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Math Colloquium
Sergey Nadtochiy University of Michigan Title: Particle Systems with Singular Interaction: Application in Systemic Risk Modeling Abstract: In this talk, I will analyze a system of particles with singular interaction through hitting times. Such systems have been used in Neuroscience, but are also well suited for modeling Systemic Risk. I will briefly discuss the latter application and will proceed to the analysis of the associated particle system. In particular, I will discuss the large-population limit of this system and will provide insights into the behavior of the limiting process. The main challenges in this work stem from the very singular type of interaction between the particles, which requires the use of non-standard mathematical methods. In particular, our analysis naturally leads to a non-local and non-linear Cauchy-Dirichlet problem, whose solution may exhibit explosions in finite time.Date: Monday, April 24, 2017Time: 4:30 pmLocation: Wean Hall 8220Submitted by: ShreveNote: Refreshments at 4:00 pm, Wean Hall 6220 |