
Mon 2 Mar 2015, 1:00pm
Math Education Research Reading
MATX1118

Communities in university mathematics by Biza, Jaworski and Hemmi

MATX1118
Mon 2 Mar 2015, 1:00pm2:00pm
Abstract
hide

UBC Mathematics

Mon 2 Mar 2015, 3:00pm
Institute of Applied Mathematics
LSK 460

Stochastic domain decomposition for parallel grid generation

LSK 460
Mon 2 Mar 2015, 3:00pm4:00pm
Abstract
In this talk a method for the parallel generation of adaptive meshes using stochastic domain decomposition is presented. The method rests on numerically evaluating the stochastic representation of the exact solution of a linear elliptic or linear parabolic mesh generator for generating the mesh at the interfaces of the subdomains. Unlike traditional domain decomposition, this method hence does not require iteration on the subdomains or optimization of the transmission conditions to generate adaptive meshes over the entire domain. We show the generation of adaptive meshes for prescribed mesh density functions and study the scaling properties of the algorithm. A few physical examples for the parallel generation of adaptive meshes for Burgers equation and the shallowwater equations are presented. This is joint work with Ronald Haynes and Emily Walsh.
hide

UBC

Mon 2 Mar 2015, 3:10pm
CRG Geometry and Physics Seminar
ESB 4127

Dgmanifolds as derived manifolds

ESB 4127
Mon 2 Mar 2015, 3:10pm4:10pm
Abstract
Given two smooth maps of manifolds f:M \to L and g:N \to L, if they are not transverse, the fibered product M \times_L N may not exist, or may not have the correct cohomological properties. In the world of derived manifolds, such a fibered product always exists as a smooth object, regardless of transversality. In this talk we will describe recent progress of ours with D. Roytenberg on giving an accessible geometric model for derived manifolds using differential graded manifolds.
hide

Stanford University

Tue 3 Mar 2015, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

On the topology and index of minimal surfaces

ESB 2012
Tue 3 Mar 2015, 3:30pm4:30pm
Abstract
We show that for an immersed twosided minimal surface in R^3, there is a lower bound on the index depending on the genus and number of ends. Using this, we show the nonexistence of an embedded minimal surface in R^3 of index 2, as conjectured by Choe. Moreover, we show that the index of an immersed twosided minimal surface with embedded ends is bounded from above and below by a linear function of the total curvature of the surface. (This is joint work with Otis Chodosh)
hide

UBC

Tue 3 Mar 2015, 4:00pm
Discrete Math Seminar
ESB 4127

Spectrum in Simplicial Complexes

ESB 4127
Tue 3 Mar 2015, 4:00pm5:00pm
Abstract
Ramanujan graphs are kregular graphs admitting optimal connectivity properties (namely, optimal expanders). Infinite families of such graphs were first constructed by Lubotzky, Phillips and Sarnak in 1988 by relating the spectrum of a graph with certain representations of GL_2(Q_p). These ideas were generalized to simplical complexes by Lubotzky, Samuels and Vishne in 2005.
We will present a further generalization, showing that there is a natural way to relate spectral properties of simplicial complexes with certain representations of groups acting on their universal covers. Several results of this connection will be discussed. In particular, we strengthen the spectral properties of the complexes constructed by LSV. (Roughly speaking, we show that the complexes constructed by LSV have "optimal spectrum in all dimensions".)
hide

University of British Columbia

Wed 4 Mar 2015, 3:10pm
Probability Seminar
ESB 2012

An upper bound for the probability of visiting a distant point by critical branching random walk in $Z^4$

ESB 2012
Wed 4 Mar 2015, 3:10pm4:00pm
Abstract
We solve an open question raised by Le Gall and Lin. We study the probability of visiting a distant point $a \in Z^4$ by critical branching random walk starting from the origin. We prove that this probability is bounded by $1/(a^2 loga)$ up to a constant.
hide

Bilkent University and McMaster University

Wed 4 Mar 2015, 3:15pm
Topology and related seminars
ESB 4133

Finite group actions on homotopy spheres

ESB 4133
Wed 4 Mar 2015, 3:15pm4:15pm
Abstract
We are interested in classifying all finite groups which can act on a finite CWcomplex homotopy equivalent to a sphere, such that all isotropy subgroups are rank one groups, i.e., they do not include Z/pxZ/p for any prime p. The equivalent question for free actions (all isotropy subgroups are trivial) has been answered completely by the works of P.A. Smith and R. Swan. For actions with rank one isotropy, we give a list of group theoretical conditions which guarantee the existence of such actions. Some of these conditions are necessary conditions depending on assumptions on fixed point subspaces. This is a joint work with Ian Hambleton.
hide

