University of Georgia
Department of Mathematics
Seminar Schedule
November 7 – November 11, 2005
All Seminars are held in Boyd Graduate Studies Bldg. unless otherwise noted.
MONDAY, November 7, 2005
Topology/Geometry
2:30pm, Room 303
Speaker: Mohammad Ghomi
Title of talk: h-Principles for knots of constant curvature
Abstract: We prove that smooth knots of constnt curvature satisfy,
in the sense of Gromov, the C1-dense h-principle in the space of curves in 3-
space. In particular, we show that in the isotopy class of any knot in 3-space
there exists a smooth knot of constant curvature which is C1-close to the given
knot. Further, the curvature of the new knot may be set equal to any constant
equal to or bigger than the curvature of the intial knot.
Algebra
2:30-3:30pm., Room 410
Speaker: Patrick Bahls, UNC, Ashville
Title of talk: Rewriting systems and orderability for Artin
monoids
Abstract: A group G (or monoid M) is said to be left-orderable
by the linear order \leq if given any elements g, g', and h in G (or M), g \leq
g' implies h•g \leq h•g'.
The notions of right-orderability and bi-orderability can be defined analogously.
The property of orderability is related to local indicability, satisfaction of the Unique Product Property, and truth of the Zero Divisor Conjecture of Kaplansky.
We will work in the context of Artin monoids, monoids defined by presentations of the form <S | R> for S = {s_{i}}_{i \in I} and R = {u(m_{ij},s_{i},s_{j}) = u(m_{ij},s_{j},s_{i}) | m_{ij} \in {2,3,...,\infty} } for alternating products u(m,g,h) = ghgh••• in which precisely m terms appear. We demonstrate a constructive means of left-ordering certain monoids of this sort, using rooted, labeled trees. We also indicate a number of related problems and directions of research
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Cookies, Tea
TUESDAY, November 8, 2005
VIGRE-Graduate
Student Seminar
2:00p.m., Room 303
Speaker: Patrick Bahls, UNC-Asheville
Title: Groups and monoids and a trick of Magnus
Abstract:
Number Theory Seminar/Oral exam
3:30pm, Room 304
Speaker: Jerry Hower, University of Georgia
Title of talk: Abelian varieties with good reduction everywhere
Joint Analysis Seminar
1:00pm, Georgia Tech, Skilles Hall
Speaker: Steve Hoffman (U.Missouri)
Title: "Local Tb Theorems and applications."
Abstract: The Tb Theorem, and its predecessor, the T1 Theorem,
were introduced in large part to better understand the Cauchy integral operator
on a Lipschitz curve. The rough idea of these theorems is that the L2 boundedness
of a singular integral T can be deduced from sufficiently good behavior of the
operator on some suitable test function, namely, the constant function f(x)
:= 1, in the case of the T1 theorem, or a sufficiently non-degenerate function
b, in the case of the Tb theorem. However, in some PDE applications, it may
be easier to test the operator T locally (say on any given cube Q), on a test
function b_Q that depends upon Q, rather than on a single, globally defined
b. Or to be more precise, in the applications, it may be easier to find a family
of local b_Q's on which T is well behaved, than it is to find a single global
b for which Tb is nice. In this talk, we'll discuss some versions of local Tb
theorems, as well as some applications to PDE.
WEDNESDAY, November 9, 2005
Algebraic Geometry
2:30-3:45pm, Room 410
Speaker: Elham Izadi, University of Georgia
Title of talk: The Hodge conjecture for the primitive
cohomology of theta divisors.
Abstract: I will first discuss the meaning of the Hodge conjecture
in general and then specialize to abelian varieties. The primitive cohomology
of the theta divisor of an abelian variety gives a special Hodge structure for
which one can ask whether the Hodge conjecture is true. Using Prym-embedded
curves, this question was answered in the affirmative by myself and van Straten
for abelian fourfolds. In this talk which is about joint work with Csilla Tamas,
I will discuss the case of abelian fivefolds and show in particular that Prym-embedded
curves do NOT solve the Hodge conjecture. I will, however, introduce a different
family of curves which is very likely to give an answer to the Hodge conjecture.
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Cookies, Tea
VIGRE-Algebra Group
3:45p.m., Room 302
THURSDAY, November 10, 2005
VIGRE – Feynman Diagrams
2:00pm, Room 326
VIGRE – Cardiac Physiology
2:00p.m., Room 640
VIGRE-Algebraic Geometry Group
3:30pm, Room 323
Faculty and Graduate Social
3:00pm, Room 409
Coffee, Cookies, Tea
Colloquium
3:30p.m., Room 304
Speaker: Sergei Levendorski, Dept. of Economics, University
of Texas, Austin
Title of talk: Financial Mathematics
In the talk, it will be explained how finance have served as a source of new
mathematical objects and new variations of mathematical methods; why many problems
in mathematical finance remain unsolved, and why new methods will be needed
as long as financial markets exist; why mathematical methods applied to finance
lead to explosion of financial markets, and why, sometimes, the influence of
the mathematical methods on finance lead to very serious crises; that, contrary
to the wide-spread perception, mathematical finance cannot be reduced to a subfield
of Statistics and the theory of Stochastic Processes in general and Stochastic
Differential Equations and Optimal Stopping theory in particular; there are
important applications for Complex Analysis, Integrals Transforms, Partial Differential
Equations and Pseudo-Differential equations, Lie groups, Dynamic Systems, Lattice
models and related fields in Algebra, nothing to say about Numerical Analysis.
Several basic types of problems will be discussed in some detail.
FRIDAY, November 11, 2005
Probability Theory
2:30-4:00pm, Room 303
Speaker: Chao Zhuang, University of Georgia
Title of talk: Modelling default in bond portfolios