Month: October 2020

https://bucknell.zoom.us/j/95413936042
Student Colloquium Talk by Professor Sanjay Dharmavaram

Abstract: Ever wonder why  mathematics classes focus so much on linear problems? In Calculus we learn about linear approximations. In Differential Equations, after classifying differential equations as linear and nonlinear, we mostly focus on linear problems. Linear Algebra focuses exclusively on systems of linear equations. There are two reasons for this: 1) nonlinear problems are hard!! Unlike linear equations, there is no unified theory that works for all nonlinear equations. 2) linear approximations are often a good starting point to study nonlinear problems.

In this talk, we will make a foray into the marvelous world of nonlinear systems and discuss techniques under the umbrella of “Bifurcation Theory” to analyze them. Bifurcation theory is a branch of mathematics that investigates, albeit qualitatively, nonlinear equations containing a tunable parameter. Such equations routinely arise in biology, engineering, physical and social sciences. Some examples include models for understanding cardiac arrhythmia, synchronization of fireflies’ flashing, pattern formation in reaction-diffusion systems, and buckling of structures under mechanical loads. In this talk, we will also see how the tools of bifurcation theory can be used to analyze some of these problems.

Watch on Mediaspace: https://mediaspace.bucknell.edu/media/1_gzca3xpq

https://bucknell.zoom.us/j/95413936042

Student Colloquium Talk by Professor Michael Reeks.

Abstract:

Anyone who has ever shoved a pair of headphones in their pocket knows about the following general principle of the universe:”Any flexible strand will tie itself in knots as soon as it’s given the opportunity.” As such, knots are ubiquitous in nature and art:

– DNA strands, so often pictured as tidy helices, actually spend most of their time hopelessly knotted;
– the way in which proteins interact and function depends heavily on the way they are folded, or knotted, together;
– and some of the oldest known art is based on complex patterns of knots.

Mathematicians, always ready to help out, have therefore tried to study and classify knots for decades. In this sadly pizza-less talk, I’ll introduce the mathematical theory of knots and knot invariants, which are tools that can help us tell knots apart. I’ll explain how some basic questions in knot theory tie into sophisticated topics of current research, and explain a few fascinating ways in which knots arise in chemistry, biology, physics, and art.

Flyer: https://tinyurl.com/y4fwvzjh

Video (Bucknell login required): https://mediaspace.bucknell.edu/channel/Mathematics%2BDepartment/184494973