Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, January 16, 2018.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, January 16, 2018

12:00 pm in 243 Altgeld Hall,Tuesday, January 16, 2018

A Higgs bundle construction for representations in exceptional components of $\text{Sp(4}\text{,}\mathbb{R}\text{)}$-character varieties.

Georgios Kydonakis (UIUC)

Abstract: For a compact Riemann surface of genus $g\ge 2$, the components of the moduli space of $\text{Sp(4}\text{,}\mathbb{R}\text{)}$-Higgs bundles, or equivalently the $\text{Sp(4}\text{,}\mathbb{R}\text{)}$ character varieties, are partially labeled by an integer $d$ known as the Toledo invariant. The subspace for which this integer attains a maximum has been shown to have $3\cdot {{2}^{2g}}+2g-4$ many components. A gluing construction between parabolic Higgs bundles over a connected sum of Riemann surfaces provides model Higgs bundles in a subfamily of particular significance. This construction is formulated in terms of solutions to the Hitchin equations, using the linearization of a relevant elliptic operator.

1:00 pm in 345 Altgeld Hall,Tuesday, January 16, 2018

Turing and Machines

Kay Kirkpatrick (Illinois Math)

Abstract: We will discuss newly defined machines that out-perform Turing machines. In his unpublished 1948 paper, Intelligent Machinery, Alan Turing identified several types of machines, with one dichotomy that is false, between active and controlling machines. This mistake became an assumption in his famous 1950 paper and has probably been the source of the confusion about the Turing Test and the Chinese Room Argument. I'll introduce a new type of machine and define a subtype that cannot be simulated by a deterministic Turing machine.

4:00 pm in 245 Altgeld Hall,Tuesday, January 16, 2018

Nonparametric Inference for Sensitivity of Haezendonck-Goovaerts Risk Measure

Xing Wang (Georgia State University)

Abstract: Recently Haezendonck-Goovaerts (H-G) risk measure has been popular in actuarial science. When it is applied to an insurance or a financial portfolio with several loss variables, sensitivity analysis becomes useful in managing the portfolio, and the assumption of independent observations may not be reasonable. This paper first derives an expression for computing the sensitivity of the H-G risk measure, which enables us to estimate the sensitivity nonparametrically via the H-G risk measure. Further, we derive the asymptotic distributions of the nonparametric estimators for the H-G risk measure and the sensitivity by assuming that loss variables in the portfolio follow from a strictly stationary α-mixing sequence. A simulation study is provided to examine the finite sample performance of the proposed nonparametric estimators. Finally, the method is applied to a real data set.

4:00 pm in Illini Hall 1,Tuesday, January 16, 2018

Organizational meeting

Abstract: We'll have a cookies party while deciding what'll be in the seminar this semester.