Colloquia — Fall 2003
Thursday, November 20, 2003
| Title |
Nucleic-Acid-Based Sensors and Logic Gates |
| Speaker |
Dr. Milan Stojanovic
Department of Medicine
Brookhaven National Laboratory |
| Time |
4:00-5:00 p.m. |
| Place |
CHE 100 |
| Sponsor |
Dr. N. Jonoska |
| Note |
This colloquium is joint with the Chemistry Department. |
Abstract
- Starting from a three-way DNA junction structure, various sensors for
hydrophobic molecules could be constructed. These sensors could be arrayed into
cross-reactive arrays capable of fingerprinting hydrophobic molecules in
solution.
- Deoxyribozymes could be turned into sensors for the presence of one or more
oligonucleotides. Arrays of these sensors could be used to perform
decision-making in solution.
Friday, November 14, 2003
| Title |
Strictly Hermitian Positive Definite Functions |
| Speaker |
Dr. Allan Pinkus
Technion University
Haifa, Israel |
| Time |
3:00-4:00 |
| Place |
PHY 013 |
| Sponsor |
Professor V. Totik |
Abstract
We talk about characterizations of various classes of positive definite and
Hermitian positive definite functions. In particular we are interested in when
f(<x,y>) is a (Hermitian) positive
definite, and strictly (Hermitian) positive definite function for x,
y ∈ H, where H is an arbitrary (complex)
inner product space.
Friday, November 7, 2003
| Title |
Quasi-Stationary Behavior in a Simple Discrete-Time Population Model |
| Speaker |
Professor Göran Högnäs
Åbo Akademi University
Åbo, Finland |
| Time |
3:00-4:00 |
| Place |
PHY 013 |
| Sponsor |
Professor A. Mukherjea |
Abstract
We discuss some stochastic versions of the classical deterministic Ricker
model xt+1 = xt
exp(r - γxt), t = 0, 1, 2... of the time evolution of the density
of a population. Here r > 0 models the intrinsic growth rate and
γ >0 is an inhibitive environmental factor. The introduction of
demographic stochasticity leads us to a size-dependent branching process whose
quasi-stationary behavior (for some values of r) tends to concentrate
around the attracting period cycle of the deterministic system. When we allow
the environment to vary, modeled by an i.i.d. sequence of parameters
γt, the branching process may exhibit
growth-catastrophe behavior.
Friday, October 24, 2003
| Title |
Primes is in P |
| Speaker |
Dr. Rani Siromony
Madras Christian College/
Chennai Mathematical Institute
India |
| Time |
3:00-4:00 |
| Place |
PHY 013 |
| Sponsor |
Dr. N. Jonoska |
Abstract
On August 8, 2002, a polynomial time algorithm for recognizing Primes was
given by three young computer scientists, Agrawal, Kayal and Saxena of IIT,
Kanpur, India. This is a milestone in centuries-old journey towards understanding
prime numbers, solving a longstanding open problem in Computational Number
Theory and Complexity Theory.
Friday, October 17, 2003
| Title |
The Blaschke Conjecture |
| Speaker |
Dr. Benjamin McKay
University of South Florida, St. Petersburg |
| Time |
3:00-4:00 |
| Place |
PHY 013 |
| Sponsor |
Dr. M. Elhamdadi |
Abstract
On a thin sphere of glass, all light rays leaving one point will focus on
the antipodal point. A surface on which all light rays from any single point
collide at some other point is called a Blaschke surface. Leon Green (1961)
showed that all Blaschke surfaces are spheres; his techniques were very hard.
The classification of Blaschke objects in higher dimensions is open. I will
present my new results on this old (1921) problem; I employ only elementary
calculus of differential forms and elementary projective geometry.
Friday, October 10, 2003
| Title |
Asymptotics of Orthogonal Polynomials, the Riemann-Hilbert
Problem and Universality in Matrix Models |
| Speaker |
Professor Alexander Its
Indiana Univesity-Purdue University at Indianapolis |
| Time |
3:00-4:00 |
| Place |
PHY 013 |
| Sponsor |
Professor V. Totik |
Abstract
Recent developments in the theory of random matrices and orthogonal polynomials
reveal striking connections of the subject to integrable nonlinear differential
equations of both the KP and the Painlevé types. These connections,
in particular, make it possible to use nontraditional analytical schemes of
the theory of integrable systems, such as the Riemann-Hilbert asymptotic method,
for proving Dyson's universality conjecture concerning the scaling limit of
correlations between eigenvalues for a wide class of exponential weights. In
the talk, the essence of the Riemann-Hilbert approach to matrix models will
be presented together with an exposition of their occurrence in diverse areas
of mathematics and physics.