Department of

# Mathematics

Seminar Calendar
for events the day of Monday, January 30, 2017.

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events for the
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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, January 30, 2017

4:00 pm in 245 Altgeld Hall,Monday, January 30, 2017

#### What is a root system?

###### William Haboush (Department of Mathematics, University of Illinois)

4:00 pm in 156 Henry Admin Bldg,Monday, January 30, 2017

#### Discounted Sums at Renewal Times

###### Daniel Dufresne (Director of the Centre for Actuarial Science, University of Melbourne)

Abstract: Actuarial models usually include discounting, to take the time value of money into account. Mathematically this has proved difficult when amounts are paid at random times, for instance in risk theory. We assume that i.i.d. amounts {C(k)} are paid at renewal times {T(k)}. Of practical interest is the distribution of Z(t), the discounted value of claims occurring over the period [0,t]. New results on how to find the distribution of Z(t) will be presented. An important tool is sampling the process {Z(t)} at an independent exponential time, which leads to explicit distributions of Z(t) in specific cases. Joint work with Zhehao Zhang.

4:00 pm in 243 Altgeld Hall,Monday, January 30, 2017

#### Geometric Lie 2-algebras

###### Cristian Ortiz (University of Sao Paulo)

Abstract: Lie 2-algebras were introduced by Baez and Crans as groupoid objects in the category of Lie algebras. In this talk we will present a class of examples of Lie 2-algebras, those coming from sections of LA-groupoids. We will see that the category of sections of an LA-groupoid has a natural structure of Lie 2-algebra which is Morita invariant in a suitable sense. In the particular case of the tangent groupoid, one gets a Lie 2-algebra structure on the category of multiplicative vector fields on a Lie groupoid. We will explain how this can be used to introduce a geometric notion of vector field on the quotient stack of a Lie groupoid. This is joint work with James Waldron.

5:00 pm in 241 Altgeld Hall,Monday, January 30, 2017

#### Dixmier traces and limit sets of quasi-Fuchsian groups

###### Edward McDonald (NSW)

Abstract: Alain Connes in 1994 provided a formula for integration against the Hausdorff measure on the limit set of a quasi-Fuchsian group in terms of a Dixmier trace. This talk discusses the formulation of this result and its proof.