UBC

Thu 5 Mar 2015, 3:30pm
Number Theory Seminar
room MATH 126

Diophantine quadruples

room MATH 126
Thu 5 Mar 2015, 3:30pm4:30pm
Abstract
A Diophantine mtuple is a set A of m positive integers such that ab+1 is a perfect square for every pair a,b of distinct elements of A. We derive an asymptotic formula for the number of Diophantine quadruples whose elements are bounded by x. In doing so, we extend two existing tools in ways that might be of independent interest. The ErdősTurán inequality bounds the discrepancy between the number of elements of a sequence that lie in a particular interval modulo 1 and the expected number; we establish a version of this inequality where the interval is allowed to vary. We also adapt an argument of Hooley on the equidistribution of solutions of polynomial congruences to handle reducible quadratic polynomials. (joint work with Scott Sitar)
hide

Mathematics, University of Bath

Fri 6 Mar 2015, 4:00pm
SPECIAL
Institute of Applied Mathematics
Canfor Policy Rm 1600, SFU Harbour Centre, Downtown Vancouver

Data Assimilation and Adaptivity

Canfor Policy Rm 1600, SFU Harbour Centre, Downtown Vancouver
Fri 6 Mar 2015, 4:00pm5:00pm
Abstract
Data assimilation is the process of systematically including (often noisy) data into a forecast. It is now widely used in numerical weather prediction and its positive impact on the accuracy of weather forecasts is unquestionable. Indeed improvements in our ability to forecast the weather over the last decade are a reflection on the increasing volume of data available, improved computational methods and (significantly) much improved algorithms for incorporating this data into the forecast. However, many problems remain, including dealing with the sheer volume of the data and the inherent complexity of the weather and climate, understanding the effects of data and model error, and of reducing spurious correlations between the data and the forecast.
In this talk I will give a survey of various techniques that are used operationally to implement data assimilation procedures in weather (and climate) forecasting including the Ensemble Kalman Filter, and the 4DVar method.
I will discuss their various advantages and disadvantages, the nature of the errors and ways to minimise these. In particular I will show that the use of adaptive numerical methods can significantly improve the performance
of the 4DVar method. Hopefully I will show that used carefully Data Assimilation techniques can significantly improve our ability to forecast the weather of Planet Earth.
Joint work with Mike Cullen and Chiara Piccolo at the Met Office.
hide

Wolfgang Pauli Institute and at the UBC Math Department

Mon 9 Mar 2015, 3:00pm
Institute of Applied Mathematics
LSK 460

Invariant turbulence modeling

LSK 460
Mon 9 Mar 2015, 3:00pm4:00pm
Abstract
Numerical weather prediction models can only operate at finite resolution. However, processes below the model resolution have an impact on the processes resolved by the model and therefore cannot be omitted in the model. The proper formulation of subgridscale processes in terms of resolved grid scale quantities is referred to as parameterization. The aim of this talk is to discuss a method for constructing parameterization schemes that preserve invariance properties. The method is based on group classification of differential equations. By assuming a general functional dependency of the unknown subgridscale in terms of the known gridscale quantities in a system of averaged differential equations turns the original unclosed differential equations into a class of differential equations which is approachable using tools from the classical group classication. The result of this procedure yields various forms of local closure ansatzes for the unresolved subgrid scale terms leading the closed differential equations having symmetry properties that are related to the original unaveraged differential equations.
hide

UBC

Mon 9 Mar 2015, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127

The DonaldsonThomas theory of K3xE via motivic and toric methods

ESB 4127
Mon 9 Mar 2015, 3:00pm4:00pm
Abstract
DonaldsonThomas invariants are fundamental deformation invariants of CalabiYau threefolds. We describe a recent conjecture of Oberdieck and Pandharipande which predicts that the (three variable) generating function for the DonaldsonThomas invariants of K3xE (the product of a K3 surface and an elliptic curve) is given by the reciprocal of the Igusa cusp form of weight 10. For each fixed K3 surface of genus g, the conjecture predicts that the corresponding (two variable) generating function is given by a particular meromorphic Jacobi form. We prove the conjecture for K3 surfaces of genus 0 and genus 1. Our computation uses a new technique which mixes motivic and toric methods.
hide

Department of Mathematics & Computer Science, Emory University, USA

Tue 10 Mar 2015, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

Seminar: JEMI  A Julia package for Electromagnetic Inversion

ESB 4133 (PIMS Lounge)
Tue 10 Mar 2015, 12:30pm1:30pm
Abstract
Electromagnetic inverse problems are now commonly solved in geophysical imaging applications. Many imaging techniques involve estimating the parameters of a PDE model from noisy measurements. This can be formulated as an optimization problem with constraints given by the PDE. The computational bottleneck are PDE simulations that need to be carried out for each measurement and at each iteration of the optimization algorithm. Most modern applications involve a very large number of measurements whose inversion requires optimization algorithms that converge quickly, but also allow for parallel and distributed computing.
In this talk, I will present recent developments in JEMI  a Julia package for electromagnetic inversion. JEMI is designed in a modular way and is thus offers great modeling potential. A particular focus of my talk will be on using Julia to adapt electromagnetic inversion codes to parallel systems.
hide

Mathematics Department, UBC

Tue 10 Mar 2015, 3:30pm
Mathematical Biology Seminar
PIMS Lounge, Earth Sciences Bldg. (ESB) 4th Floor

MathBio Works in Progress: Spatially Structured Neural Systems

PIMS Lounge, Earth Sciences Bldg. (ESB) 4th Floor
Tue 10 Mar 2015, 3:30pm4:30pm
Abstract
Scintillating Scotoma is a phenomenon in the visual cortex which may signal the onset of migraine, or may happen for no apparent reason. Initial steps to model this use a stochastic reaction diffusion system. A stochastic version of Turing patterns, called quasipatterns is introduced. This idea is analogous to oscillations sustained by noise in a stochatic ODE setting.
hide

Colorado State University

Tue 10 Mar 2015, 4:00pm
Discrete Math Seminar
ESB 4127

Nilpotence, Simplicity, and Exotic Geometries.

