Index | This week | Schedule & abstracts | Past talks | Organizer notes | Graduate page |

Date | Speaker | Title |
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28 August, 2013 | Gleb Zhelezov | Organizational Meeting |

Sign up to give a talk! | ||

04 September, 2013 | Gleb Zhelezov | Singularities and Coalescence in the Keller-Segel Model |

Abstract: In its reduced form, the Keller-Segel chemotaxis model is a conservative system in which particle density is described by a convectionâ€“diffusion equation that's coupled to an elliptic equation for the evolution of the chemoattractant. For total mass above a certain threshold, the solution to this equation becomes singular in finite time, which causes most finite difference, spectral, and finite element methods to perform poorly. In this talk, we will introduce this system, investigate some of its analytic properties, and introduce a stochastic particle-in-cell method for its solution. | ||

11 September, 2013 | Dylan Murphy | Algebraic curves and the KP equation |

Abstract: The Kadomtsev-Petviashvili (KP) equation is an analogue of the famous Korteweg-de Vries (KdV) equation, which was the starting point for the modern theory of integrable systems. Several years after the development of the inverse scattering method for KdV, a different approach or constructing solutions was devised. This approach encodes the solution to the equation in the expansion coefficients of a special function on an algebraic curve. By using techniques from classical algebraic geometry, this function can be constructed explicitly and the corresponding solution calculated.
In this talk, I will discuss the application of this method to the KP equation and show some simple examples of the solutions that result. |
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18 September, 2013 | Cody Gunton | The Cohen-Lenstra Heuristics |

Abstract: The ideal class group of a number field is an essential and very mysterious invariant. For even the simplest classes of number fields, little is known about the collection of all ideal class groups. The Cohen-Lenstra heuristics, first presented in 1983, successfully predict certain statistics of ideal class groups. This talk will introduce the basic players, conjectures and theorems the theory of ideal class groups, assuming no prior knowledge of algebraic number theory, and will discuss the Cohen-Lenstra heuristics and related results. | ||

25 September, 2013 | Erik Davis | Wavelets |

In this talk I will discuss wavelets & while you enjoy bagels. | ||

02 October, 2013 | Megan McCormick | Jucys-Murphy elements and the center of the symmetric group ring |

Abstract: Jucys-Murphy elements are specific sums of transpositions in the symmetric group ring, C[S_n]. These elements show up frequently in the representation theory of the symmetric group, and have some beautiful properties that lead to powerful results. I will go into some detail about how these elements are related to the center of the symmetric group ring and give a neat result (due to Jucys) about their eigenvalues. I will also discuss how they are helpful in a specific random matrix theory problem. | ||

09 October, 2013 | Rachel Baumann, Amy Been and Doron Shahar | Topological Groups and Duality |

Abstract: Topological groups represent objects in the intersection of the theory of groups and topological spaces. We can obtain some significantly stronger results about objects which are both groups and topological spaces. The goal of this talk will be to introduce topological groups and their Pontryagin duals, and explore what happens to nice topological properties upon dualizing. | ||

16 October, 2013 | Tova Brown | The Loop Equations of Random Matrices |

Abstract: The loop equations of random matrix theory have been used for quite some time to obtain explicit formulas for map enumeration generating functions. I want to use them to count certain families of graphs embedded on Riemann surfaces. But putting these loop equations on a rigorous mathematical foundation takes considerable work. Ercolani and McLaughlin did this in 2007. In this talk, I will be giving a broad overview of the steps in this derivation, as well as motivation for why we want to do it. Probability measures, random matrix theory, linear algebra, asymptotics, Riemann-Hilbert problems, contour integrations, and more will take their respective parts in this drama. |