Department of

Mathematics


Seminar Calendar
for events the day of Monday, September 14, 2015.

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Monday, September 14, 2015

4:00 pm in 145 Altgeld Hall,Monday, September 14, 2015

D-modules and noncommutative geometry

Matej Penciak (UIUC Math)

Abstract: The purpose of this talk is to introduce the theory of D-modules and analyze a possible connection with quantization and noncommutative geometry. I will begin by introducing the Weyl algebra, and D-modules on algebraic varieties. After defining useful invariants of D-modules, I will switch to a discussion of Rosenberg's reconstruction theorem and describe how D-modules could fit into the theory.

A Unified Approach to Systemic Risk Measures via Acceptance Sets

Jean-Pierre Fouque (UCSB)

Abstract: We propose a general methodological framework that is flexible enough to cover a wide range of possibilities to design systemic risk measures via multi-dimensional acceptance sets and aggregation functions, and to study corresponding examples. Existing systemic risk measures can usually be interpreted as the minimal amount of cash needed to secure the system after aggregating individual risks. In contrast, our approach also includes systemic risk measures that can be interpreted as the minimal amount of cash that secures the aggregated system by allocating capital to the single institutions before aggregating the individual risks. This allows for a possible ranking of the institutions in terms of systemic riskiness measured by the optimal allocations. Another important feature of our approach is the possibility of allocating cash according to the future state of the system (scenario-dependent allocation). We illustrate with several examples the advantages of this feature. Joint work with Francesca Biagini, Marco Frittelli, and Thilo Meyer-Brandis.

This seminar series is jointly sponsored by the Departments of Mathematics, Finance, Industrial Enterprise and Systems Engineering.

4:00 pm in 245 Altgeld Hall,Monday, September 14, 2015

Research in algebraic combinatorics

Alexander Yong (Department of Mathematics, University of Illinois)

5:00 pm in 241 Altgeld Hall,Monday, September 14, 2015

Some operator space version of the AGM inequality (continued)

Mingyu Zhao (UIUC Math)