Lauren Williams

Abstract:   Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili proposed a two-dimensional nonlinear dispersive wave equation now known as the KP equation. It is well-known that one can use the Wronskian method to construct a soliton solution to the KP equation from each point of the real Grassmannian. In my talk I'll describe the beautiful combinatorics (permutations, triangulations, etc) that arises when one studies the regular soliton solutions that come from the Grassmannian. We'll also see how the theory of total positivity and cluster algebras provide a natural framework for studying KP solitons.

Regular KP soliton solutions provide a good model for shallow water waves (like beach waves), and I'll end the talk with some pictures. This is joint work with Yuji Kodama.

Here are some directions to Northeastern University. Lake Hall and Nightingale Hall can be best accessed from the entrance on the corner of Greenleaf Street and Leon Street. The two halls are connected, with no well-defined boundary in between. In particular, 509 Lake Hall is on the same corridor as 544 Nightingale Hall.

There is free parking available for people coming to the Colloquium at Northeastern's visitor parking (Rennaisance Garage). The entrance is from Columbus Avenue. If coming by car, you should park there and take the parking talon. After the lecture, you may pick up the payment coupon from Andrei Zelevinsky.