Mathematics Dept.
  Events
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, 1:00pm-2:00pm

Abstract

 
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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, 3:00pm-4:00pm

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 sub-domains. Unlike traditional domain decomposition, this method hence does not require iteration on the sub-domains 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 shallow-water equations are presented. This is joint work with Ronald Haynes and Emily Walsh.
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UBC
Mon 2 Mar 2015, 3:10pm
CRG Geometry and Physics Seminar
ESB 4127
Dg-manifolds as derived manifolds
ESB 4127
Mon 2 Mar 2015, 3:10pm-4:10pm

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.
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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, 3:30pm-4:30pm

Abstract

We show that for an immersed two-sided 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 two-sided 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)

 
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UBC
Tue 3 Mar 2015, 4:00pm
Discrete Math Seminar
ESB 4127
Spectrum in Simplicial Complexes
ESB 4127
Tue 3 Mar 2015, 4:00pm-5:00pm

Abstract

 

Ramanujan graphs are k-regular 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 L-S-V. (Roughly speaking, we show that the complexes constructed by L-S-V have "optimal spectrum in all dimensions".)
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Qingsan Zhu
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, 3:10pm-4:00pm

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 $1/(|a|^2 log|a|)$ up to a constant.
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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, 3:15pm-4:15pm

Abstract

We are interested in classifying all finite groups which can act  on a finite CW-complex 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.
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UBC
Thu 5 Mar 2015, 3:30pm
Number Theory Seminar
room MATH 126
Diophantine quadruples
room MATH 126
Thu 5 Mar 2015, 3:30pm-4:30pm

Abstract

A Diophantine m-tuple 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 Erdős-Turán 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)
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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, 4:00pm-5:00pm

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 4D-Var 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 4D-Var 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.

Note for Attendees

Note SFU downtown venue. Reception at 3:30 pm (light refreshments).
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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, 3:00pm-4:00pm

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 subgrid-scale 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 classifi cation of diff erential equations. By assuming a general functional dependency of the unknown subgrid-scale in terms of the known grid-scale quantities in a system of averaged diff erential equations turns the original unclosed di fferential equations into a class of diff erential equations which is approachable using tools from the classical group classi cation. The result of this procedure yields various forms of local closure ansatzes for the unresolved subgrid scale terms leading the closed diff erential equations having symmetry properties that are related to the original unaveraged diff erential equations.

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UBC
Mon 9 Mar 2015, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127
The Donaldson-Thomas theory of K3xE via motivic and toric methods
ESB 4127
Mon 9 Mar 2015, 3:00pm-4:00pm

Abstract

 Donaldson-Thomas invariants are fundamental deformation invariants of Calabi-Yau threefolds. We describe a recent conjecture of Oberdieck and Pandharipande which predicts that the (three variable) generating function for the Donaldson-Thomas 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.  
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Lars Ruthotto
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, 12:30pm-1:30pm

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. 
 

Note for Attendees

Lunch will be provided.
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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, 3:30pm-4:30pm

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 quasi-patterns is introduced. This idea is analogous to oscillations sustained by noise in a stochatic ODE setting.
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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, 4:00pm-5:00pm

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. finite-dimensional 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 zero-divisors and thus have storied histories in discrete and differential geometry.

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Duke University
Wed 11 Mar 2015, 3:00pm
CRG Geometry and Physics Seminar
PIMS 4105
TBA
PIMS 4105
Wed 11 Mar 2015, 3:00pm-4:00pm

Abstract

 TBA
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University of Washington
Wed 11 Mar 2015, 3:10pm
Probability Seminar
ESB 2012
The frog model on trees
ESB 2012
Wed 11 Mar 2015, 3:10pm-4:00pm

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 d-ary tree with one-frog-per-site we prove a phase transition from recurrence to transience as d increases. Alternatively, for fixed d with Poi(m)-frogs-per-site 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.
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Osaka University
Wed 11 Mar 2015, 3:15pm
Topology and related seminars
ESB 4133
Pseudo-Anosovs with small dilatations in the hyperelliptic handlebody groups and spherical Hilden groups
ESB 4133
Wed 11 Mar 2015, 3:15pm-4:15pm

