UBC

Mon 24 Oct 2016, 3:00pm
Harmonic Analysis Seminar
Math 126

(p,q)strong unboundedness for the maximal directional Hilbert transform in dimension n

Math 126
Mon 24 Oct 2016, 3:00pm4:00pm
Abstract
In 2007 G.A.Karagulyan proved that the maximal directional Hilbert transform over a set U of directions in the plane cannot be extended to a (2,q)strongly bounded operator for any q in the range 1 ≤ q < +∞. In this talk, I will describe my proof of the generalization of this result and show that, for any 1 < p ≤ 2, any 1 ≤ q < +∞ and any dimension n ≥ 2, the maximal directional Hilbert transform over an infinite set of directions in IR^n, cannot be extended to a (p,q)strongly bounded operator.
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UBC

Mon 24 Oct 2016, 3:00pm
Algebraic Geometry Seminar
MATX 1102

Tstructures on coherent sheaves and categorical actions

MATX 1102
Mon 24 Oct 2016, 3:00pm4:00pm
Abstract
I will review the notion of a tstructure and discuss some recent uses of tstructures on categories of coherent sheaves in (geometric) representation theory. After reviewing some traditional methods to obtain tstructures I will present a new construction that uses categorical Lie actions. As an application one recovers the category of "exotic sheaves", used in a recent proof of Lusztig's conjectures on a canonical bases for the Grothendieck group of Springer fibers by Bezrukavnikov and Mirković. The new construction is purely geometric, instead of using deep results from modular representation theory. This is joint work with Sabin Cautis.
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Departments of Mathematics, Earth and Ocean Science, UBC

Tue 25 Oct 2016, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

Mimetic Multiscale Methods and their application to Maxwell's equations

ESB 4133 (PIMS Lounge)
Tue 25 Oct 2016, 12:30pm1:30pm
Abstract
Solving Maxwell's equations for earth science applications requires the discretization of large domains with sufficiently small mesh to capture local conductivity variation. Multiscale methods are discretization techniques that allow to use a coarse mesh and still obtain accuracy that is obtained through finer meshes. However, when considering the multiscale solution of vector equations, basic operator properties are not conserved. In this talk we will show how to extend multiscale methods for vector quantities and demonstrate their use for Maxwell's equations.
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McGill University

Tue 25 Oct 2016, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB2012

Curvature flows and the isoperimetric problems in geometry

ESB2012
Tue 25 Oct 2016, 3:30pm4:30pm
Abstract
Abstract: We will discuss two types of curvature flows designed to prove isoperimetric type inequalities. The first one is a mean curvature type flow, it was introduced in a previous joint work with Junfang Li in space forms. In a recent joint paper with Junfang Li and MuTao Wang, we consider a similar normalized hypersurface flow in the more general ambient setting of warped product spaces with general base. Under a natural necessary condition, the flow preserves the volume of the bounded domain enclosed by a graphical hypersurface, and monotonically decreases the hypersurface area. Under another condition with is related to the notion of “photon sphere” in general relativity, we establish the regularity and convergence of the flow, thereby solve the isoperimetric problem in warped product spaces. In a similar spirit, I will discuss a inverse mean curvature type flow in hyperbolic space to deal with AlexandrovFenchel type isoperimetric inequalities.
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UBC

Tue 25 Oct 2016, 4:00pm
Discrete Math Seminar
ESB 4127

A Hard Problem in Lattice Theory

ESB 4127
Tue 25 Oct 2016, 4:00pm5:00pm
Abstract
Lattice theory is the study of an intriguing class of partially ordered sets known as lattices. Within this subject, there are many hard open problems. One such problem is to determine which countable lattices are sublattices of free lattices. In this talk, we will describe past progress on this problem and propose possible methods of attack using finite and finite width lattices. This research was done while I was a masters student at the University of Calgary.
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Université de Montréal

Wed 26 Oct 2016, 1:45pm
Mathematical Biology Seminar
PIMS (ESB 4th floor)

