2026-27 Department of Mathematics and Statistics Events

 Fall 2026

August 2026

Thurs.
Aug. 27 
11 am
SE-215                                                      

Analysis & Applications Seminar

 Speaker:  J.D. Mireles James, Professor, Department of Mathematics & Statistics, Florida Atlantic Universtiy 

Title: Validated numerical computations with power series for analytic functions

Abstract: I will talk about a method for computing mathematically rigorous enclosures of power series.  This task is important in many different kinds of computer assisted proofs in nonlinear analysis and dynamical systems theory.  The idea is to use an interpolation scheme on the boundary of a disk in the complex plane, which turns out to be equivalent to the discrete Fourier transform (DFT) for Fourier series.  This interpolation introduces errors, which can they be bound using ideas from complex analysis.  Moreover, one can take advantage of fast algorithms such as the FFT for the numerical computations.  I will focus on obtaining bounds on the so called "aliasing" errors (which are really just interpolation errors, i.e. the mistake you make when you interpolate when you wanted to project... all of this will be discussed!). 

In later talks I will explain how these ideas appear in computer assisted proofs.  In particular, I want to show you some computer assisted proofs of the existence of chaotic motion in mathematical billiards.  Of course, I will introduce these models when the time comes.  

NOTE:   There is an open invitation to all faculty and graduate students to talk in the seminar.  If you would like to speak this semester, please just contact me or Professor Lundberg and we will get you on the schedule!

September 2026

Thurs.
Sept. 3 
11 am
SE-215 

Analysis & Applications Seminar

 Speaker:  J.D. Mireles James, Professor, Department of Mathematics & Statistics, Florida Atlantic Universtiy 

Title: Validated numerical computations with power series for analytic functions

Abstract: I will talk about a method for computing mathematically rigorous enclosures of power series.  This task is important in many different kinds of computer assisted proofs in nonlinear analysis and dynamical systems theory.  The idea is to use an interpolation scheme on the boundary of a disk in the complex plane, which turns out to be equivalent to the discrete Fourier transform (DFT) for Fourier series.  This interpolation introduces errors, which can they be bound using ideas from complex analysis.  Moreover, one can take advantage of fast algorithms such as the FFT for the numerical computations.  I will focus on obtaining bounds on the so called "aliasing" errors (which are really just interpolation errors, i.e. the mistake you make when you interpolate when you wanted to project... all of this will be discussed!). 

In later talks I will explain how these ideas appear in computer assisted proofs.  In particular, I want to show you some computer assisted proofs of the existence of chaotic motion in mathematical billiards.  Of course, I will introduce these models when the time comes.  

NOTE:   There is an open invitation to all faculty and graduate students to talk in the seminar.  If you would like to speak this semester, please just contact me or Professor Lundberg and we will get you on the schedule!