## Past Events at the University of British Columbia

### Past Events

- 27-Sep-07

lambda(lambda(n)): A case study in analytic number theory

A 2005 result of Carl Pomerance and myself identifies the normal order (that is, the asymptotic size for 100% of integers) of the twice-iterated Carmichael lambda-function ?(?(n)), a function that arises when considering an exponential pseudorandom n more››

Scientific Event

- 27-Sep-07

Powers in progression, Chebotarev, and Hilbert class polynomials

I will sketch some rather odd connections between ternary Diophantine equations, the Chebotarev Density Theorem and heights of Hilbert class polynom more››

Scientific Event

- 27-Sep-07

Modeling the Spread of West Nile Virus

West Nile virus was detected in New York State in 1999, and has spread rapidly across the continent causing bird, horse and human mortality. The aim of this lecture is to model this spread. Biological assumptions are summarized and lead to the dev more››

Scientific Event

- 26-Sep-07

- 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››

Scientific Event

- 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››

Scientific Event

- 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››

Scientific Event

- 20-Sep-07

Stable segregation of PAR proteins in the early C elegans embryo

PAR proteins, collectively termed the anterior and posterior PAR proteins, establish distinct intracellular spatial domains in the one cell C elegans embryo, polarizing the cell. This polarization is persistent, lasting approximately 10-20 minutes more››

Scientific Event

- 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››

Scientific Event

- 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››

Scientific Event

- 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››

Scientific Event

- 18-Sep-07

We present a mathematical theory for a biochemical switch system, which can be either the phosphorylation-dephosphorylation cycle (PdPC) reactions catalyzed by a kinase and a phosphatase, or GTPase cycles catalyzed by a guanine exchange factor (GE more››

Scientific Event

- 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››

Scientific Event

- 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››

Scientific Event

- 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››

Scientific Event

- 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››

Scientific Event

- 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››

Scientific Event

- 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››

Scientific Event

- 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››

Scientific Event