## Scientific Lectures

- 29-Mar-07

Portfolio optimization in a hidden Markov model for stock returns with jumps

In a market consisting of a money market and one stock with price process dS(t)=S(t)[a(t) dt + b dW(t) + g dM(t)] where W is a Wiener process and M is a compensated Poisson process, an agent invests his initial wealth in a portfolio to maxim more››

University of British Columbia

- 29-Mar-07

Variations on a theme of Stark

Zeta functions and L-functions contain arithmetic information when evaluated at special values, such as s = 0. In the 1970s, Stark conjectured that the derivatives of L-functions at s = 0 can be evaluated by certain algebraic units. Under certain cir more››

University of British Columbia

- 28-Mar-07

Matchings of exponential tail on coin flips in Z^d

We construct a translation-invariant matching between vertices of different labels of Bernoulli(1/2) percolation on Z^d, in such a way that the probability that a vertex is at distance > r from its pair decays as an exponential function of the more››

University of British Columbia

- 27-Mar-07

Reconstruction and subgaussian operator

Candes, Romberg and Tao recently studied problems of approximate and exact reconstruction of sparse signals from incomplete random measurements and related them to the eigenvalue behavior of submatrices of matrices of random measurements. In parti more››

University of British Columbia

- 26-Mar-07

The interface between Bayesian and frequentist statistics

Statistical theory is often categorized as either "Bayesian" or "frequentist", and statisticians often self-identify in the same categories. During the development of theoretical statistics as a separate field in the twentieth more››

University of British Columbia

- 23-Mar-07

Minimal determinants for the centres and topological centres of some

The algebraic centre of the uniformly continuous compactification GUC of an abelian locally compact group G is G itself. There is a stronger result: if u commutes with just two (carefully chosen) elements of more››

University of Alberta

- 22-Mar-07

William Thurston conjectured over twenty years ago that every compact hyperbolic 3-manifold whose boundary is a possibly empty union of tori is virtually fibred, that is, has a finite cover which fibres over the circle. If true, it provides a sign more››

University of British Columbia

- 22-Mar-07

The Role of Mathematics in Physical Ecology

The natural link between mathematics and ecology is evident in the field of physical ecology, which uses physical models to explore some fundamental issues. These include how aquatic organisms use the constraints imposed by physical environment to more››

University of British Columbia

- 22-Mar-07

Local Interaction Games with Random Matching

We state conditions for existence and uniqueness of equilibria in evolutionary models with an infinity of locally and globally interacting agents. Agents face repeated discrete choice problems. Their utility depends on the actions of some designat more››

University of British Columbia

- 21-Mar-07

Differentiability of Quadratic BSDEs

We consider Backward Stochastic Differential Equations (BSDE) with generators that grow quadratically in the control variable. In a more abstract setting, we first allow both the terminal condition and the generator to depend on a vector parameter more››

University of British Columbia

- 21-Mar-07

On families of virtually fibred Montesinos link exteriors

William Thurston conjectured over twenty years ago that every compact hyperbolic 3-manifold whose boundary is a possibly empty union of tori is virtually fibred, that is, has a finite cover which fibres over the circle. If true, it provides a sign more››

University of British Columbia

- 20-Mar-07

Amenable groups that are left orderable

Let G be an abstract group. It is known that if every finitely generated subgroup of G has an infinite cyclic quotient, then G is left orderable. Using an idea of E.Ghys, we prove that the converse is true for all amenable groups. (This generalize more››

University of British Columbia

- 19-Mar-07

Mathematical Models of Protein Receptor Trafficking and Its Role in Synaptic Plasticity

AMPA receptors mediate the majority of fast excitatory synaptic transmission in the central nervous system, and recent experimental evidence suggests that AMPA receptor trafficking regulates synaptic strength, a phenomenon implicated in learning a more››

University of British Columbia

- 19-Mar-07

Some arithmetic groups that are not left orderable

It is known that finite-index subgroups of the arithmetic group SL(3,Z) are not left orderable. (In other words, they have no interesting actions on the real line.) This naturally led to the conjecture that most other arithmetic groups (of higher more››

University of British Columbia

- 19-Mar-07

Issues with Bayesian Analysis of Inverse Problems

A computer/math model of a process often contains numerous unknown parameters. To utilize the model, these parameters either must be determined from expert knowledge or estimated from data. In the mathematical community, the most common methods of more››

University of British Columbia

- 16-Mar-07

Black Hole Physics and Mathematics Through Scientific Computing

I will give an overview of ongoing calculations in numerical relativity at UBC and elsewhere. The talk will include a gentle introduction to Einstein's theory of gravity (general relativity) and the role of black holes in the theory. The nature of more››

University of British Columbia

- 15-Mar-07

Intermittent behaviour in hydrodynamical systems with spherical symmetry: theory and an experiment

Auxiliary variable methods for the incompressible Navier-Stokes equations approximate the evolution of the velocity through a dynamic variable which does not satisfy a divergence constraint but from which the correct incompressible velocity can be more››

University of British Columbia

- 15-Mar-07

Pricing and Hedging in Illiquid Financial Markets

Ever since the seminal work of Black, Scholes, and Merton, typical models studied in Mathematical Finance specify price dynamics exogenously via some more or less explicit semimartingale dynamics. This is in contrast to the basic economic paradigm more››

University of British Columbia

- 15-Mar-07

Characters and Primitive Ideal Spaces of Nilpotent Discrete Groups

If G is a discrete abelian group, then the space of maximal ideals of the L1- and the C*-algebra of G is homeomorphic to the compact dual group of G. This generalizes to some extent to discrete nilpotent groups G, where the the dual gro more››

University of British Columbia

- 15-Mar-07