ESB 4127
Tue 10 Mar 2015, 4:00pm5:00pm
Abstract
In a quantifiable way most groups, rings, and Lie algebras are nilpotent. In fact even the extension of two abelian groups, or two trivial algebras, has enough variation to match the total quantity of all finite groups, resp. finitedimensional algebras. However, our most developed theories concern groups, rings, and algebras that are simple, semisimple, or highly related to simplicity.
In this talk I will demonstrate a simple way to convert questions about nilpotence into questions about simple and semisimple groups and nonassociative rings. The process is recursive and captures new structure in a positive proportion of all products. In fact 4/5 of the 11 million groups of size at most 1000 are explained by this mechanism. I will close with a a surprising characterization of the base case of these recursive techniques: they are products without zerodivisors and thus have storied histories in discrete and differential geometry.
hide

Duke University

Wed 11 Mar 2015, 3:00pm
CRG Geometry and Physics Seminar
PIMS 4105

TBA

PIMS 4105
Wed 11 Mar 2015, 3:00pm4:00pm
Abstract
TBA
hide

University of Washington

Wed 11 Mar 2015, 3:10pm
Probability Seminar
ESB 2012

The frog model on trees

ESB 2012
Wed 11 Mar 2015, 3:10pm4:00pm
Abstract
Fix a graph G and place some number (random or otherwise) of sleeping frogs at each site, as well as one awake frog at the root. Set things in motion by having awake frogs perform independent simple random walk, waking any "sleepers" they encounter. Say the model is recurrent if the root is a.s. visited by infinitely many frogs and otherwise transient. When G is the rooted dary tree with onefrogpersite we prove a phase transition from recurrence to transience as d increases. Alternatively, for fixed d with Poi(m)frogspersite we prove a phase transition from transience to recurrence as m increases. The proofs use two different recursions and two different versions of stochastic domination. Several open problems will be discussed. Joint with Christopher Hoffman and Tobias Johnson.
hide

Osaka University

Wed 11 Mar 2015, 3:15pm
Topology and related seminars
ESB 4133

PseudoAnosovs with small dilatations in the hyperelliptic handlebody groups and spherical Hilden groups

ESB 4133
Wed 11 Mar 2015, 3:15pm4:15pm
Abstract
This is a joint work with Susumu Hirose. We consider pseudoAnosov elements of the mapping class groups on orientable surfaces. We are interested in a numerical invariant of pseudoAnosovs, called the dilatation. The logarithm of the dilatation of a pseudoAnosov mapping class is called the entropy. If we fix a surface, then the set of dilatations of pseudoAnosovs defined on the surface is closed and discrete. In particular we can talk about a minimum of any subset of dilatations defined on the surface in question.
Penner proved that the minimal entropy of pseudoAnosovs defined on a closed surface of genus g behaves like 1/g. Later Hironaka proved that the minimal entropy of pseudoAnosovs in the handlebody subgroup on a closed surface of genus g also behaves like 1/g. We prove that the the minimal entropy of the hyperelliptic handlebody sugbroup of genus g has the same asymptotic behavior. (Our examples of pseudoAnosovs improve the upper bound of the minimal entropy of the handlebody sugbroup given by Hironaka.) To do this, we study the spherical Hilden subgroup of the mapping class group defined on a sphere with 2n punctures, and we construct a sequence of pseudoAnosovs with small dilatations in the spherical Hilden subgroups.
hide

UBC

Thu 12 Mar 2015, 1:30pm
Graduate Student Seminar
Math 202

A survey of the Basel Problem

Math 202
Thu 12 Mar 2015, 1:30pm2:00pm
Abstract
We briefly discuss the history of the Basel problem (that is, finding the sum of the reciprocals of the positive
squares) whose solution gave Euler fame at a young age. We'll look closely at three different proofs of varying levels of rigour to compare different
approaches allowed by this seemingly innocuous series.
hide

Colorado State University

Thu 12 Mar 2015, 3:30pm
Number Theory Seminar
room MATH 126

Local heuristics and exact formulas for elliptic curves over finite fields

room MATH 126
Thu 12 Mar 2015, 3:30pm4:30pm
Abstract
An isogeny class of elliptic curves over a finite field is determined by a quadratic Weil polynomial. Gekeler has given a beautiful product formula, purely in terms of congruence considerations involving that polynomial, for the size of such an isogeny class; an equidistribution hypothesis too strong to be true apparently calculates this cardinality.
I will give a new, transparent explanation, worked out with Julia Gordon, for this phenomenon. It turns out that Gekeler's formula computes an adelic orbital integral which, thanks to work of Langlands and Kottwitz, visibly calculates the desired quantity.
hide

