Department of Mathematics
The Florida State University

This Week in Mathematics

13 -- 17 April 1998

Monday: 13 April 1998

No Graduate Seminar, 2:30 p.m., 204B Love Building

Knot Theory Seminar, 3:35 p.m., 104 Love Building

Irma Cruz, Florida State University
Spiral Waves in Excitable Media

Special Colloquium Coffee, 3:00 p.m., 204 Love Building
Special Colloquium, 3:45 p.m., 102 Love Building

Evans Harrell II, Georgia Institute of Technology
Optimizing the Eigenvalues of Schrödinger Equations with Potential Energy Determined by Curvature
The Schrödinger equation with a potential depending on curvature arises naturally in the context of quantum wires and waveguides. Among the other, non-quantum, contexts in which it arises is that of the motion of interfaces in materials with two phases. In this work, which is joint in part with M. Loss of Georgia Tech, we consider the design problem of finding the geometries of curves and surfaces for which a given eigenvalue is maximized and for which it is minimized. In particular, we prove some new "isoperimetric" theorems, whereby the optimizer is spherical or circular.

Tuesday: 14 April 1998

Wednesday: 15 April 1998

(Real) Analysis Seminar, 2:30 p.m., 102 Love Building

Working through Carlos Kenig's lecture notes on oscillatory integrals and nonlinear pde.

Complex/Symbolic Coffee, 3:15 p.m., 105 Love Building
Complex/Symbolic, 3:35 p.m., 102 Love Building

Mika Seppälä, Florida State University
Teichmüller Spaces of Riemann Surfaces with Applications to Hurwitz Spaces

Thursday: 16 April 1998

Algebra Seminar, 2:00 p.m., 104 Love Building

Warren Nichols, Florida State University
Algorithms in Invariant Theory

Topology Tea Time, 3:00 p.m., 204 Love Building
Topology Seminar, 3:35 p.m., 104 Love Building

[to be announced]

Friday: 17 April 1998

Colloquium Coffee, 3:00 p.m., 204 Love Building
Colloquium, 3:30 p.m., 101 Love Building

Sylvia Wiegand, University of Nebraska
Prime Ideals and Decompositions of Modules
Let R be a commutative Noetherian ring. We consider the set Spec(R) of prime ideals of R as a partially ordered set, ordered by inclusion. (For Noetherian rings, the partial ordering determines the Zariski topology.) For example, if R=Z, the ring of integers, Spec(Z) has a unique minimal element 0 and a countably infinite set of height-one elements, one for each prime number. Similarly, Spec(R) looks the same for every countable principal ideal domain. If R has more than one minimal prime ideal, or if R has dimension greater than one, the description of Spec(R) is more interesting. For example, it is known that Spec(Z[X]) \cong Spec(k[X,Y]), for any finite field k, but Spec(Z[X]) and Spec(Q[X,Y]) are not isomorphic. The question: ``Which partially ordered sets arise as Spec(R) for some Noetherian ring R?" is completely open, even if only two-dimensional sets are considered.
There is a fascinating interplay between the prime ideal structure of a ring and the structure of its finitely generated modules. Concentrating on the case of rings of dimension one (with several minimal primes), we show how knowledge of Spec(R) gives information about direct-sum decompositions of finitely generated R-modules.

Scientific Computing Seminar, 4:30 p.m., 200 Love Building

Stewart Glegg, Florida Atlantic University
Specifying Inflow Turbulence for Aeroacoustic Calculations

Seminars and colloquia at "that other" university [a.k.a. the University of Florida]

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