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