Every academic year, the Department of Mathematics hosts the Martin Guterman lecture, funded by a gift from the Guterman family to commemorate our late colleague Martin Guterman and his exceptional ability to communicate real mathematics to a broad audience. For this lecture we invite a mathematician known as an engaging speaker.
David Richeson, Dickinson College
"Tales of Impossibility"
Abstract: "Nothing is impossible!" It is comforting to believe this greeting card sentiment; it is the American dream. Yet there are impossible things, and it is possible to prove that they are so. In this talk we will look at some of the most famous impossibility theorems—the so-called "problems of antiquity." The ancient Greek geometers and future generations of mathematicians tried and failed to square circles, trisect angles, double cubes, and construct regular polygons using only a compass and straightedge. It took two thousand years to prove conclusively that all four of these are mathematically impossible.
Gigliola Staffilani, MIT
"The Many Faces of Dispersive Equations"
Abstract: In recent years great progress has been made in the study of dispersive and wave equations. Over the years the toolbox used in order to attack highly nontrivial problems related to these equations has developed to include a variety of techniques from Fourier and harmonic analysis, analytic number theory, math physics, dynamical systems, probability and symplectic geometry. In this talk I will introduce a variety of problems connected with dispersive, such as the derivation of a certain nonlinear Schrodinger equations from a quantum many-particles system, periodic Strichartz estimates, the concept of energy transfer, the invariance of a Gibbs measure associated to an infinite dimension Hamiltonian system and more.
Susan Loepp, Williams College
"The Key to Sending Secret Messages"
Abstract: Suppose Alice wants to send secret messages to Bob, but the channel over which they communicate is not secure. Suppose also that their arch enemy, Eve, can intercept all communication between them. It is perhaps counterintuitive that Alice and Bob can send secret messages to each other over their insecure channel with reasonable confidence that Eve cannot decipher their messages. In this talk, we will discuss the history of, and the ideas behind public-key exchanges; the first step Alice and Bob use to send their messages. No particular mathematics background will be assumed.
John Urschel, MIT
"Voronoi Tessellations in Today's World"
Abstract: A Voronoi tessellation is a partition of space into regions defined by distance from a given set of points. What does this have to do with nature, technology, and sociology? Everything! I will introduce the concept of Voronoi tessellations and how they apply to the world we live in. In addition, I will prove new results for energy-minimizing tessellations, the so-called centroidal Voronoi tessellations.