UAlberta

Mon 24 Nov 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UBC)

Modules of differentials for Lie algebras

ESB 4127 (host: UBC)
Mon 24 Nov 2014, 3:00pm4:00pm
Abstract
In this talk, I will attempt to introduce/discuss modules of differentials for Lie algebras modelled after the corresponding notion for rings. This is relevant to the structure of certain infinite dimensional Lie algebras. This is joint work with Arturo Pianzola.
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Mathematics Department, University of Oxford, UK

Tue 25 Nov 2014, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)

Preconditioning for models of coupled magma/mantle dynamics

ESB 4133 (PIMS Lounge)
Tue 25 Nov 2014, 12:30pm1:30pm
Abstract
We will describe some recent work in the numerical simulation of problems of Geodynamics. The relevant partial differential equations share some of the features of the wellknown Stokes equations, but there are significant differences. Our work has been to create rapid solvers for the large systems of equations arising from finite element approximation. We will briefly describe the relevant models and our preconditioned Krylov subspace iterative solvers which enable some of the first computations on these models.
This is joint work with Sander Rhebergen, Richard Katz, Garth Wells, John Rudge and Laura Alisic.
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Pont. Cat. Univ. Chile

Tue 25 Nov 2014, 3:30pm
Diff. Geom, Math. Phys., PDE Seminar
ESB 2012

Nondegeneracy of nonradial nodal solutions to Yamabe problem

ESB 2012
Tue 25 Nov 2014, 3:30pm4:30pm
Abstract
We prove the existence of a sequence of nondegenerate, in the sense of DuyckaertsKenigMerle, nodal nonradial solutions to the critical Yamabe problem or stationary energycritical wave equation.
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Tue 25 Nov 2014, 4:00pm
SPECIAL
One Time Event
Graduate Student Center, Room 203

Doctoral Exam

Graduate Student Center, Room 203
Tue 25 Nov 2014, 4:00pm6:30pm
Details
Spin systems such as the Ising model are central topics in statistical mechanics and probability theory. In the late 1960s Symanzik made the important discovery that properties of spin systems could be expressed in terms of the behaviour of random walks. This thesis contributes to the understanding of these connections by developing and analyzing random walk representations of graphical models arising in statistical mechanics.
Concretely, the results of this thesis can be divided into two parts. The first part is a lace expansion analysis of a model called loopweighted walk. Loopweighted walk is a nonMarkovian model of random walks that are discouraged (or encouraged), depending on the value of a parameter, from completing loops. The model arises naturally as a random walk representation of correlations in a statistical mechanics model called the cycle gas. A challenging aspect of this model is that it is not repulsive, meaning the weight of the future of a walk may either increase or decrease if the past is forgotten. Loopweighted walk is the first finite range walk model with this property to be analyzed with lace expansion techniques.
The second part of this thesis is an essentially elementary derivation of a random walk representation for the partition function of the Ising model on any finite graph. Such representations have a long history for planar graphs. For nonplanar graphs the additional ingredient needed is a way to compute the intersection numbers of curves on surfaces. The representations for nonplanar graphs lead to random walk representations of spinspin correlation functions that were previously unknown.
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UBC

Tue 25 Nov 2014, 4:00pm
Discrete Math Seminar
ESB 4127

Some aspects of rational triangle decompositions.

ESB 4127
Tue 25 Nov 2014, 4:00pm5:00pm
Abstract
Given a simple graph $G$, a triangle decomposition of $G$ is a set of subgraphs isomorphic to $K_3$ whose edges partition the edge set of $G$. Further, a rational triangle decomposition of $G$ is a nonnegative rational weighting of the copies of $K_3$ in $G$ such that the total weight on any edge of $G$ equals one. In this thesis, we will explore sufficient conditions for rational triangle decomposability. A famous conjecture in the area due to NashWilliams states that any sufficiently large graph (satisfying some divisibility conditions) with minimum degree at least $3/4v$ is admits a triangle decomposition; the same conjecture stands for rational triangle decomposability (no divisibility conditions required). By perturbing and restricting the coverage matrix of a complete graph, we show that minimum degree of at least $22/23v$ is sufficient to guarantee that the given graph is rationally triangle decomposable. This density bound is a great improvement over the previously known results and is derived using estimates on the matrix norms and structures originating from association schemes.
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UAlberta

