## Past Events at the University of British Columbia

### Past Events

- 14-Feb-07

The lace expansion and the enumeration of self-avoiding walks

The lace expansion is an elegant combinatorial construction that provides a recursion relation for the number of self-avoiding walks. We first give an introduction to the lace expansion, and then explain how it has been used recently (in joint wor more››

Scientific Event

- 14-Feb-07

Homological stability theorems have been proved for many families of groups like symmetric groups, linear groups, mapping class groups of surfaces and of 3-manifolds. I will review some examples and explain how such theorems are proved. As a more more››

Scientific Event

- 13-Feb-07

Leray-type regularizations of the Burgers and the isentropic Euler equations

We start from the Burgers equation vt + vvx = 0 and investigate a smoothing mechanism that replaces the convective velocity v in the nonlinear term by a smoother velocity field u. This type of regularization was first proposed in 1934 by Leray, wh more››

Scientific Event

- 12-Feb-07

Essential dimension and algebraic stacks

The talk will be preceded by an organizational meeting. I will discuss recent work with Z. Reichstein and A. Vistoli on the subject of essential dimension. more››

Scientific Event

- 12-Feb-07

In several shallow-dipping subduction zones, including Cascadia, the seafloor undergoes episodes of more rapid than usual creep-slippage under the overlying margin, but at rates vastly slower than usual earthquake slip. In some locations, also inc more››

Scientific Event

- 8-Feb-07

Let M be a 3-manifold with boundary consisting of one torus. I will show how Culler and Shalen defined a norm on the (real) Dehn-surgery space R2=H_1(partial M; R) associated to the canonical component of the character variety of M. I will then sh more››

Scientific Event

- 8-Feb-07

Neil Immerman is one of the key developers of 'descriptive complexity', which he is currently applying to research in model checking, database theory, and computational complexity theory. Immerman is the winner, jointly with Róbert Szelepcsényi, more››

Scientific Event

- 7-Feb-07

The term structure of interest rates

The interest rate r(t,t+x) between time t and time t+x is a smooth function of x, say ho_t(x). We consider ho_t as a stochastic process on (0,infty) into a suitable Hilbert space of curves, and we seek to define it as the solution of more››

Scientific Event

- 7-Feb-07

Proof of Yuzvinsky's conjecture in the case of square matrices

Yuzvinsky's conjecture, posed in 1981, is concerned with a certain matrix coloring problem which arose from the classical studies of sums of squares. In this talk I will present a proof of the conjecture in the case of square matrices. The ideas o more››

Scientific Event

- 6-Feb-07

- 1-Feb-07

Strong normality and modular normality

The notion of normality was intended to capture random behaviour in the digits of numbers, but some clearly patterned numbers pass the normality test; we propose a stronger test of normality that is passed by almost all numbers but failed by Champ more››

Scientific Event

- 1-Feb-07

Quartic K3 surfaces without nontrivial automorphisms

We will deal with a gap in a result of Bjorn Poonen. He found explicit examples of hypersurfaces of degree d³3 and dimension n³1 over any field, such that the group of automorphisms over the algebraic closure is trivial, except for the pairs (n, more››

Scientific Event

- 1-Feb-07

MITACS Math Biology Seminar 2007

As the systems approaches are actively adopted in biology, studies for revealing the link between physical dynamics and corresponding molecular mechanism will be crucial to better understanding of the inherent complexity and dynamics of biological more››

Scientific Event

- 31-Jan-07

Nilpotent commutators and reducibility of semigroups

Let f be a noncommutative polynomial in two variables. Let mathcal{S} be a multiplicative semigroup of linear operators on a finite-dimensional vector space and T a fixed linear operator such that f(T,S)=0 for all S in mathcal{S}. What can w more››

Scientific Event

- 29-Jan-07

Computation of plurigenera of a canonical threefold

For a canonical threefold, there are few known results about plurigenera. We know that a sufficient multiple of canonical divisor generates a nontrivial linear system and that there is a universal multiple. In this talk, we are going to introduce more››

Scientific Event

- 25-Jan-07

Robust Stochastic Discount Factors

When market is incomplete a new non-redundant derivative security cannot be priced by no arbitrage arguments alone. Moreover there will be a multiplicity of stochastic discount factors and each of them may give a different price for the new deriva more››

Scientific Event

- 25-Jan-07

UBC Mathematics Department Colloquium Hosted by PIMS-UBC 2007

A discrete group has 'Property (T)' if every isometric (affine) action of the group on Hilbert space has a global fixed point. This is a spectral-gap property and was originally defined by Kazhdan to study lattices in Lie groups. Recently Gromov f more››

Scientific Event

- 24-Jan-07

Long-term evolution of polygenic traits under frequency-dependent intraspecific competition

We analytically investigate the long-term evolution of a continuously varying quantitative character in a diploid population that is determined additively by a finite number of loci. The trait is under a mixture of frequency-dependent disruptive s more››

Scientific Event

- 23-Jan-07

New singular solutions of the Nonlinear Schrodinger equation (NLS)c

The study of singular solutions of the NLS goes back to the 1960s, with applications in nonlinear optics and, more recently, in BEC. Until recently, the only known singular solutions had a self-similar 'peak-type' profile that approaches a delta f more››

Scientific Event

- 23-Jan-07

Mirkovic-Vilonen cycles on the affine Grassmannian

The geometric Satake correspondence relates representation theory to the geometry of the affine Grassmannian. In particular, certain subvarieties of the affine Grassmanian, called Mirkovic-Vilonen cycles, give bases for representations of complex more››

Scientific Event