## Scientific Lectures

- 26-Sep-07

Bounds on the Crosscap Numbers of Torus Knots

In joint work with Sizemore, we build on Teragaito's calculation of the crosscap number $c(K)$ of a torus knot $K$ to give bounds in terms of the genus $g(K)$ and crossing number $n(K)$: $c(K) leq lfloor (g(K) + 9)/6 floor$ and $c(K) leq l more››

University of British Columbia

- 25-Sep-07

- 24-Sep-07

Turbulent heat transport: upper bounds by a priori estimates

We are interested in the transport of heat through a layer of viscous fluid which is heated from below and cooled from above. Two mechanisms are at work: Heat is transported by simple diffusion and by advection through the flow. The transport by a more››

University of British Columbia

- 24-Sep-07

Fast Iterative Solution of Models of Incompressible Flow

We discuss new efficient algorithms for computing the numerical solution of the incompressible Navier-Stokes equations. We show that preconditioning algorithms that take advantage of the structure of the linearized equations can be combined with K more››

University of British Columbia

- 21-Sep-07

Design of a high quality optical resonator more››

Simon Fraser University

- 21-Sep-07

Design of a high quality optical resonator

We consider resonance phenomena for the scalar wave in an inhomogeneous medium. Resonance can be described as a solution to the wave equation that is spatially localized while its time dependence is (mostly) harmonic except for decay due to radiat more››

Simon Fraser University

- 20-Sep-07

Gradient Flows and Energy Landscapes II

Micromagnetics deals with the spatial pattern formed by the magnetization of a ferromagnet. From the point view of mathematics, micromagnetics is an ideal testbed for a pattern-forming system in materials science: There are abundant experiments on more››

Simon Fraser University

- 19-Sep-07

Boundary Slope Diameter and Crossing Number of 2-Bridge Knots

In joint work with Maybrun and Robinson, we prove that for 2-bridge knots, the diameter of the set of boundary slopes is twice the crossing number. We also show that 2-bridge knots with four or fewer boundary slopes have a boundary slope of genus two more››

University of British Columbia

- 19-Sep-07

Linear Stochastic Differential-Algebraic Equations

A Differential-Algeraic Equation is, essentially, an Ordinary Differential Equation F(x,dot x)=0 that cannot be solved for the derivative dot x . In a recent joint paper with A. Alabert of UAB, Barcelona, we studied the linear st more››

University of British Columbia

- 18-Sep-07

Gradient Flows and Energy Landscapes I

Micromagnetics deals with the spatial pattern formed by the magnetization of a ferromagnet. From the point view of mathematics, micromagnetics is an ideal testbed for a pattern-forming system in materials science: There are abundant experiments on more››

Simon Fraser University

- 18-Sep-07

Exact Bounds for Forbidden Configurations

We explore some exact bounds for Forbidden Configurations, which have a design theory flavour. Let q be given. Consider an m-rowed (0,1)-matrix A, which has no repeated columns. Assume there is no qx2 submatrix of A which is a r more››

University of British Columbia

- 17-Sep-07

Donaldson-Thomas and Gromov-Witten theory of orbifolds and their resolutions

A general principle in physics asserts that string theory on a Calabi-Yau orbifold should be equivalent to string theory on any Calabi-Yau resolution of the orbifold. A mathematical realization of this principle is the idea that Donaldson-Th more››

University of British Columbia

- 14-Sep-07

Early History of Singular Perturbations (1904-1940)

This equationless talk will describe how singular perturbations began in the ten-minute talk of Ludwig Prandtl at the 3rd International Congress of Mathematicians and how it developed slowly, culminating in the efflux out of Goettingen after 1933 more››

University of British Columbia

- 13-Sep-07

Cubic points on cubic curves and the Brauer-Manin obstruction on K3 surfaces

It is well-known that not all varieties over Q satisfy the Hasse principle. The famous Selmer curve given by 3x3 + 4y3 + 5z3 = 0 in P2, for instance, indeed has points over every completion of Q, but no points over Q itself. Though it is trivial to f more››

University of British Columbia

- 13-Sep-07

Deligne's functorial Riemann-Roch formula

We shall formulate a refinement, due to Deligne, of the Riemann-Roch theorem for fibrations of curves. This theorem provides canonical isomorphisms between certain determinant bundles. We shall show how this theorem leads to a new co more››

University of British Columbia

- 12-Sep-07

Spaces of Homomorphisms and Group Cohomology

In this talk I will discuss the construction of a family of simplicial spaces built of spaces of homomorphisms. This family yields a filtration of the classifying space of a group and it is parametrized by group theoretical data. more››

University of British Columbia

- 12-Sep-07

A balls and boxes Markov chain

Consider N boxes, each with R balls in. Each step, pick two boxes uniformly at random. If the first box is not empty, move a ball from the first box to the second. The empirical distribution tends to the geometric law with mean R. We look at the t more››

University of British Columbia

- 11-Sep-07

Pattern formation in micromagnetics

Micromagnetics deals with the spatial pattern formed by the magnetization of a ferromagnet. From the point of view of mathematics, micromagnetics is an ideal testbed for a pattern-forming system in materials science: There are abundant experiments more››

Simon Fraser University

- 11-Sep-07

On Some Inverse Problems, Regularization, Level Sets, Conjugate Gradients and Sparse Solutions

In this informal talk I will attempt to draw some connections among the various items appearing in the title. Emphasis will be placed on the role of regularization and on efficient solution techniques for tough reconstruction problems. more››

University of British Columbia

- 7-Sep-07

The fixed formula and Nori's approach to the Riemann-Roch theorem

We shall explain the content of the Lefschetz fixed point formula in the coherent setting and we shall explain its connection, established by M. Nori, with the Riemann-Roch theorem. Detailed computations in the case of curves will be given. more››

University of British Columbia