Wed 26 Nov 2014, 3:00pm
CRG Geometry and Physics Seminar
ESB 4127 (host: UAlberta)

TBA

ESB 4127 (host: UAlberta)
Wed 26 Nov 2014, 3:00pm4:00pm
Abstract
TBA
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Warwick University

Wed 26 Nov 2014, 3:10pm
Probability Seminar
ESB 2012

Phase Transitions in Continuum Delaunay Potts Models

ESB 2012
Wed 26 Nov 2014, 3:10pm4:10pm
Abstract
We discuss recent results on phase transitions of Delaunay Potts models in dimension two where the interaction depends on Delaunay edges respectively Delaunay triangles.
This work is an extension of the Lebowitz & Lieb softcore continuum Potts model to geometrically dependent interaction systems. The main tool is a FK (FortuinKasteleyn) random cluster representation adapted to the Delaunay structure and percolation in the FK model. If time permits we discuss the VoronoiIsing model where the interaction is function of the length of the common boundary and its connection to variants of the RSW (RussoSeymourWelsh) theorem in continuum percolation.
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MIT

Wed 26 Nov 2014, 3:15pm
Topology and related seminars
ESB 4133

The six operations of Grothendieck in equivariant motivic homotopy theory

ESB 4133
Wed 26 Nov 2014, 3:15pm4:15pm
Abstract
The formalism of six operations encodes the functorial behavior of (co)homology theories. It was first introduced by Grothendieck for the ladic cohomology of schemes, and was later developed in a variety of other geometric contexts: Dmodules on schemes, spectra parametrized by topological spaces, motivic spectra parametrized by schemes, etc. Equivariant homotopy theory is also best understood as a formalism of six operations for topological stacks.
In this talk I will discuss the basics and the significance of this formalism, and I will then describe an extension of motivic homotopy theory to algebraic stacks.
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Witwatersrand University

Wed 26 Nov 2014, 3:30pm
Symmetries and Differential Equations Seminar
MATH 125

Symmetry structures of manifolds Part II

MATH 125
Wed 26 Nov 2014, 3:30pm4:30pm
Abstract
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Oxford University

Thu 27 Nov 2014, 3:30pm
Number Theory Seminar
room MATH 126

Autocorrelations of divisor functions in function fields

room MATH 126
Thu 27 Nov 2014, 3:30pm4:30pm
Abstract
In this seminar I will discuss a function field analogue of a classical problem in analytic number theory, concerning the autocorrelations of divisor functions, in the limit of a large finite field.
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University of Oregon

Fri 28 Nov 2014, 2:00pm
SPECIAL
Diff. Geom, Math. Phys., PDE Seminar
ESB 4133 (PIMS lounge)

Geometric flow on almost Hermitian manifolds

ESB 4133 (PIMS lounge)
Fri 28 Nov 2014, 2:00pm3:00pm
Abstract
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UBC

Fri 28 Nov 2014, 3:00pm
Department Colloquium
MATX 1100

Graduate Research Award lecture: Magnetized Target Fusion: Insights from Mathematical Modelling

MATX 1100
Fri 28 Nov 2014, 3:00pm4:00pm
Abstract
Magnetized target fusion reactors are a modern design to for hydrogen fusion energy on earth. The design entails confining a plasma with a magnetic field and crushing it in an imploding shell of molten metal. Such a design has many unresolved questions in terms of its feasibility as a power source and the most important elements in making it efficient. In this talk, we will look into two of the approaches undertaken to explore these questions. Firstly, through a coordinate transformation and implementing a novel fluxlimited, splitstep, finite volume scheme for nonlinear coupled hyperbolic partial differential equations, we do a parameter sensitivity analysis for the design performance. Secondly, by a careful series of asymptotic arguments, we establish a leading order asymptotic expression for the plasma compression. This expression is qualitatively consistent with the numerical work, but it also gives new insights into how the device operates. We will conclude with a look into the viability of magnetized target fusion and its future work.
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Note for Attendees
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