work of Cimasoni and Loebl has removed the restriction that G is planar. I'll outline an alternative proof of these facts and explain what this means for the Ising model.

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Bath
Wed 28 Mar 2012, 3:00pm
Probability Seminar
WMAX 110
Zero dissipation limit in Abelian sandpiles
WMAX 110
Wed 28 Mar 2012, 3:00pm-4:00pm

#### Abstract

The Abelian sandpile model on the d-dimensional integer lattice is a particle system that is critical, in the sense well-known from lattice models of statistical physics. That is, several observables follow power law distributions, at least numerically, and occasionally this can be proved. Here we study a natural one parameter family of models called dissipative sandpiles, where a small amount gamma of mass can be lost (dissipated) on each toppling. As gamma approaches 0, the critical model is recovered, while for any gamma>0, the model has exponential decay of correlations. After discussing some basic properties, I will present estimates in d = 2 and 3, on how fast the stationary measure of the dissipative model approaches the critical sandpile measure. (Partly joint work with F. Redig and E. Saada.)

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University of Michigan
Wed 28 Mar 2012, 3:00pm
Topology and related seminars
WMAX 216 (PIMS)
Strong accessibility of torsion free (relatively) hyperbolic groups
WMAX 216 (PIMS)
Wed 28 Mar 2012, 3:00pm-4:00pm

#### Abstract

Let G be a finitely presented group. If the process of iteratively passing to vertex groups in a maximal graph of groups decomposition of G over finite subgroups, and then to vertex groups in maximal decompositions of the factors over two-ended subgroups, terminates, we say that G is strongly accessible. Delzant and Potyagailo argue that this process always terminates for certain types of splittings of finitely presented groups, in particular hyperbolic groups without two-torsion. I will give an example showing that their proof cannot be correct, and sketch a new proof that (relatively) hyperbolic groups without two-torsion are strongly accessible. This is joint work with N. Touikan.
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UCLA
Thu 29 Mar 2012, 2:00pm SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
--Cancelled---
Liquid drops sliding down an inclined plane.
--Cancelled---
Thu 29 Mar 2012, 2:00pm-3:00pm

#### Abstract

We investigate a one-dimensional model describing the motion of liquid drops sliding down an inclined plane (the so-called quasi-static approximation model). We prove existence and uniqueness of a solution and investigate its long time behavior for both homogeneous and inhomogeneous medium (i.e. constant and non-constant contact angle). This is joint work with Antoine Mellet (U.Maryland).
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UBC
Thu 29 Mar 2012, 3:00pm
Number Theory Seminar
Room WMAX 216 (PIMS - UBC Campus)
Special values of anticyclotomic L-functions
Room WMAX 216 (PIMS - UBC Campus)
Thu 29 Mar 2012, 3:00pm-3:50pm

#### Abstract

Associated to a newform F in S20(N)) and an anticyclotomic finite-order Hecke character χ of an imaginary quadratic field K, one defines the twisted L-function L(F,χ,s). Prof. Vatsal obtained various results pertaining to the non-vanishing modulo a prime λ in the algebraic closure of Q of the special values of these L-fuctions in the anticyclotomic tower of conductor p over K when the sign in the functional equation is +1. In this talk, we report on a work in progress to establish some generalizations of such results.

#### Note for Attendees

Refreshments will be served between the two talks.
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UBC
Thu 29 Mar 2012, 3:30pm
Algebraic Groups and Related Structures
Matx 1101
On lifting fixed curves equivariantly
Matx 1101
Thu 29 Mar 2012, 3:30pm-4:30pm

#### Abstract

A continuation on a statement about pushing curves equivariantly.
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Costanza Piccolo
UBC
Thu 29 Mar 2012, 4:00pm
Mathematical Education
MATH 126
Teaching Seminar: Interacting with students
MATH 126
Thu 29 Mar 2012, 4:00pm-5:00pm

#### Abstract

This week Costanza Piccolo will conduct the discussion. We will study the section titled "Interacting with students". This section is composed of four papers:

• Meeting new teaching challenges: teaching strategies that mediate between all lecture and all student discovery (pdf)
• Examining interaction patterns in college-level mathematics classes: a case study (pdf)
• Mathematics as a constructive activity: exploiting dimensions of possible variation (pdf)
• Supporting high achievement in introductory mathematics courses: what we have learned from 30 years of the emerging scholars program (pdf)

Please see the Seminar's wiki page available at: http: // wiki.ubc.ca/Sandbox: Math Teaching Seminar

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Vijaykumar Singh
PIMS/SFU
Thu 29 Mar 2012, 4:10pm
Number Theory Seminar
Room WMAX 216 (PIMS - UBC Campus)
Classification of isogeny classes of supersingular abelian varieties over finite fields
Room WMAX 216 (PIMS - UBC Campus)
Thu 29 Mar 2012, 4:10pm-5:00pm

#### Abstract

I will give a complete classification of the isogeny classes of supersingular abelian varieties for all dimensions by explicitly finding all possible characteristic polynomial of Frobenius endomorphism up to dimension 7 and giving an algorithm to find for all dimensions using Honda-Tate Theory. This is joint work with Gary McGuire and Alexey Zaytsev.
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UBC
Fri 30 Mar 2012, 1:00pm
Stochastic Dynamics Working Group
IAM Lounge
Parametric estimation of the infinitesimal generator of a diffusion process from data
IAM Lounge
Fri 30 Mar 2012, 1:00pm-2:00pm

#### Abstract

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University of Utah
Fri 30 Mar 2012, 3:00pm
Department Colloquium
GEOG 100 (PIMS Public Lecture)
Mathematics and the melting polar ice caps (PIMS Public Lecture)
GEOG 100 (PIMS Public Lecture)
Fri 30 Mar 2012, 3:00pm-4:00pm

#### Abstract

Sea ice is a leading indicator of climate change. It also hosts extensive microbial communities which support life in the polar oceans. The precipitous decline of the summer Arctic sea ice pack is probably the most visible, large scale change on Earth's surface in recent years. Most global climate models, however, have significantly underestimated these losses. We will discuss how mathematical models of composite materials and statistical physics are being used to study key sea ice processes such as melt pond evolution, snow-ice formation, and nutrient replenishment for algal communities. These processes must be better understood to improve projections of the fate of sea ice, and the response of polar ecosystems. Video from recent Antarctic expeditions where we measured sea ice properties will be shown.

#### Note for Attendees

Reception will be held at 2:30 pm in the WMAX 110 at PIMS.
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