Brown University

Fri 13 Mar 2015, 3:00pm
Department Colloquium
ESB 2012 (PIMS)

The mathematics of latticebased cryptography (PIMSUBC Distinguished Colloquium)

ESB 2012 (PIMS)
Fri 13 Mar 2015, 3:00pm4:00pm
Abstract
hide

UBC

Fri 13 Mar 2015, 4:35pm
Harmonic Analysis Seminar
TBA

On Some Functional Analytic Properties on Some Algebras related to the Fourier Algebra

TBA
Fri 13 Mar 2015, 4:35pm10:00am
Abstract
hide

McGill University

Mon 16 Mar 2015, 3:00pm
Harmonic Analysis Seminar
Math 225

Strong scarring and closed hyperbolic geodesics

Math 225
Mon 16 Mar 2015, 3:00pm4:00pm
Abstract
Let (M,g) be a compact surface without boundary. In this
lecture, we present some joint work with S. Nonnenmacher (Saclay)
giving the construction of logarithmic scale quasimodes of the
LaplaceBeltrami operator which concentrate around a given closed
hyperbolic geodesic. This result is related to a strengthened version
of the Quantum Unique Ergodicity conjecture and generalizes a previous
result of S. Brooks for logarithmic scale quasimodes on compact
hyperbolic surfaces. Our proof is microlocal and utilizes a quantum
Birkhoff normal form due to Sjöstrand as well as a result concerning
propagation around hyperbolic fixed points due to CombescureRobert.
hide

Imperial College

Mon 16 Mar 2015, 3:10pm
CRG Geometry and Physics Seminar
ESB4127

Mirror Symmetry and the Classification of Fano Manifolds

ESB4127
Mon 16 Mar 2015, 3:10pm4:10pm
Abstract
We discuss a surprising connection between Mirror Symmetry and the classification of Fano manifolds. This is joint work with Akhtar, Corti, Galkin, Golyshev, Kasprzyk, and Prince.
hide

UBC

Tue 17 Mar 2015, 2:00pm
SPECIAL
Topology and related seminars
ESB 4133

On the volumes of complements of geodesics on surfaces

ESB 4133
Tue 17 Mar 2015, 2:00pm3:00pm
Abstract
Given a hyperbolic surface S, consider any closed geodesic gamma on S. gamma is naturally embedded as a knot in the unit tangent bundle of S, and the complement of gamma is almost always a hyperbolic three manifold and thus has an intrinsic volume. In this talk I will describe a way to obtain an upper bound for this volume, linear with respect to the length of gamma. The proof goes through careful analysis of volumes for geodesics on the modular surface. This is joint work with Maxime Bergeron and Lior Silberman.
hide

Ecole Polytechnique

Tue 17 Mar 2015, 4:00pm
Discrete Math Seminar
ESB 4127

Introduction to maps II: planar map enumeration

ESB 4127
Tue 17 Mar 2015, 4:00pm5:00pm
Abstract
In the planar case a map can be seen as a connected graph embedded on the sphere (or in the plane) up to continuous deformation. The enumeration of (rooted) planar maps has started in the 60's with the seminal work of Tutte who found surprisingly simple counting formulas for several families of planar maps. We will briefly review on Tutte's method and present in details the more recent bijective approach, focusing on the CoriVauquelinSchaeffer bijection for planar quadrangulations. This bijection has become famous since it makes it possible to trace the distances (from a distinguished vertex) in the map, and as such it has proven a fundamental tool in the recent proof that random planar quadrangulations (rescaled by n^{1/4}) converge to the socalled Brownian map.
This the second talk of a series of 3 talks, the 3rd one will focus on distance properties in random planar maps
hide

SFU

Thu 19 Mar 2015, 12:00pm
Mathematics of Information and Applications Seminar
4133 ESB (PIMS lounge)

Cancelled: Compressed sensing with local structure: theory, applications and benefits

4133 ESB (PIMS lounge)
Thu 19 Mar 2015, 12:00pm1:00pm
Abstract
Compressed sensing concerns the recovery of signals and images from seemingly incomplete data sets. Introduced nearly a decade ago, it has since become an intensive area of research in applied mathematics, engineering and computer science. However, many practical problems in which compressed sensing is applied, e.g. medical imaging, are not adequately explained by existing theory. In this talk I will present a new framework for compressed sensing that bridges this gap. This framework is based on replacing some of the standard principles of compressed sensing with new local notions; specifically, sparsity in levels, local coherence in levels and multilevel random subsampling. When combined, they lead to nearoptimal recovery guarantees that explain the effectiveness of compressed sensing in such applications. Moreover, this framework is not just useful in understanding existing compressed sensing approaches. In the final part of this talk I will demonstrate how leveraging local sparsity through appropriatelydesigned locally incoherent sensing matrices also leads to substantially improved compressed sensing algorithms in a range of other applications.
hide

