Princeton University

Department of Mathmenatics

Schedule of Seminars

Current info:** **http://www.math.princeton.edu/~web/seminar.html

Current as of 4-26-2000

Week of April 24 - 28, 2000

Colloquium Wednesday 4:30 Fine 314

Topic: On the Quantum Mechanics of Individual Systems April 26

Presenter: **J. Ax**, Princeton University

Abstract: Taking standard quantum mechanics (SQM) as a statistical theory, we extend the standard Hilbert space formulation to a mathematical model of the individuals which comprise the statistical ensembles of SQM. The model of two interacting systems is a singular toroidal bundle over the unit sphere in the Hilbert space of the composite system, together with a natural connection which permits the Schrodinger evolution in the sphere to be lifted to the bundle.The main mathematical innovation required is the construction of convex periodic tilings of Euclidian spaces (which is new even in 3 dimensions). These tilings descend to partitions of the toroidal fibers. The states of the subsystems are determined by which tile contains the lifted evolution. The toroidal tilings are the unique functorial convex partitions consistent with SQM. This is joint work with Simon Kochen.

Ergodic Theory & Mathematical Physics Thursday 2:30 Fine 110

Topic: Gromov's Mean Dimension April 27

Presenter: **Elon Lindenstrauss**, Institute for Advanced Studies

Abstract: Recently, Gromov has introduced a new invariant for dynamical systems called mean dimension. This invariant, originally introduced to study algebraic varieties and spaces of meromorphic functions, has found applications in topological dynamics (including a one line answer to a question that has been open for 25 years), and is probably also relevant to mathematical physics.

Topic: Dynamic Percolation

Presenter: **A. Skorokhod**

Date: Thursday, April 27, 2000, Time: 3:30 - 4 p.m., Location: Fine 110

Topology Seminar Thursday 4:30 Fine 314

Topic: "New" geometry and topology of orbifolds April 27

Presenter: **Y. B. Ruan**, University of Wisconsin at Madison

Abstract: Orbifold appears naturally in many branches of mathematics and has been studied by mathematicians since 70’s. Traditionally, orbifolds were studied as an extension of the theory of smooth manifolds. The central theme is that if we are willing to work over the field of rational coefficients the theory of smooth manifolds can be extended to orbifold. Hence, "old" geometry and topology can be considered as part of theory of smooth manifolds. Very recently, the situation started to change where a "new" theory of geometry and topology is emerging. The motivation of the new theory is from orbifold string theory. Therefore, the "new" Geometry and topology can be thought as a stringy geometry and topology of orbifolds. The mathematical motivation is follows: if we have a complex orbifold, there are two ways to desingulize the orbifold by either a resolution or a smoothing. We would like to construct a theory on orbifold to capture the information of manifolds obtained by desingulization. The core of the new theory is a new cohomology of orbifold (orbifold cohomology) introduced by Chen-Ruan. In my talk, I will try to touch many aspects of the new theory. It includes orbifold cohomology ring, discrete torsion and twisted orbifold cohomology ring, orbifold K-theory, orbifold stable map, orbifold quantum cohomology, relation to log-quantum cohomology and orbifold mirror symmetry.

Princeton Discrete Math Seminar Friday 2:30 Fine 322

Speaker: **John Conway**, Princeton University April 28

Abstract: I'll talk about two little theories, both started by A. Tarski. First, with A. Lindenbaum he proved without the axiom of choice that (for instance) $3m=3n$ implies that $m=n$, for cardinal numbers $m$ and $n$. Unfortunately the original proof of this was lost, but Peter Doyle and I believe we have recovered it. Second, Tarski proved that axioms $[2]$ and $[4]$ are equivalent, where $[n]$ is the axiom that guarantees the existence of a choice function for any collection of $n$-element sets. This led to some very interesting investigations of other relations between such finite choice axioms. I'll show how these relate to elementary group theory.

Geometry Seminar Friday 3:00 Fine 314

Topic: Complex Geometry of Tangent Bundles April 28

Presenter: **Daniel Burns**, University of Michigan

Analysis seminar Monday 4:00 Fine 314

Topic: On discrete Schroedinger operators with potentials defined May 1

by the skew-shift (joint work with J. Bourgain and M. Goldshtein

Presenter: **Wilhelm Schlag**, Princeton University

Algebraic Geometry Seminar Tuesday 4:15 Fine 322

Topic: TBA May 2

Presenter: **K. Conrad**, Ohio State University

Geometry Seminar Friday 3:00 Fine 314

Topic: Optimizing shapes and eigenvalues May 5

Presenter: **Sagun Chanillo**, Rutgers University

Geometry Seminar Friday 4:00 Fine 314

Topic: The Chern-Levine-Nirenberg instrinsic norm and May 5

a homogeneous complex Monge-Ampere equation

Presenter: **Guan Peifei**, McMaster University

Analysis seminar Monday 4:00 Fine 314

Topic: TBA May 8

Presenter: **Gabor Francsics**, Columbia University

Mathematical Physics Seminar Wednesday 4:30 Jadwin A06

Topic: Towards a microscopic theory of classical liquids May 10

Presenter: **Philippe Choquard**, Ecole Polytechnique, Lausanne