First meeting.

O-minimal structures are categories of sets and mapping having nice geometrical properties. To each o-minimal expansion of a real closed field, one can associate the set of germs at infinity of its unary functions, which form a Hardy field. Valuational properties of these Hardy fields give good information about the initial structure. After a lengthy introduction of all the previously named objets and motivated by a conjecture of L. van den Dries and a result of F.-V. and S. Kuhlmann, I will discuss whether an o-minimal expansions of the field of the reals is, in general, fully determined by its associated Hardy field. I will also relate this question to the Hilbert's 13th Problem.

I will review the notion in the title (which, as it turns out, is not a group), and show how to construct in certain cases an "exponential" in the complexification. The construction is motivated by quantum mechanics.

CS Department colloquium

It would be nice to have a mathematical understanding of basic biological concepts and to be able to prove that life must evolve in very general circumstances. At present we are far from being able to do this. But I'll discuss some partial steps in this direction plus what I regard as a possible future line of attack.

Given a fixed binary form $f(u,v)$ of degree $d$ over a field $k$, the associated Clifford algebra is the $k$-algebra $C_f=k\{u,v\}/I$, where $I$ is the two-sided ideal generated by elements of the form $(\alpha u+\beta v)^{d}-f(\alpha,\beta)$ with $\alpha$ and $\beta$ arbitrary elements in $k$. All representations of $C_f$ have dimensions that are multiples of $d$, and occur in families. In this article we construct fine moduli spaces $U=U_{f,r}$ for the $rd$-dimensional representations of $C_f$ for each $r \geq 2$. Our construction starts with the projective curve $C \subset \mathbb{P}^{2}_{k}$ defined by the equation $w^d=f(u,v)$, and produces $U_{f,r}$ as a quasiprojective variety in the moduli space $\mathcal{M}(r,d_r)$ of stable vector bundles over $C$ with rank $r$ and degree $d_r=r(d+g-1) $, where $g$ denotes the genus of $C$.