* ChangeThe Brown University Symposium for Undergraduates in the Mathematical Sciences (SUMS) has been held annually since 2002. The symposium's goal is to foster greater undergraduate interest and scholarship in mathematics by demonstrating the ubiquity of mathematics throughout the sciences. The conference also provides an environment in which motivated undergraduates can come together to share their own work and learn from distinguished faculty and researchers from around the country.
This year's symposium will be held on April 5th, 2014 in Barus & Holley 166/168, 184 Hope Street, Providence, and features the topic of Visualizing Mathematics.
Very light breakfast refreshments will be served prior to the first lecture on Saturday.
Registered participants will be invited to a banquet dinner on Saturday evening. There is no cost to attend the banquet. Deadline for Registration is March 29, 2014.
Check-in - 900am - 9:50am
1st talk - 10:00am Professor Richard Schwartz
2nd talk 11:00am Professor Sarah Koch
Lunch break - 12:00pm - 1:30pm
Student talks - 1:30pm - 3:00pm
3rd talk - 3:00pm Professor Kelly Delp
4th talk - 4:00pm Professor Thomas Banchoff
Banquet - 5:00pm Chancellor's Dining Room and Annex, Wriston Quad
Thomas Banchoff, Professor of Mathematics, Brown University
Abstract: Visualization Revolutions in Geometry and Topology
What images and models have fueled mathematical exploration in geometry and topology over the past couple of centuries, and why is visualization now taking off in so many new directions? The story starts with paper and plaster models, leading to questions only successfully answered with the advent of modern computer technology, algebraic as well as geometric. Moebius bands and Klein bottles, projective planes and Riemann surfaces all play starring roles in this ongoing story. What will come next?
Kelly Delp, Ithaca College, New York
Abstract: Playing with Surfaces: Spheres, Monkey Pants, and Zippergons
I will describe a process, inspired by clothing design, of smoothing an octahedron into a round sphere. This process was adapted to build many surfaces out of paper and craft foam. The pattern pieces for the surfaces were designed using a dynamic Mathematica notebook, and cut using a digital cutter. This project was joint with Bill Thurston.
Sarah Koch, Assistant Professor of Mathematics, University of Michigan
Mating habits of polynomials
Given two suitable complex polynomial maps, one can construct a new dynamical system by mating the polynomials; that is, by ``gluing'' the polynomials together in a dynamically meaningful way. In this talk, we focus on quadratic polynomials -- we begin with a brief discussion of parameter space for quadratic polynomials (where the Mandelbrot set lives), we then define the mating of two quadratic polynomials, and finally we explore examples where the mating does exist, and examples where it does not. There will be many pictures and movies in this talk.
* Richard E. Schwartz, Professor of Mathematics, Brown UniversityVisualizing Outer Billiards
Abstract: Outer billiards is a kind of game in which a point bounces around the outside of a shape according to a simple rule. I will
describe how outer billiards works and then demonstrate a graphical user interface I made, which explores the intricate structure of outer billiards when it is defined relative to the Penrose kite.
Funding for SUMS 2014 was provided by the Brown University Department of Mathematics, the Institute for Computational and Experimental Research in Mathematics (ICERM) , and Brown University Division of Applied Mathematics.