Department of Mathematics

The Florida State University

This Week in Mathematics

8 - 12 February 1999

Monday: 8 February 1999

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

Brian Felkel, Florida State University

Van der Corput's Lemma
To quote from Stein's "Harmonic Analysis", "Oscillatory integrals in one form or another have been an essential part of harmonic analysis from the very beginnings of that subject." Oscillatory integrals have a number of applications and are quite interesting. On a more personal level, my dissertation topic involves investigating a specific type of oscillatory integral and applying a theorem known as Van der Corputs Lemma. It is this lemma that I want to share with the group. It says the following:
Suppose f is real-valued and smooth in (a,b) and the kth derivative of f is bounded below (in absolute value) by 1 for all x in (a,b). Then |int(exp{I*r*f(x)}dx,x=a..b)|< = C*r^{-1/k} holds when:
(i) k= 2, or
(ii) k=1 and f' is monotonic.
The bound C is independent of f and r.

Tuesday: 9 February 1999

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

Chia Stockwell, Florida State University

Intersection Multiplicities

No Applied Topology Seminar, 3:35 p.m., 104 Love Building

Wednesday: 10 February 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

Differential Galois Theory

Thursday: 11 February 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

Penelope Kirby, Florida State University

Splitting Manifold Approximate Fibrations

Friday: 12 February 1999

Colloquium Coffee, 3:00 p.m., 499 SCL
Colloquium, 3:30 p.m., 499 SCL

Richard Petti, CEO, Macsyma

The Role of Symbolic Computation in Mathematics

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

Leon van Dommelen, Mechanical Engineering, Florida State University

Toward a Fractal Representation of Turbulence

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

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