1. Friday, September 5, 2003, 3:00 p.m. - 4:00 p.m. Room: MPCS 3314 (not 3311).
Speaker: Dr. Francis Jordan
Title: Continuous-like images of Peano continua
Abstract: A continuum is a nonempty compact connected metric space. A Peano
continuum is a locally connected continuum. The classical
Hahn-Mazurkiewicz Theorem states that continuous images of Peano continua are
Peano continua. We consider images of Peano
contina under functions which
are close to being continuous. Such functions arise in fixed point theory
and other areas. We will be particularly interested in images of the unit
disk. The talk will be of an introductory nature.
2. Friday, September 12, 2003, 3:00 p.m. - 4:00 p.m. Room: MPCS 3314.
Speaker: Dr. Scott Kersey
Title: Constrained subdivision curves
Abstract: In mathematics, curves (and surfaces)are typically represented by
an explicit (parametric) equation. Subdivision curves, on the other hand, are
defined procedurally, as the limit of a sequence of parametrized broken lines
(piecewise linear curves). At each level of subdivision the broken lines are
refined (more points are added), so that in the limit one hopes to achieve a
smooth curve. In this talk, a particular variational and constrained subdivision
scheme is described. The characterization of the piecewise linear curves at each
level of subdivision reduces to a problem in convex optimization. To do so, we
apply a particular separation theorem from convex analysis -- a theorem which is
by now some 40 years old.
3. Friday, September 19, 2003, 3:00 p.m. - 4:00 p.m. Room: MPCS 3314.
Speaker: Dr. Vladimir Chelyshkov
Title: Direct Numerical Simulation of Quasi-Regular External Flows
Abstract: Phenomenon of turbulence in fluids involves a large range of space scales and represents complicated patterns of chaos in space and time. This makes it difficult to describe the phenomenon in general. We consider a class of quasi-regular lengthy external flows where advances are possible on the basis of direct numerical simulation. This opportunity is based on experimental evidence of coherent structures in the flows. Existence of the structures shows that lengthy disturbances carry small amount of energy in thin layers. It allows applying a local approach for the flows modeling. Thus, introduced restriction on scales weakens the requirements on the dimension of dynamic models.
We combine these physical restrictions with a
mathematical model
(the SFM* slow-fast model) based on the Navier-Stokes
equations that includes features of the boundary layer theory and is valid for
turbulence modeling. Local approach introduces an uncertainty in in/outflow
boundary conditions. To avoid the uncertainty we develop the concept of
selecting the particular solution that correspond the phenomenon. The concept
requires application of spectral methods in space that leads o extracting finite
dimensional dynamic system.
Numerical results are presented for the boundary
layer near a flat plate for high Reynolds numbers. It appears that organized
space structures have a chaotic background in time.
4. Friday, September 26, 2003, 3:00 p.m. - 4:00 p.m. Room: MPCS 3314.
Speaker: Dr. Chaohui Zhang
Title: Teichmuller spaces and Bers fiber spaces
Abstract: Let S be a hyperbolic Riemann surface with genus g and n punctures.
The Teichmuller space T(S) of S is the space (endowed with some
complex
structure) of conformal structures of S modulo an equivalent relation, where two
conformal structures are equivalent if they are
isotopic to each other rel a
pre-determined choice of generators of the fundamental group of S.
It is well known that T(S) is a simply connected complex
manifold of dimension 3g-3+n, it can thus be viewed as a universal covering
space of
the Riemann moduli space of S.
For each Teichmuller space T(S) there is a complex disc
fibration F(S) over T(S). F(S) is called the Bers fiber space over T(S).
It was proved by Bers in early 70s that under certain circumstances F(S) can be
identified
with (biholomorphically equivalent to) a new Teichmuller space
T(S).
In this talk, we will investigate relationships among
various moduli spaces of Riemann surfaces. Among other things, relationships
among
Teichmuller spaces and relationships between Teichmuller spaces and
Bers fiber spaces are carefully examined.
5. Friday, October 3, 2003, 2:30 p.m. - 3:30 p.m. (Note time change !) Room: MPCS 3314.
Speaker: Dr. Viktor Maymeskul
Title: Lagrange Interpolation on Algebraic Curves in R2.
Abstract: We will discuss known and recent results in multivariate polynomial
interpolation on curves in R2. In particular, the asymptotic behavior of
nodes of interpolation schemes for which the norms of the corresponding
interpolation operators do not grow geometrically large with n will be described
in terms of a weighted equilibrium measure. In addition, a computationally
simple algorithm for construction of goodinterpolation
schemes will be
given.
6. Friday, October 10, 2003, 3:00 p.m. - 4:00 p.m. Room: MPCS 3314.
Speaker: Mr. Marshall Ransom
Title: Advanced Placement Calculus: Curriculum, Testing, and Transitions from High School to College.
Abstract: The Advanced Placement Calculus program provides high
school teachers with a curriculum and guidelines for preparing their students
for calculus of one variable and preparing for the final exam. The exam is
administered in early May by a joint effort of the College Board and the
Educational Testing Service (ETS), and allows students the possibility of
receiving college credit at over 800 colleges and universities. This
colloquium will give an overview of the curriculum for the two calculus courses,
examples of problems from the final exam and grading procedures, and some
applications of the graphing calculator (both routine and surprising). The
graphing calculator is allowed during half of the final exam.
Implications
for curriculum at Georgia Southern may arise based on knowledge of what these
students have been taught.
7. Thursday, October 16, 2003, 3:00 p.m. - 4:00 p.m. Room: MPCS
3314. Visiting
lecture, Professor M. Sambandham, Morehouse College.
8. Friday, October 24, 2003, 3:00 p.m. - 4:00 p.m. Room: MPCS 3314.
Speaker: Dr. Yang Liu
Title: An invitation to Cartan geometry.
Abstract: Cartan geometry is a way to compare a general manifold with a nice
model.
Typically a nice model means a homogeneous manifold given by quotient
of Lie groups.
The construction involves principal bundles and connections.
We shall present in detail
the example of projective geometry on Riemann
surfaces of genus greater than 1.
9. Friday, October 31, 2003, 3:00 p.m. - 4:00 p.m. Room: MPCS
3314. Visiting
lecture, Professor Jianzhong Wang, Sam Houston State University.
10. Friday, November 7, 2003, 3:00 p.m. - 4:00 p.m. Room: MPCS
3314. Visiting
lecture, Professor Rani Siromoney, Chennai Mathematical Institute,
India.
11. Friday, November 14, 2003, 3:00 p.m. - 4:00 p.m. Room: MPCS 3314.
Speaker: Dr. Sze-Man Ngai
Title: The multifractal formalism.
Abstract: The multifractal formalism was first proposed by physicists
in the
mid 1980's. It is a powerful formalism to study fractal measures.
However, for
many fractal measures, it is difficult to prove rigorously that
the formalism is
valid. This talk presents some major mathematical results
obtained for the class
of self-similar measures.