Mathematics, UBC

Thu 19 Mar 2015, 12:30pm
SPECIAL
Room 203 of the Graduate Student Centre (6371 Crescent Rd.), UBC

Doctoral Exam: Group Actions on Curves over Arbitrary Fields

Room 203 of the Graduate Student Centre (6371 Crescent Rd.), UBC
Thu 19 Mar 2015, 12:30pm2:30pm
Details
This thesis consists of three parts. The common theme is finite group actions on algebraic curves defined over an arbitrary field k.
In Part I we classify finite group actions on irreducible conic curves defined over k. Equivalently, we classify finite (constant) subgroups of SO(q) up to conjugacy, where q is a nondegenerate quadratic form of rank 3 defined over k. In the case where k is the field of complex numbers, these groups were classified by F. Klein at the end of the 19th century. In recent papers of A. Beauville and X. Faber, this classification is extended to the case where k is arbitrary, but q is split. We further extend their results by classifying finite subgroups of SO(q) for any base field k of characteristic not 2 and any nondegenerate ternary quadratic form q.
In Part II we address the Hyperelliptic Lifting Problem (or HLP): Given a faithful Gaction on the projective line defined over k and a double cover H of a finite group G, determine the conditions for the existence of a hyperelliptic curve C/k endowed with a faithful Haction that lifts the prescribed Gaction on the projective line. In this thesis, we find a complete solution to the HLP in characteristic 0 for every faithful group action on the projective line and every exact sequence as above.
In Part III we determine whether, given a finite group G and a base field k of characteristic 0, there exists a strongly incompressible Gcurve defined over k. Recall that a Gcurve is an algebraic curve endowed with the action of a finite group G. A faithful Gcurve C is called strongly incompressible if every dominant Gequivariant rational map of C onto a faithful Gvariety is birational. We prove that strongly incompressible Gcurves exist if G cannot act faithfully on the projective line over k. On the other hand, if G does embed into PGL(2,k), we show that the existence of strongly incompressible Gcurves depends on finer arithmetic properties of k.
hide

University of Alberta

Thu 19 Mar 2015, 3:00pm
PIMS Seminars and PDF Colloquiums
ESB 2012

Concentration of Stationary Measures

ESB 2012
Thu 19 Mar 2015, 3:00pm4:00pm
Abstract
The talk concerns limit behaviors of stationary measures of diffusion processes generated from whitenoise perturbed systems of ordinary differential equations. By relaxing the notion of Lyapunov functions associated with the stationary FokkerPlanck equations, new existence and nonexistence results of stationary measures will be presented. As noises vanish, concentration and limit behaviors of stationary measures will be described with particular attentions paying to the special role played by multiplicative noises. Connections to problems such as stochastic stability, stochastic bifurcations, and the ergodicity hypothesis will also be discussed.
http://www.pims.math.ca/scientificevent/150319pcyy
hide

University of Waterloo

Thu 19 Mar 2015, 4:00pm
SPECIAL
Harmonic Analysis Seminar
Math 104

Local dimensions of singular measures

Math 104
Thu 19 Mar 2015, 4:00pm5:00pm
Abstract
One way to quantify the level of singularity of a singular measure is to compute its local dimensions. For many interesting classes of measures, including selfsimilar measures and Cantorlike measures that satisfy a suitable separation condition, it is well known that the set of attainable values of the local dimensions is a closed interval. In contrast, convolutions of continuous measures often have an isolated point in their set of local dimensions. More generally, the structure of the set of local
dimensions of even selfsimilar measures which do not satisfy the separation condition can be surprising.
hide

UBC and Beijing Institute of Technology

Thu 19 Mar 2015, 4:30pm
Symmetries and Differential Equations Seminar
Math 125

Symmetry analysis and conservation laws for fractional order partial differential equations Part II

Math 125
Thu 19 Mar 2015, 4:30pm5:30pm
Abstract
In this second talk, we again consider symmetries and conservation laws of FPDEs equation with RiemannLiouville derivatives. Within the framework of Lie group theory, we extend Lie group analysis to solve problems involving FPDEs. Finally, we give further examples to illustrate applications of the methods. Some open questions will be discussed.
hide

UBC

Fri 20 Mar 2015, 3:00pm
Department Colloquium
LSK 200

Graduate Research Award Lecture: Quasisymmetric Schur functions and the 0Hecke algebra

LSK 200
Fri 20 Mar 2015, 3:00pm4:00pm
Abstract
The most prominent basis of the ring of symmetric functions is that of Schur functions. This basis captures a significant amount of the interplay between algebraic combinatorics and fields such as representation theory and algebraic geometry. Recently, a natural refinement of Schur functions, called quasisymmetric Schur functions, was introduced by Haglund, Luoto, Mason, and van Willigenburg. While various analogues of Schur function properties were established for quasisymmetric Schur functions, one key property  that of a representationtheoretic interpretation  was lacking.
In this talk, I will start by giving a combinatorial description using diagrams for quasisymmetric Schur functions and then proceed to describe how they arise in the setting of the representation theory of the 0Hecke algebra using easy to understand operations on diagrams. This is joint work with Steph van Willigenburg. The talk is aimed at a general audience and no knowledge of any of the above terms is assumed.
hide

