University of Georgia
Department of Mathematics
Seminar Schedule
November 28 – December 2, 2005
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
MONDAY, November 28, 2005
Topology/Geometry
2:30pm, Room 303
Speaker: TBA
Title of talk: TBA
Algebra
2:30-3:30pm., Room 410
Speaker: Bill Graham, University of Georgia
Title of talk: TBA
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Cookies, Tea
TUESDAY, November 29, 2005
Analysis Seminar
1:30pm, Room 326
Speaker: Konstantin Oskolkov
Title of talk: "On oscillometry of Fourier sums and
Schroedinger particle".
Abstract: In the talk, quantitative estimates will be discussed,
of the oscillations of the
1) sequence of the partial sums of the trigonometric Fourier series;
2) the solution of the Cauchy initial value problem for the Schroedinger equation,
and also the linearized KdV.
Namely, how do the oscillatory properties of the initial data are reflected by the Fourier sums, and the "Schroedinger particle" ?
VIGRE-Graduate Student Seminar
2:00p.m., Room 303
Speaker: Rafal Zbikowski
Title of talk: TBA
WEDNESDAY, November 30, 2005
Algebraic Geometry
2:30-3:45pm, Room 410
Speaker: Roy Smith, University of Georgia
Title of talk: Riemann singularity theorems, and the classification
of singular points on low dimensional theta divisors.
Abstract: By focusing on the theta divisor, the moduli space
of principally polarized abelian varieties of fixed dimension g is analogous
to that of hypersurfaces of a fixed degree in projective space. Similar questions
have interest, such as describing the subvarieties N(r+1, rho) of theta divisors
whose locus sing(r+1, theta) of (r+1) - tuple points, has dimension at least
rho, and counting those singular points when rho = 0.
A few general statements exist, e.g. N(r+1, rho) is empty unless r+rho < g. For Jacobians, modern generalizations of Riemann's singularity theorem and Clifford's theorem, imply that "N(r+1,rho) intersect Jacobians" is non empty only if 2r+rho < g.
I will review briefly the classical results known to me, and then describe some recent generalizations by Casalaina - Martin, and with Robert Varley that allow some calculations of "N(r+1,rho) intersect Prym varieties".
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Cookies, Tea
Number Theory Seminar/Arithmetic Geometry
3:30pm, Room 304
Speaker: D. Lorenzini, University of Georgia
Title of talk: Early history of elliptic curves at UGA;
Papers by G. Huff and by his student W. Peeble.
Abstract: I knew that in 1974, David Penney and Carl Pomerance
were the first to exhibit an elliptic curve of rank 6 over Q, and in 1975 they
obtained examples with rank 7 over Q. I had not realized that even earlier work
was done on the subject of elliptic curves by UGA faculty. In 1948, Gerald Huff
(1909- 2001) studied the rank of curves having torsion Z/2 x Z/4 or Z/2 x Z/8.
To do this, he generalized to number fields a very pretty result proven over
the rationals in a paper of Giovanni Sansone
(1888--1979) in 1941: a K-point P=(x,y) on the curve y2=(x-e_1)(x-e_2)(x-e_3)
is of the form 2Q with Q a K-point if and only if (x-e_1), (x-e_2), and (x-e_3)
are squares in K.
VIGRE-Algebra Group
3:45p.m., Room 302
THURSDAY, December 1, 2005
VIGRE – Feynman Diagrams
2:00pm, Room 326
VIGRE – Cardiac Physiology
2:00p.m., Room 640
VIGRE-Algebraic Geometry Group
3:30pm, Room 323