University of Georgia
Department of Mathematics

Seminar Schedule
November 1 – 5, 2004

All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.

MONDAY, November 1, 2004

Algebra
2:30-3:30p.m., Room 410
Speaker: Brian Boe, University of Georgia
Title of talk: Cohomology from Graphs II
Abstract: This talk will be a continuation of last week's Algebra seminar

Probability Theory
2:45-4:00pm, Room 302
Speaker: Jinzhi Tie, University of Georgia
Title of talk: European Options and Stochastic Volatility

Faculty and Graduate Social
3:00 p.m., Room 409
Coffee, Cookies, Tea

VIGRE Algebraic Geometry Group
3:30-4:30 p.m., Room 304

Topology
3:30-4:30pm, Room 326
Speaker: Gordana Matic
Title of talk: Ozsvath-Szabo invariants (cont)

Lie Theory
3:30p.m., Room 303
No meeting this week


TUESDAY, November 2, 2004

VIGRE Graduate Student Seminar
2:00p.m., Room 304
Speaker: Kyunglim Nam, University of Georgia
Title of talk: Box Spline Tight Frames for Edge Detection.
Abstract: A Wavelet is a function in $L_2$ whose dialations and translations form an orthonormal basis of $L_2$. In image processing, it is well known that edges of an image can be detected by using Wavelet Transformation. If the orthonormal condition in the defintion of a Wavelet is dropped, the corresponding function is called a Wavelet Frame. I will talk about construction of box spline tight wavelet frames, and apply this wavelet frames to several images for edge detection.

The edge detection using box spline tight wavelet frames will be compared with the edge detection using Haar wavelet, Daubechies' wavelet and Laplacian method. I will show the numerical evidence that the edge detection of smooth curve part of images by box spline tight frames works better than edge detection with the other methods mentioned above.

Dynamics on Berkovich Space
3:30-5:30p.m., Room 326
Speaker: Robert Rumely, University of Georgia
Title of talk: The structure of the Berkovich Fatou Set of a rational function.


WEDNESDAY, November 3, 2004

Algebraic Geometry
2:30-3:45 p.m., Room 410
Speaker: Roy Smith, University of Georgia
Title of talk: Riemann Roch, Brill Noether, and Riemann's singularity theorem
Abstract: The classical Riemann Roch problem is "Mittag Leffler" for algebraic curves C, to compute the dimension h^0(D) of the space of rational functions on C whose pole divisor is bounded by a given D. The index h^0(D)-h^1(D) admits a topological formula, but h^0(L) does not when deg(D) < 2genus(C)-1.

The approach of Riemann and Brill - Noether (1855-1873) was to describe the subvarieties W(r,d) = {O(D): deg(D) = d, and h^0(D) > r} of the Jacobian variety J^d. Mumford and Kempf (1960-1970) re-interpreted these varieties as "rank loci" of matrices. If d < g, and h^0(D) = r+1, there is a map from an open nbhd of O(D) in J^d, to the affine space of h^0(D) by h^1(D) matrices, such that W(0,d) is the pullback of those matrices with non trivial kernel, and W(r,d) is the pullback of the zero matrix.

Kempf thus naturally recovered classical results on the structure of W(r,d) and extended them. We will discuss his point of view, its implications, and a recent generalization for "Prym" varieties, carried out with Robert Varley.

The talk is G - rated, i.e. introductory and aimed at grad students.

VIGRE – Cardiac Physiology
2:30p.m., Room 323

VIGRE – Clifford Algebras
2:30p.m., Room 322

Faculty and Graduate Social
3:00 p.m., Room 409
Coffee, Cookies, Tea

Number Theory
3:45-5:15pm, Room 304
Speaker: Charles Pooh, University of Georgia
Title of talk: TBA

THURSDAY, November 4, 2004

VIGRE – Rational Points on curves
2:00p.m., Room 304
Speaker: Professor Gang Yu, University of South Carolina
Title of talk: Rank of quadratic twists of elliptic curves over Q

Faculty and Graduate Social
3:00 p.m., Room 409
Coffee, Cookies, Tea

Colloquium
3:30p.m., Room 304
Speaker: John McCuan, Georgia Tech/University of Georgia
Title of talk: Symmetric constant mean curvature surfaces in the three-sphere
Abstract: The constant mean curvature (CMC) surfaces in Euclidean three dimensional space represent locally the shapes of soap bubbles. The sphere is, of course, an example, but there are many others.

In 1841 C. Delaunay classified all rotationally symmetric CMC surfaces. He showed, in fact, that they are exactly the surfaces whose meridians
can be obtained as the path of a focal point of a conic section as it rolls along the axis of rotation.

I will describe these surfaces of Delaunay and some recent work which gives a similar classification for certain symmetric CMC surfaces in the
three-sphere.


FRIDAY, November 5, 2004

Student Arithmetic/Algebraic Geometry Seminar
12:20p.m., Room 326
Speaker: Sungkon Chang, University of Georgia
Title of talk: On the arithmetic of quadratic twists of an elliptic curve.
Abstract: I shall present results and proofs of my work on the rank of quadratic twists of an elliptic curve over a global field.

Geometry
2:30p.m., Room 323
Speaker: Jingzhi Tie, University of Georgia
Title of talk: Isoperimetric problem on the Heisenberg Group

VIGRE – Algebra
2:30p.m., Room 410
Speaker: Dave Benson, University of Georgia
Title of talk: Computing varieties of Specht modules and simple modules

Spline Analysis
2:30p.m., Room 303
Speaker: Taytana Sorokina, University of Georgia
Title of talk: Construction of 3D macro-elements (cont.)

Wavelet Analysis
3:30p.m., Room 303
Speaker: O. Cho, University of Georgia
Title of talk: Construction of Orthonormal Spline Wavelets