Feedback, delays and oscillations in blood cell production

PIMS (ESB 4th floor)
Wed 26 Oct 2016, 1:45pm2:45pm
Abstract
The production and control of blood cells is regulation by an intricate system of coupled mechanisms built around differentiation and proliferation of cells emerging from a common pool, with hormonal feedback at various stages of the maturation process. By developing physiologically correct models of this system, and its perturbation under pharmaceutical interventions, such as oncological treatments, we are lead to the investigation of nonlinear systems of delaydifferential equations, some with statedependent delays. I will review the evolution of models for erythropoiesis (red blood cell production), and present recent models for neutrophils (white blood cells), incorporating the pharmacokinetics and pharmacodynamics of an oncological drug, together with the main regulating hormone, GCSF, and platelets.
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UBC Math

Wed 26 Oct 2016, 3:00pm
Probability Seminar
ESB 2012

Models of Gradient Type with SubQuadratic Action

ESB 2012
Wed 26 Oct 2016, 3:00pm4:00pm
Abstract
We consider models of gradient type, which is the density of a collection of realvalued random variables \phi :=\{\phi_x: x \in \Lambda\} given by Z^{1}\exp({\sum\nolimits_{j \sim k}V(\phi_j\phi_k)}). We focus our study on the case that V(\nabla\phi) = [1+(\nabla\phi)^2]^\alpha with 0 < \alpha < 1/2, which is a nonconvex potential. We introduce an auxiliary field t_{jk} for each edge and represent the model as the marginal of a model with logcancave density. Based on this method, we prove that finite moments of the fields \left<[v \cdot \phi]^p \right> are bounded uniformly in the volume. This leads to the existence of infinite volume measures. Also, every ergodic infinite volume Gibbs measure with mean zero for the potential V above scales to a Gaussian free field.
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NTNU Norwegian University of Science and Technology

Wed 26 Oct 2016, 3:15pm
Topology and related seminars
ESB 4133 (PIMS Lounge)

Freaks of algebra  a topologist's exhibition

ESB 4133 (PIMS Lounge)
Wed 26 Oct 2016, 3:15pm4:15pm
Abstract
For this survey talk I will bring a bestiary of algebraic structures that are often less well known than they deserve to be. As I will explain, these are all related to symmetries and topology, and they have interesting symmetries of their own. This observation leads to new homology computations, and those will be the results that I will present along the way. Part of this work is joint with N. Wahl.
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Université de Savoie, Chambéry

Thu 27 Oct 2016, 3:30pm
Number Theory Seminar
MATH 126

Wave front sets of distributions in nonarchimedean analysis

MATH 126
Thu 27 Oct 2016, 3:30pm5:15pm
Abstract
In 1969, Sato and Hörmander introduced the notion of wave front set of a distribution in the real context. This concept gives a better understanding of operations on distributions such as product or pullback and it plays an important role in the theory of partial differential equations. In 1981, Howe introduced a notion of wave front set for some Lie group representations and in 1985, Heifetz gave an analogous version in the padic context. In this talk, in the tadic context in characteristic zero, using CluckersLoeser motivic integration we will present analogous constructions of test functions, distributions and wave front sets. In particular, we will explain how definability can be used as a substitute for topological compactness of the sphere in the real and padic contexts to obtain finiteness. This a joint work with R. Cluckers, and F. Loeser.
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McGill University

Fri 28 Oct 2016, 3:00pm
Department Colloquium
ESB 2012

CRMFieldsPIMS Award Lecture: The Cubical Route to Understanding Groups

ESB 2012
Fri 28 Oct 2016, 3:00pm4:00pm
Abstract
Cube complexes have come to play an increasingly central role within geometric group theory, as their connection to rightangled Artin groups provides a powerful combinatorial bridge between geometry and algebra. This talk will introduce nonpositively curved cube complexes, and then describe the developments that have recently culminated in the resolution of the virtual Haken conjecture for 3manifolds, and simultaneously dramatically extended our understanding of many infinite groups.
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Note for Attendees