Abstract

This is a joint work with Susumu Hirose. We consider pseudo-Anosov elements of the mapping class groups on orientable surfaces. We are interested in a numerical invariant of pseudo-Anosovs, called the dilatation. The logarithm of the dilatation of a pseudo-Anosov mapping class is called the entropy. If we fix a surface, then the set of dilatations of pseudo-Anosovs 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 pseudo-Anosovs defined on a closed surface of genus g behaves like 1/g. Later Hironaka proved that the minimal entropy of pseudo-Anosovs 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 pseudo-Anosovs 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 pseudo-Anosovs with small dilatations in the spherical Hilden subgroups.
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UBC
Thu 12 Mar 2015, 1:30pm
Graduate Student Seminar
Math 202
A survey of the Basel Problem
Math 202
Thu 12 Mar 2015, 1:30pm-2:00pm

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.

Note for Attendees

 Special Pi-day event! Pies will be served!
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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, 3:30pm-4:30pm

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.
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Brown University
Fri 13 Mar 2015, 3:00pm
Department Colloquium
ESB 2012 (PIMS)
The mathematics of lattice-based cryptography (PIMS-UBC Distinguished Colloquium)
ESB 2012 (PIMS)
Fri 13 Mar 2015, 3:00pm-4:00pm

Abstract


Note for Attendees

Coffee, tea and cookies served at 2:30pm in the PIMS Lounge, ESB 4133.
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Ed Granirer
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, 4:35pm-10:00am

Abstract


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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, 3:00pm-4:00pm

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
Laplace-Beltrami 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 Combescure-Robert.

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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, 3:10pm-4:10pm

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.
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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, 2:00pm-3:00pm

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.
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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, 4:00pm-5:00pm

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 Cori-Vauquelin-Schaeffer 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 so-called Brownian map.

This the second talk of a series of 3 talks, the 3rd one will focus on distance properties in random planar maps
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Ben Adcock
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, 12:00pm-1:00pm

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 near-optimal 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 appropriately-designed locally incoherent sensing matrices also leads to substantially improved compressed sensing algorithms in a range of other applications.
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Mario Garcia Armas
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, 12:30pm-2:30pm

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 G-action 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 H-action that lifts the prescribed G-action 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 G-curve defined over k. Recall that a G-curve is an algebraic curve endowed with the action of a finite group G. A faithful G-curve C is called strongly incompressible if every dominant G-equivariant rational map of C onto a faithful G-variety is birational. We prove that strongly incompressible G-curves 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 G-curves depends on finer arithmetic properties of k.
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Yingfei Yi
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, 3:00pm-4:00pm

Abstract

The talk concerns limit behaviors of stationary measures of diffusion processes generated from white-noise perturbed systems of ordinary differential equations. By relaxing the notion of Lyapunov functions associated with the stationary Fokker-Planck equations, new existence and non-existence 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/scientific-event/150319-pcyy
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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, 4:00pm-5:00pm

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 self-similar measures and Cantor-like 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 self-similar measures which do not satisfy the separation condition can be surprising.
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Gangwei Wang
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, 4:30pm-5:30pm

Abstract

In this second talk, we again consider symmetries and conservation laws of FPDEs equation with Riemann-Liouville 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.
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UBC
Fri 20 Mar 2015, 3:00pm
Department Colloquium
LSK 200
Graduate Research Award Lecture: Quasisymmetric Schur functions and the 0-Hecke algebra
LSK 200
Fri 20 Mar 2015, 3:00pm-4:00pm

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 representation-theoretic 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 0-Hecke 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.

