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University of Massachusets
Mon 24 Sep 2018, 4:00pm
Algebraic Geometry Seminar
MATH 126
Knot invariants, Hilbert schemes and arc spaces
MATH 126
Mon 24 Sep 2018, 4:00pm-5:00pm


In my talk I will explain (partially conjectural) relation between

1) Homology of Hilbert scheme of points on singular curves

2) Knot homology of the links of curve singularities

3) Space functions on the moduli space of maps from the formal disc to the curve singularities.

I will center my talk around discussion of the case of cuspidal curve x^m=y^n and its singularity. In this case it is now known that 1) 2) and 3) are essentially equal. Talk is based on the joint projects with Gorsky, Rozansky, Rasmussen, Shende and Yun.

James Hewett
Department of Mechanical Engineering, University of Canterbury
Tue 25 Sep 2018, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Evolution of Solid Bodies due to Melting, Erosion and Deposition
ESB 4133 (PIMS Lounge)
Tue 25 Sep 2018, 12:30pm-1:30pm


Moving boundary problems are found in many contexts including coastlines and the seabed on the large scale to atherosclerosis and blood clotting on the micro scale. The coupling between the fluid flow and evolving solid bodies is an important consideration when modelling these problems. We have run numerical simulations for the melting front of ice for both interior and exterior flows; classical examples of the Stefan problem. We also modelled erosion and colloidal deposition problems which involved other constitutive equations. The terminal shape of an eroding cylinder in cross flow was a rounded triangular profile pointed upstream, which agreed well with experimental results. All of these problems require careful attention to deformation of the mesh at the interface, and we have developed a node shuffle algorithm for preserving mesh quality at these boundaries.
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


 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.
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


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.
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


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.