Below are a few titles and abstracts from presentations I give.
The mathematics of coloring and doodling
A beautiful world of mathematics surrounds even the simplest doodles that you draw on a piece of paper. We discuss a number of classical and recent connections between doodling, coloring, and math.
This talk can be scaled up or down to any level: elementary, junior high, high school, and college students.
Sometimes Pi Equals Four
We explore new ways to define distance between two points. Leaving behind the usual Euclidean definition, we introduce the taxicab metric, flower shop metric, the teleportation metric, and more. This, in turn, forces a domino effect of changes in the shape of circles, trig functions, and -- yes -- even the value of pi.
Here is an article that I wrote on this topic for Math Horizons.
Here is a video of me giving this talk at the Museum of Mathematics as a public lecture.
This talk is perfect for college students or general audiences.
Torus knots and nonorientable surfaces
We investigate the nonorientable surfaces which torus knots bound, both in the three-sphere and in the four-ball. Given a torus knot, we describe a surface construction given by Teragaito in 2004 that produces a nonorientable surface of minimal genus in the three-sphere which the knot bounds. Then, we broaden our perspective to the four-ball. In this setting, we describe similar surface constructions, and we prove that difference the nonorientable three- and four-genus can be arbitrarily large. This is joint work with Slaven Jabuka.
This talk is appropriate for a math department colloquium or a topology seminar.
Stanford Topology Seminar (November 2019)
American Math Society Sectional Meeting, UC Riverside (November 2019)
Museum of Mathematics, New York City (September 2019) -- See video below!
Bay Area Teachers and Mathematicians Immersion Workshop (July 2019)
Unknot IV Conference, University of Washington - Bothell (July 2019)
University of Durham Geometry & Topology Seminar (May 2019)
Dartmouth Topology Seminar (May 2019)
UC Davis Topology Seminar (April 2019)
Claremont Topology Seminar (February 2019)
California Math Council for Community Colleges Fall Conference (December 2018)