Speaker: Harvey Diamond (WVU)

Title: Insights and Revelations: Computational exploration with MATLAB

Abstract: Computation is generally understood to be a dreary assemblage of epsilons in its theory, decimal  points in its output, and arcane programming syntax in its execution. But advances over the last two decades in the technology of computation, along with the development of compact, efficient, programming languages – yes, MATLAB – that provide, between them, a comprehensive environment for computation and visualization, have opened a new world for exploration. It is a world that interacts with mathematics, with inspiration passing in both directions, and as well, with the physical world, and the artistic. But it can also pose its own questions, and prompt its own natural paths, take you to remarkable vistas, both conceptual and visual, and might suddenly drop you right into the middle of some interesting mathematics you would not have otherwise encountered. We present some of those questions, paths, vistas, and mathematics, many that arose serendipitously, while teaching an introductory course in computation and MATLAB for nearly 20 years. We conclude with an obvious question: shouldn’t we be teaching computation, for these, and a myriad of other practical reasons, to our freshman math students?

Zoom link: https://bit.ly/allemo

Flyer: link

To be added to the mailing list, please email klp65@psu.edu.

Speaker: Dr. Samantha Allen (Duquesne University)

Title: The algebra of knots: searching for primes

Abstract: A mathematical knot is a knotted up loop in 3-dimensional space: think of tying a knot in a piece of rope and then fusing the ends of the rope together. Two knots are called equivalent if one can be deformed to another via an ambient isotopy (put simply, without breaking the loop or passing it through itself).  There is a way to add two knots to create another knot (called the connected sum) and a knot which is not a connected sum is called prime.

In this talk, I will explain some basic properties of mathematical knots and the connected sum operation.  We will see why this operation is well-defined and, in light of this operation, define the concept of a prime knot in a way analogous to a prime number.  The remainder of the talk will be spent discussing how to identify prime knots, the state of the search so far, and some new research that makes identifying a prime knot an algebraic exercise (rather than a geometric one).

This talk will be accessible to students at all levels.

Zoom link: https://bit.ly/allemo

Flyer: link

To be added to the mailing list, please email klp65@psu.edu.