Mathematics, UBC

Fri 20 Mar 2015, 4:00pm
SPECIAL
Room 203 of the Graduate Student Centre (6371 Crescent Rd), UBC

Doctoral Exam: Kakeyatype Sets, Lacunarity, and Directional Maximal Operators in Euclidean Space

Room 203 of the Graduate Student Centre (6371 Crescent Rd), UBC
Fri 20 Mar 2015, 4:00pm6:00pm
Details
Given a Cantortype subset Ω of a smooth curve in ddimensional Euclidean space, we construct random examples of Euclidean sets that contain unit line segments with directions from Ω and enjoy analytical features similar to those of traditional Kakeya sets of infinitesimal Lebesgue measure. We also develop a notion of finite order lacunarity for direction sets in arbitrary ddimensional space, and use it to extend our construction to direction sets Ω that are sublacunary according to this definition. This generalizes to higher dimensions a pair of planar results due to Bateman and Katz. In particular, the existence of such sets implies that the directional maximal operator associated with the direction set Ω is unbounded on the Lebesgue spaces of finite exponent.
hide

Sandra Merchant & Kseniya Garaschuk
Department of Mathematics, UBC

Mon 23 Mar 2015, 12:00pm
Lunch Series on Teaching & Learning
MATH 126

Twostage or not twostage? Using twostage assessments in math courses

MATH 126
Mon 23 Mar 2015, 12:00pm1:00pm
Abstract
In a twostage assessment, students first complete and turn in the questions individually and then, working in small groups, answer the same questions again. This technique was first introduced in the UBC Faculty of Science in 2009 and is now being used in at least 20 science courses. In this session, we will discuss the advantages and disadvantages of twostage assessments and describe some past experiences with this method at UBC and in the math department in particular. We will also consider different formats and options for implementing twostage reviews or exams in your courses. Pizza and pop are provided.
hide

UAlberta

Mon 23 Mar 2015, 3:00pm
CRG Geometry and Physics Seminar
ESB4127

Algebraic groups and maximal tori

ESB4127
Mon 23 Mar 2015, 3:00pm4:00pm
Abstract
We will survey recent developments dealing with characterization of absolutely almost simple algebraic groups having the same
isomorphism/isogeny classes of maximal tori over the field of
definition. These questions arose in the analysis of weakly commensurable Zariskidense subgroups. While there are definitive results over number fields (which we will briefly review), the theory over general fields is only emerging. We will formulate the existing conjectures, outline their potential applications, and report on recent progress. Joint work with A. Rapinchuk and I. Rapinchuk.
hide

School of Earth and Ocean Science, University of Victoria

Mon 23 Mar 2015, 3:00pm
Institute of Applied Mathematics
LSK 460

Stochastic Dynamics of NearSurface winds: Observations and Physical Models

LSK 460
Mon 23 Mar 2015, 3:00pm4:00am
Abstract
Understanding physical controls on the variability of nearsurface winds is of interest from the perspective of climate (as winds influence surface fluxes), of environmental hazards (particularly extreme winds), and of renewable energy. There is a long history of empiricallybased probabilistic models of wind variability, but until recently relatively little physical attention has been paid to this problem.
In this talk, I will discuss how we have been using approaches from nonlinear time series, dynamical systems, and stochastic differential equations in the development of physicallybased probabilistic models of nearsurface wind variability. The focus will be on winds over land, characterized by a marked day/night contrast in the shape of the wind speed probability density function (pdf). I will first present an analysis of long time series of wind, temperature, and turbulence data from a 213m tower in Cabauw, Netherlands. After this, I will discuss an idealized stochastic model of the boundary layer momentum budget that captures some of the basic features of variations in the wind speed pdf.
hide

Mathematics, UBC

Tue 24 Mar 2015, 12:00pm
SPECIAL
Room 126 of the Mathematics Bldg.

Doctoral Exam: Markov random fields and Gibbs States

Room 126 of the Mathematics Bldg.
Tue 24 Mar 2015, 12:00pm2:00pm
Details
The wellknown HammersleyClifford Theorem states (under certain conditions) that any Markov random field is a Gibbs state for a nearest neighbour interaction. Following Petersen and Schmidt we utilise the formalism of cocycles for the homoclinic relation and introduce “Markov cocycles”, reparametrisations of Markov specifications. We exploit this formalism to deduce the conclusion of the HammersleyClifford Theorem for a family of Markov random fields which are outside the theorem’s purview (including Markov random fields whose support is the ddimensional “3coloured chessboard”). On the other extreme, we construct a family of shiftinvariant Markov random fields which are not given by any finite range shiftinvariant interaction.
The techniques that we use for this problem are further expanded upon to obtain the following results: Given a “fourcycle free” finite undirected graph H without selfloops, consider the corresponding ‘vertex’ shift, Hom(Zd, H) denoted by XH. We prove that XH has the pivot property, meaning that for all distinct configurations x, y in XH which differ only at finitely many sites there is a sequence of configurations (x = x1), x2 , . . . , (xn = y) in XH for which the successive configurations (xi, xi+1) differ exactly at a single site. Further if H is connected then we prove that XH is entropy minimal, meaning that every shift space strictly contained in XH has strictly smaller entropy. The proofs of these seemingly disparate statements are related by the use of the ‘lifts’ of the configurations in XH to their universal cover and the introduction of ‘height functions’ in this context.
Further we generalise the HammersleyClifford theorem with an added condition that the underlying graph is bipartite. Taking inspiration from Brightwell and Winkler we introduce a notion of folding for configuration spaces called strong configfolding to prove that if all Markov random fields supported on X are Gibbs with some nearest neighbour interaction so are Markov random fields supported on the “strong configfolds” and “strong configunfolds” of X.
hide

