Department of Mathematics

The Florida State University

This Week in Mathematics

15 - 19 March

Monday: 15 March 1999

Graduate Student Seminar, 1:30 p.m., 204B Love Building

Nancy Domm, Florida State University

Experiments in Topology

FSU Math Society Meeting, 5:00 p.m., 204 Love Building

Edward Dunne, American Mathematical Society

Pianos and Continued Fractions

You can't tune a piano perfectly. In some way, the instrument must always be out of tune with itself. The origin of the problem, naturally, is in physics. Once the problem is translated into mathematics, only a small amount of effort reveals that the difficulty is unavoidable. However, mathematics does offer some compromises, many of which music already knew about.
     Topics covered will include some elementary music theory, an introduction to continued fractions and some variations on the twelve-tone theme. If time and equipment permit, examples from old and new music will be presented. The only prerequisites are familiarity with the arithmetic of fractions and an interest in music.

Tuesday: 16 March 1999

Algebraic Geometry Seminar, 2:00 p.m., 102 Love Building

Bill Adams, Florida State University

Projective Curves

Applied Topology Seminar, 3:35 p.m., 104 Love Building

Irma Cruz-Rodriguez, Florida State University

The Geometry of Spiral Waves in Excitable Media

Wednesday: 17 March 1999

(Real) Analysis Seminar, 2:30 p.m., 201 Love Building

Reading through “Oscillatory Integrals with Polynomial Phases” by Phong and Stein

Complex/Symbolic Seminar, 3:35 p.m., 102 Love Building

Mark van Hoeij, Florida State University

Liouvillian Solutions of Linear Differential Equations

Thursday: 18 March 1999

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

Eriko Hironaka, Florida State University

Lie Algebras and Representation Theory

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

Topology Seminar, 3:35 p.m., 104 Love Building

Eric Klassen, Florida State University

The Cohomology of Moduli Space

Friday: 19 March 1999

No Colloquium Coffee, 3:00 p.m., 204 Love Building
No Colloquium, 3:30 p.m., 101 Love Building

Join Financial Mathematics Festival

No Scientific Computing Seminar, 4:30 p.m., 200 Love Building

Join Financial Mathematics Festival

Financial Mathematics Festival, 3:00 p.m., SCRI, 499 Dirac Science Building

Edward Qian, PhD FSU '93, Vice-President, Putnam Investments

Schwarz Inequality and Sharpe Ratio

Many investment products nowadays are actively managed against broad market indices. It is not an easy task to beat the market indices. The finance sections of newspapers are full of stories about a high percentage of US equity mutual funds under-performing S&P 500 index. TAA (Tactical Asset Allocation) is one quantitative technique designed for active fund managers to beat the market. The basic premise is to forecast returns for various segments of the market and then to combine the segments in ways that are different from the index to obtain a higher return.
     In this talk, I will discuss various aspects of TAA in mathematical terms, from performance measure (Sharpe ratio), to portfolio construction (mean-variance optimization). Many results are analytically tractable in terms of multivariate statistics. Curiously, Schwarz inequality appears in our analysis as we discuss a portfolio strategy that optimizes TAA's Sharpe ratio.

Financial Mathematics Festival, 4:30 p.m., SCRI, 499 Dirac Science Building

Jay Webb, PhD FSU '93, Director, Energy Trading Systems, Enron Capital & Trade Resources

Value at Risk - An Overview

Value at Risk has become an increasingly important metric for risk analysis and control within investment banks and other financial institutions. There is, however, no clearly defined recipe for its implementation. In particular, the appropriate implementation will depend on the size of the institution's portfolio and the complexity of the financial instruments contained within it. In all cases, the problem presents many interesting mathematical, statistical and computational challenges.
     This presentation will introduce Value at Risk, discuss why it is a valuable tool in portfolio analysis and address some of the complex business and technical issues it raises.

Saturday: 20 March 1999

Financial Mathematics Festival, 10:30 a.m., SCRI, 499 Dirac Science Building

Careers Discussion

Panel: “Careers in Financial Mathematics”

Professors James Ang (Finance) and Paul Beaumont (Economics) will join Jay Webb and Edward Qian for a discussion about opportunities and preparation needed for those careers. Undergraduates are invited.

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

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