Department of

Mathematics

Seminar Calendar
for events the day of Monday, March 17, 2014.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, March 17, 2014

11:00 am in Altgeld Hall 141,Monday, March 17, 2014

Option Pricing Without Tears: Valuing Equity-Linked Death Benefits

Elias S.W. Shiu (The University of Iowa, Statistics and Actuarial Science)

Abstract: Nowadays, many products sold by life insurance companies are investment funds wrapped around with (exotic) options and guarantees. These financial options and guarantees should be priced, hedged, and reserved using modern option-pricing theory, which involves sophisticated mathematical concepts such as Brownian motion, stochastic differential equation, and so on. This talk will show that, if the options or guarantees are exercisable only at the moment of death of the policyholder, the mathematics simplifies to an elementary calculus exercise.

2:00 pm in 147 Altgeld Hall,Monday, March 17, 2014

Random Walks on Simplicial Complexes and Harmonics

Sayan Mukherjee (Duke Statistics)

Abstract: In this paper, we introduce random walks with absorbing states on simplicial complexes. Given a simplicial complex of dimension d, a random walk with an absorbing state is defined which relates to the spectrum of the k-dimensional Laplacian. We also examine an application of random walks on simplicial complexes to a semi-supervised learning problem. Specifically, we consider a label propagation algorithm on oriented edges, which applies to a generalization of the partially labelled classification problem on graphs.

3:00 pm in 145 Altgeld Hall,Monday, March 17, 2014

Legendrian Knots and Constructible Sheaves

Eric Zaslow (Northwestern)

Abstract: We study the unwrapped Fukaya category of Lagrangian branes ending on a Legendrian knot. Our knots live at contact infinity in the cotangent bundle of a surface, the Fukaya category of which is equivalent to the category of constructible sheaves on the surface itself. Consequently, our category can be described as constructible sheaves with singular support controlled by the front projection of the knot. We use a theorem of Guillermou-Kashiwara-Schapira to show that the resulting category is invariant under Legendrian isotopies, and conjecture it is equivalent to the representation category of the Chekanov-Eliashberg differential graded algebra of the knot. This sounds harder than it is. Briefly-- INPUT: Knot diagram, OUTPUT: Category. I will illustrate the above with simple examples. This work is joint with David Treumann and Vivek Shende.

4:00 pm in 241 Altgeld Hall,Monday, March 17, 2014

Attracting domains for holomorphic maps tangent to the identity

Sara Lapan (Northwestern)

Abstract: One of the guiding questions behind the study of holomorphic dynamics is: given a germ of a holomorphic self-map of C^m that fixes a point (say the origin), can it be expressed in a simpler form? If so, then the dynamical behavior of the map can be more easily understood. In general, we want to know how points near the origin behave under iteration by the map. More specifically, we want to know when there exists a domain whose points are attracted to the origin under iteration by the map and, if such a domain exists, what can be said about how the points converge to the oriign. In this talk, we will focus on maps tangent to the identity. We will begin by discussing what happens in one complex dimension; in particular, we will discuss the Leau-Fatou flower theorem, which describes the existence of attracting domains in dimension one and serves as inspiration for this study in higher dimensions. We will discuss what is known about the existence of attracting domains in higher dimensions, focusing on a collection of maps in C^2 with a unique (and non-degenerate) characteristic direction.

4:00 pm in 145 Altgeld Hall,Monday, March 17, 2014

Families of elliptic curves and quantum moduli of Seiberg-Witten theory

Sheldon Katz (Illinois Math)

Abstract: Last time, we saw that the classical moduli space of Seiberg-Witten theory for SU(2) is given by the u-plane, with $u=\mathrm{Tr}(\Phi^2)$. Singularities arise in the quantum theory from BPS states that become massless at $u=\pm\Lambda^2$. The quantum theory can be completely described in terms of the family of elliptic curves $y^2=(x-u)(x^2-\Lambda^4)$. In this talk, we will see how families of elliptic curves already arise in describing N=1 theories. The Seiberg-Witten solution is obtained by imposing the requirements of N=2 SUSY, but details will be deferred to a subsequent lecture.

4:00 pm in 143 Altgeld Hall,Monday, March 17, 2014

Healing the Stress of Academic Life

Richard Ellis (U Mass Amherst)

5:00 pm in 241 Altgeld,Monday, March 17, 2014

Free Monotone Transport, Part 3

Michael Brannan (UIUC Math)

Abstract: I will discuss the recent paper of A. Guionnet and D. Shlyakhtenko with the same title.