Korea Institute for Advanced Study

Tue 24 Mar 2015, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

New characterizations of the catenoid and helicoid

ESB 2012
Tue 24 Mar 2015, 3:30pm4:30pm
Abstract
Bernstein and Breiner found a characterization of the catenoid that the area of a minimal annulus in a slab is bigger than that of the maximally stable catenoid in the same slab. We give a simpler proof of their theorem and extend the theorem to some minimal surfaces with genus (joint work with Benoit Daniel). New characterizations of the helicoid recently proved by Eunjoo Lee will be also presented.
hide

Ecole Polytechnique

Tue 24 Mar 2015, 4:00pm
Discrete Math Seminar
ESB 4127

Introduction to maps III: distance statistics in random planar maps

ESB 4127
Tue 24 Mar 2015, 4:00pm5:00pm
Abstract
In this third and last talk I will explain how to compute the socalled 2point function of
planar quadrangulations (i.e., the generating function of planar quadrangulations with
two vertices at prescribed distance), using the CoriVauquelinSchaeffer bijection
and some clever calculations due to Bouttier Di Francesco and Guitter.
From the exact expression of the 2point function one can then show that, if X_n denotes the graphdistance
between two random vertices in a random planar quadrangulation with n faces, then X_n/n^{1/4} converges in law
to an explicit density.
hide

UBC

Wed 25 Mar 2015, 3:15pm
Topology and related seminars
ESB 4133

Categorification of orbifold products and derived loop stacks

ESB 4133
Wed 25 Mar 2015, 3:15pm4:15pm
Abstract
The existence of interesting multiplicative cohomology theories for orbifolds was first suggested by string theorists, and orbifold products have been intensely studied by mathematicians for the last fifteen years. My work with S. Scherotzke focuses on the virtual orbifold product introduced by Lupercio et al. (2007). We construct a categorification of the virtual orbifold product that leverages the geometry of derived loop stacks. By work of BenZvi Francis Nadler, this reveals connections between virtual orbifold products and Drinfeld centers of monoidal categories, thus answering a question of Hinich.
hide

UBC

Thu 26 Mar 2015, 4:30pm
Symmetries and Differential Equations Seminar
Math 125

Recent advancements in geometric numerical integration

Math 125
Thu 26 Mar 2015, 4:30pm5:30pm
Abstract
I will discuss the construction of invariant and conservative finite
difference schemes. The methods introduced are applicable to general
systems of differential equations that possess symmetries and conservation
laws. This is a substantial generalization to symplectic or mimetic
integrators which are only applicable to specific types of differential
equations. Some numerical examples will be given illustrating the
strengths of the proposed methods.
hide

UBC

Fri 27 Mar 2015, 3:00pm
Department Colloquium
ESB 2012

CRMFieldsPIMS prize lecture: algebraic stacks and the inertia operator

ESB 2012
Fri 27 Mar 2015, 3:00pm4:00pm
Abstract
Motivated by subtle questions in DonaldsonThomas theory, we study the spectrum of the inertia operator on the Grothendieck module of algebraic stacks. We hope to give an idea of what this statement means. Along the way, we encounter some elementary, but apparently new, questions about finite groups and matrix groups. Prerequisites for this talk: a little linear algebra, and a little group theory.
hide

Mathematics, UBC

Mon 30 Mar 2015, 9:00am
SPECIAL
Room 203, Graduate Student Centre (6371 Crescent Rd), UBC

Doctoral Exam: Twisted Extensions of Fermat's Last Theorem

Room 203, Graduate Student Centre (6371 Crescent Rd), UBC
Mon 30 Mar 2015, 9:00am11:00am
Details
In 2011, Michael Bennett, Florian Luca and Jamie Mulholland showed that the equation involving a twisted sum of cubes has no pairwise coprime nonzero integer solutions for primes excluded from the set S where S is the set of primes q for which there exists an elliptic curve of conductor 18q, 36q, or 72q with at least one nontrivial rational 2torsion point. In this dissertation, I present a solution that extends the result to include a subset of the primes in S; those primes q in S for which all curves with conductor 18q, 36q, or 72q with nontrivial rational 2torsion have discriminants not of the form an integer squared or 3 times an integer squared. Using a similar approach, I will classify certain integer solutions to the equation of a twisted sum of fifth powers which in part generalizes work done from Billerey and Dieulefait in 2009.
hide


