Research Presentation

Computing with string

Dr. Robert Dawson (Department of Mathematics & Computing Science, SMU)
Date: Wednesday 8 February 2023
Time: 2:30 p.m.
Location: AT 214

Pieces or loops of string have been used for centuries to construct circles, straight lines, ellipses, and other ovals. What other curves can be computed in this way?  In this talk, I offer two rigorous answers, one valid for systems that must maintain their own tension and another for systems that are externally tensioned. 

Research Presentation

Can we give an approximate answer to whether a given regular expression matches all possible strings?

Dr. Stavros Konstantinidis (Department of Mathematics & Computing Science, SMU)
Date: Wednesday 25 January 2023
Time: 2:30 p.m.
Location: AT 214

The question of whether a given regular expression matches all strings is a hard problem (PSPACE-complete). This is equivalent to whether a given NFA (nondeterministic finite automaton) accepts all strings, which is known as the NFA universality problem. For example the regular expression (0|1)* matches all binary strings but 1* | (0|10|111*)*  does not match the strings that end with 01. We investigate the approximate problem of whether a given NFA accepts at least 99% of all strings. Is this problem any easier? In this talk we will deal with the subproblem of whether a given NFA accepts all strings of some given length n, which is still hard (coNP-complete), and its approximate version.

Research Proposal Presentation

Collocation and Runge-Kutta Software for Boundary Value Ordinary Differential Equations

Mark Adams (Department of Mathematics & Computing Science, SMU)
Date: Wednesday 14 December 2022
Time: 2:30 p.m.
Location: AT 214

Boundary value ordinary differential equations (BVODEs) are systems of ODEs with conditions imposed at both ends of the problem domain. COLNEW and BVP_SOLVER2 are state-of-the-art numerical software which can compute an approximate solution to a BVODE. These Fortran solvers are widely used directly and are also available within problem solving environments (PSEs) such as, Scilab and R, and within well known scripting languages such as Python. COLNEW and BVP_SOLVER2 are capable of efficiently computing solutions to a wide range of complex real-world problems which mathematically model many aspects of science and engineering that are based on BVODEs. In this proposal, we discuss the development of the next generation of these BVODE solvers, COLNEWSC and BVP_SOLVER3, which will have improved design, more reliability, increased efficiency, and new capabilities. We have already made substantial progress in several key areas, one of which involves the development of a more efficient approach for solving difficult and computationally intensive problems in the area of aerospace engineering.

2022-2023 Colloquium Series

Universality limits for orthogonal polynomials

Dr. Milivoje Lukic (Rice University, Houston, Texas)
Date: Wednesday 23 November 2022
Time: 2:30 p.m.
Location: AT 214

It is often expected that the local statistical behavior of eigenvalues of some system depends only on its local properties; for instance, the local distribution of zeros of orthogonal polynomials should depend only on the local properties of the measure of orthogonality. This phenomenon is studied using an object called the Christoffel-Darboux kernel. The most commonly studied case is known as bulk universality, where the rescaled limit of Christoffel-Darboux kernels converges to the sine kernel.

In this talk, we will survey this subject, prior results, and a recent result which gives for the first time a completely local sufficient condition for bulk universality. The new approach is based on a matrix version of the Christoffel-Darboux kernel and the de Branges theory of canonical systems, and it applies to other self-adjoint systems with 2x2 transfer matrices such as continuum Schrodinger and Dirac operators.

The talk is based on joint work with Benjamin Eichinger (TU Wien) and Brian Simanek (Baylor University).




Mathematics & Computing Science Department
1st Floor, McNally North
Main Office: MN 114