A few of the contributions of Poincaré to algebraic geometry are described, with emphasis on his late work on normal functions. A very brief description of some recent works is also given. Although the subject of algebraic geometry was not one of Poincaré's major preoccupations, his work in the field showed characteristic insight and brilliance and certainly has had a lasting effect. I shall br...

In this announcement we consider an eigenvalue problem which arises in the study of rectangular membranes. The mathematical model is an elliptic equation, in potential form, with Dirichlet boundary conditions. We have shown that the potential is uniquely determined, up to an additive constant, by a subset of the nodal lines of the eigenfunctions. A formula is given which, when the additive cons...

We associate to any germ of an analytic variety a Lie algebra of tangent vector fields, the tangent algebra. Conversely, to any Lie algebra of vector fields an analytic germ can be associated, the integral variety. The paper investigates properties of this correspondence: The set of all tangent algebras is characterized in purely Lie algebra theoretic terms. And it is shown that the tangent alg...

Aiming to unify known results about clustering mixtures of distributions under separation conditions, Kumar and Kannan [KK10] introduced a deterministic condition for clustering datasets. They showed that this single deterministic condition encompasses many previously studied clustering assumptions. More specifically, their proximity condition requires that in the target k-clustering, the proje...

TWO germs of 2-dimensional isolated quasi-homogeneous hypersurface singularities have the same topological type if and only if they have the same characteristic polynomial and the same fundamental group for their links. In particular, multiplicity is an invariant of topological type, an affirmative answer to Zariski's question in this case. Let (V, 0) and (W, 0) be germs of isolated hypersurfac...

The Ruelle zeta-function of the geodesic flow on the sphere bundle S(X) of an even-dimensional compact locally symmetric space X of rank 1 is a meromorphic function in the complex plane that satisfies a functional equation relating its values in s and -s . The multiplicity of its singularity in the central critical point 5 = 0 only depends on the hyperbolic structure of the flow and can be calc...

There exist two new embedded minimal surfaces, asymptotic to the helicoid. One is periodic, with quotient (by orientation-preserving translations) of genus one. The other is nonperiodic of genus one. We have constructed two minimal surfaces of theoretical interest. The first is a complete, embedded, singly periodic minimal surface (SPEMS) that is asymptotic to the helicoid, has infinite genus, ...

In recent years, imitation has played a central role in conceptions of children s memory, representational, and social cognitive abilities; in nonhuman primate cognitive competencies; and the evolution of human culture. In this paper, we combine data from three studies that assessed deferred imitation in three juvenile, enculturated (human-reared) chimpanzees (Pan troglodytes), administered ove...

If a function ip(x) is mostly concentrated in a box Q, while its Fourier transform $>(£) is concentrated mostly in Q', then we say ijj is microlocalized in Q X Q' in (x, £)-space. The uncertainty principle says that Q X Q' must have volume at least 1. We will explain what it means for ip to be microlocalized to more complicated regions S of volume ~ 1 in (x, £)space. To a differential operator ...

The K-theory of the title is described in terms of the Ktheory of finite subgroups, as generalized sheaf homology of a quotient space. A corollary is that if G is torsion-free, then the Whitehead groups Wh t(ZG) vanish for all i. 1. The main result. Suppose that G is a poly-(finite or cyclic) group. Then there is a virtually connected and solvable Lie group L that contains G as a discrete cocom...