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Mathematics & Statistics

# Colloquia — Fall 2003

## Thursday, November 20, 2003

Title
Speaker

Time
Place
Note

Nucleic-Acid-Based Sensors and Logic Gates
Milan Stojanovic
Department of Medicine
Brookhaven National Laboratory
4:00pm-5:00pm
CHE 100
Nataša Jonoska
This colloquium is joint with the Chemistry Department.

Abstract

1. 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.
2. 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
Speaker

Time
Place

Strictly Hermitian Positive Definite Functions
Allan Pinkus
Technion University
Haifa, Israel
3:00pm-4:00pm
PHY 013
Vilmos Totik

Abstract

We talk about characterizations of various classes of positive definite and Hermitian positive definite functions. In particular we are interested in when $$f(\langle x,y\rangle)$$ is a (Hermitian) positive definite, and strictly (Hermitian) positive definite function for $$x, y\in H$$, where $$H$$ is an arbitrary (complex) inner product space.

## Friday, November 7, 2003

Title
Speaker

Time
Place

Quasi-Stationary Behavior in a Simple Discrete-Time Population Model
Göran Högnäs
Åbo, Finland
3:00pm-4:00pm
PHY 013
Arunava Mukherjea

Abstract

We discuss some stochastic versions of the classical deterministic Ricker model $$x_{t+1}=x_t\exp(r-\gamma x_t)$$, $$t=0,1,2\dotsc$$ of the time evolution of the density of a population. Here $$r>0$$ models the intrinsic growth rate and $$\gamma>0$$ 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 $$\gamma_t$$, the branching process may exhibit growth-catastrophe behavior.

## Friday, October 24, 2003

Title
Speaker

Time
Place

Primes is in $$P$$
Rani Siromony
Chennai Mathematical Institute
India
3:00pm-4:00pm
PHY 013
Nataša 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
Speaker

Time
Place

The Blaschke Conjecture
Benjamin McKay
University of South Florida, St. Petersburg
3:00pm-4:00pm
PHY 013

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.

Title
Speaker

Time
Place