Mon 30 Mar 2015, 1:00pm
Math Education Research Reading
MATX1118

Finnish school system and its implementation in North America

MATX1118
Mon 30 Mar 2015, 1:00pm2:00pm
Abstract
hide

UBC

Mon 30 Mar 2015, 3:00pm
Harmonic Analysis Seminar
Math 225

On Some Functional Analytic Properties Of Some Algebras Related to the Fourier Algebra

Math 225
Mon 30 Mar 2015, 3:00pm4:00pm
Abstract
Some functional analytic properties related to optimisation, such as the KreinMilman Property and the RadonNikodym Property, for some Banach Algebras related to the Fourier Algebra are investigated.
hide

Mathematics Manchester

Mon 30 Mar 2015, 3:00pm
SPECIAL
Institute of Applied Mathematics
LSK 460

IAMPIMS Distinguished Colloquium: Modelling plant cell and tissue growth

LSK 460
Mon 30 Mar 2015, 3:00pm4:00pm
Abstract
Plant growth typically occurs through the coordinated anisotropic expansion of plant cells. Growth is regulated by hormones and is driven by high intracellular pressures generated by osmosis. This machinery allows a plant primary root, for example, to penetrate soil in a direction guided by gravity, while seeking out nutrients and avoiding obstacles. I will describe the biomechanical aspects of a computational multiscale model for root gravitropism that incorporates descriptions of cell walls as fibrereinforced viscoelastic polymer networks and adopts upscaling approaches to efficiently describe the growth of multicellular tissues.
hide

Harvard University

Mon 30 Mar 2015, 3:00pm
CRG Geometry and Physics Seminar
ESB4127

Period integrals and their differential systems

ESB4127
Mon 30 Mar 2015, 3:00pm4:00pm
Abstract
Period integrals are geometrical objects which can be realized as special functions, or sections of certain bundles. Their origin goes back to Euler, Gauss and Legendre in the study of complex algebraic curves. In their modern version, period integrals naturally arise in Hodge theory, and more recently in mathematical physics, and the theory of hypergeometric functions. I will give an overview of a recent program to use differential equations and Dmodule theory to study period integrals. Connections to hypergeometric functions of Gel'fandKapranovZelevinsky (GKZ) will also be considered. We will see that the theory is intimately related to a particular infinite dimensional representation of a reductive Lie algebra, and the topology of certain affine varieties. I will describe how the theory could help calculate period integrals, and offers new insights into the GKZ theory, and mirror symmetry for toric and flag varieties. This talk is based on joint works with S. Bloch, B. Lian, V. Srinivas, ST. Yau, and X. Zhu.
hide

Mathematics, Bath

Tue 31 Mar 2015, 12:00pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133

Optimal mesh generation for PDEs with applications to meteorology

ESB 4133
Tue 31 Mar 2015, 12:00pm2:00pm
Abstract
When numerically solving a PDE in three dimensions, it is often necessary to generate a mesh on which to discretize the solution. Often this can be expensive to do. However, by using ideas from optimal transport it is possible both to construct a mesh quickly and cheaply, and also to prove that it has the necessary regularity properties to allow an accurate approximation of the solution of the PDE. In this talk I will describe these methods, prove results about their regularity and then apply them to some problems in meteorology.
hide

Felipe Garcia Ramos Aguilar
Mathematics, UBC

Tue 31 Mar 2015, 12:30pm
SPECIAL
Room 203 of the Graduate Student Centre (6371 Crescent Road), UBC

Doctoral Exam: Randomness and Structure in Dynamical Systems: Different Forms of Sensitivity and Equicontinuity

Room 203 of the Graduate Student Centre (6371 Crescent Road), UBC
Tue 31 Mar 2015, 12:30pm2:30pm
Details
In this thesis we study topological (continuous map on a compact metric space) and measure theoretical (measure preserving map on a probability space) dynamical systems.
Dynamical systems range from chaotic (random) to predictable (high structure). Structure and randomness can be represented with different forms of equicontinuity and sensitivity to initial conditions (sensitivity).
Inspired by the classical dichotomy between sensitivity and equicontinuity we define weak forms of topological and measure theoretical equicontinuity and strong forms of sensitivity for dynamical systems, and we study their relationships with spectral properties and sequence entropy. We also prove results of how measure theoretically equicontinuous cellular automata (a particular class of topological systems with close connections to computer science) behave in the long term.
The work of this thesis answers questions from  B. Scarpellini. Stability properties of flows with pure point spectrum. Journal of the London Mathematical Society, 2(3):451–464, 1982.  F. Blanchard and P. Tisseur. Some properties of cellular automata with equicontinuity points. Annales de l’Institut Henri Poincare (B) Probability and Statistics, 36(5):569 – 582, 2000.
hide

Note for Attendees
Note SFU downtown venue. Reception at 3:30 pm (light refreshments).