Princeton University
Department of Mathmenatics
Schedule of Seminars
Current info:
http://www.math.princeton.edu/~web/seminar.htmlCurrent 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