Note for Attendees

Refreshments will be served at 2:40pm in the Math Lounge area, MATH 125 before the colloquium.
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Ed Kroc
Mathematics, UBC
Fri 20 Mar 2015, 4:00pm SPECIAL
Room 203 of the Graduate Student Centre (6371 Crescent Rd), UBC
Doctoral Exam: Kakeya-type Sets, Lacunarity, and Directional Maximal Operators in Euclidean Space
Room 203 of the Graduate Student Centre (6371 Crescent Rd), UBC
Fri 20 Mar 2015, 4:00pm-6:00pm

Details

Given a Cantor-type subset Ω of a smooth curve in d-dimensional 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 d-dimensional 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.
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Sandra Merchant & Kseniya Garaschuk
Department of Mathematics, UBC
Mon 23 Mar 2015, 12:00pm
Lunch Series on Teaching & Learning
MATH 126
Two-stage or not two-stage? Using two-stage assessments in math courses
MATH 126
Mon 23 Mar 2015, 12:00pm-1:00pm

Abstract

In a two-stage 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 two-stage 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 two-stage reviews or exams in your courses. Pizza and pop are provided.
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UAlberta
Mon 23 Mar 2015, 3:00pm
CRG Geometry and Physics Seminar
ESB4127
Algebraic groups and maximal tori
ESB4127
Mon 23 Mar 2015, 3:00pm-4:00pm

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 Zariski-dense 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. 
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School of Earth and Ocean Science, University of Victoria
Mon 23 Mar 2015, 3:00pm
Institute of Applied Mathematics
LSK 460
Stochastic Dynamics of Near-Surface winds: Observations and Physical Models
LSK 460
Mon 23 Mar 2015, 3:00pm-4:00am

Abstract

Understanding physical controls on the variability of near-surface 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 empirically-based 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 physically-based probabilistic models of near-surface 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.

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Nishant Chandgotia
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, 12:00pm-2:00pm

Details

The well-known Hammersley-Clifford 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 Hammersley-Clifford Theorem for a family of Markov random fields which are outside the theorem’s purview (including Markov random fields whose support is the ddimensional “3-coloured chessboard”). On the other extreme, we construct a family of shift-invariant 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 “four-cycle free” finite undirected graph H without self-loops, 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 Hammersley-Clifford 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 config-folds” and “strong config-unfolds” of X.
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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, 3:30pm-4:30pm

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.
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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, 4:00pm-5:00pm

Abstract

In this third and last talk I will explain how to compute the so-called 2-point function of
planar quadrangulations (i.e., the generating function of planar quadrangulations with 
two vertices at prescribed distance), using the Cori-Vauquelin-Schaeffer bijection
and some clever calculations due to Bouttier Di Francesco and Guitter. 
From the exact expression of the 2-point function one can then show that, if X_n denotes the graph-distance 
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. 
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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, 3:15pm-4:15pm

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 Ben-Zvi Francis Nadler, this reveals connections between virtual orbifold products and Drinfeld centers of monoidal categories, thus answering a question of Hinich.
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Alex Bihlo
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, 4:30pm-5:30pm

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.
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UBC
Fri 27 Mar 2015, 3:00pm
Department Colloquium
ESB 2012
CRM-Fields-PIMS prize lecture: algebraic stacks and the inertia operator
ESB 2012
Fri 27 Mar 2015, 3:00pm-4:00pm

Abstract

Motivated by subtle questions in Donaldson-Thomas 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.

Note for Attendees

Refreshments will be served at 2:30 p.m. in ESB 4133, the PIMS Lounge.
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Carmen Bruni
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, 9:00am-11:00am

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 2-torsion 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 2-torsion 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.
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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, 1:00pm-2:00pm

Abstract

 
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Ed Granirer
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, 3:00pm-4:00pm

Abstract

Some functional analytic properties related to optimisation, such as the Krein-Milman Property and the Radon-Nikodym Property, for some Banach Algebras related to the Fourier Algebra  are investigated.
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Mathematics Manchester
Mon 30 Mar 2015, 3:00pm SPECIAL
Institute of Applied Mathematics
LSK 460
IAM-PIMS Distinguished Colloquium: Modelling plant cell and tissue growth
LSK 460
Mon 30 Mar 2015, 3:00pm-4:00pm

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 fibre-reinforced viscoelastic polymer networks and adopts upscaling approaches to efficiently describe the growth of multicellular tissues.

 
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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, 3:00pm-4:00pm

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 D-module theory to study period integrals. Connections to hypergeometric functions of Gel'fand-Kapranov-Zelevinsky (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, S-T. Yau, and X. Zhu.
 
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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, 12:00pm-2:00pm

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.
 
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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, 12:30pm-2:30pm

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.
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