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 Events
UBC
Wed 26 Sep 2018, 2:50pm
Topology and related seminars
ESB 4133 (PIMS lounge)
Symmetries of the Heegaard Floer theory of 4-ended tangles
ESB 4133 (PIMS lounge)
Wed 26 Sep 2018, 2:50pm-3:45pm

Abstract

 The Heegaard Floer theory of a 4-ended tangle takes the form of
an immersed curve (with possibly non-trivial local system) on the
boundary of the tangle minus the tangle ends. The Heegaard Floer
homology of a link can be computed as the Lagrangian intersection
theory of the Heegaard Floer homologies of two 4-ended tangles
obtained by splitting the link along an embedded 2-sphere.

I will outline the construction of the tangle invariant, with
particular focus on the action of the mapping class group of the
4-punctured sphere. I will then discuss the current state of
symmetry properties for this invariant in the light of the
mutation conjecture.
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University of Ottawa
Thu 27 Sep 2018, 2:00pm
Mathematical Biology Seminar
ESB 4133
Population dynamics in patchy landscapes
ESB 4133
Thu 27 Sep 2018, 2:00pm-2:50pm

Abstract

 
Mathematical models for population dynamics have a long history in biomathematics. They are tools to explore the effects of birth and death, species interaction, landscape quality and spatial movement on the persistence, spread and spatial distribution of a species. One particular question is how spatial variation in landscape attributes affects the dynamics of populations, for example in the context of species invasions. A relatively recent approach to this question divides a landscape into "patches" and incorporates small-scale individual movement information to predict large-scale population dynamics. In this talk, I will review several aspects of this growing body of literature. I will include empirical evidence, model derivation, basic model outcomes, analytical challenges and some future ideas. The talk is aimed at a general mathbio audience.
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UBC Math
Fri 28 Sep 2018, 4:00pm
Department Colloquium
ESB 2012
Integers in many-body quantum physics
ESB 2012
Fri 28 Sep 2018, 4:00pm-5:00pm

Abstract

Although integers are ubiquitous in quantum physics, they have different mathematical origins. In this colloquium, I will give a glimpse of how integers arise as either topological invariants or as analytic indices, as is the case in the so-called quantum Hall effect. I will explain the difficulties arising in extending well-known arguments when one relaxes the approximation that the particles effectively do not interact with each other in matter. Recent advances have made such realistic generalizations possible.

Note for Attendees

Refreshments will be served in ESB 4133 from 3:45 p.m.-4:00 p.m.
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Northeastern
Mon 1 Oct 2018, 4:00pm
Algebraic Geometry Seminar
MATH 126
TBA
MATH 126
Mon 1 Oct 2018, 4:00pm-5:00pm

Abstract

 
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Lawrence Ward
Department of Psychology and Brain Research Centre, UBC
Tue 2 Oct 2018, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Rapidly Forming, Slowly Evolving, Quasi-Cycle Phase Synchronization
ESB 4133 (PIMS Lounge)
Tue 2 Oct 2018, 12:30pm-1:30pm

Abstract

A lattice-indexed family of stochastic processes has quasi-cycle oscillations if its otherwise-damped oscillations are sustained by noise. Such a family performs the reaction part of a stochastic reaction-diffusion system when we insert a local Mexican Hat-type, difference of Gaussians, coupling on a one-dimensional and on a two-dimensional lattice. In one dimension we find that the phases of the quasi-cycles synchronize (establish a relatively constant relationship, or phase locking) rapidly at coupling strengths lower than those required to produce spatial patterns of their amplitudes. The patterns of phase locking persist and evolve but do not induce patterns in the amplitudes. In two dimensions the amplitude patterns form more quickly, but there remain parameter regimes in which phase patterns form without being accompanied by clear amplitude patterns. At higher coupling strengths we find patterns both of phase synchronization and of amplitude (resembling Turing patterns) corresponding to the patterns of phase synchronization. Specific properties of these patterns are controlled by the parameters of the reaction and of the Mexican Hat coupling.
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Juncheol Pyo
Pusan National University and UBC
Tue 2 Oct 2018, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
MATH 105
Solitons for the mean curvature flow and inverse mean curvature flow
MATH 105
Tue 2 Oct 2018, 3:30pm-4:30pm

Abstract

 Self-similar solutions and translating solitons are not only special solutions of mean curvature flow (MCF) but a key role in the study of singularities of MCF. They have received a lot of attention. We introduce some examples of self-similar solutions and translating solitons for the mean curvature flow (MCF) and give rigidity results of some of them. We also investigate self-similar solutions and translating solitons to the inverse mean curvature flow (IMCF) in Euclidean space. 
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