This Week in Mathematics


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Entries for this week: 7

Tuesday October 04, 2022

Applied and Computational Math Seminar [url]
TBA
- Wojciech Ozanski, Department of Mathematics, FSU
Time: 3:05pm Room: LOV231

Topology and Geometry Semianr [url]
Fock-Goncharov Coordinates and Cluster Varieties
- Jared Miller, FSU
Time: 3:05 Room: LOV 105
Abstract/Desc: Points in Teichmuller space can be seen as conjugacy classes of representations of the fundamental group of a surface into the group PSL(2, R) satisfying several conditions including discreetness and faithfulness. In this talk we will introduce the space of framed representations of a surface group into PGL(m, C) and describe Fock-Goncharov coordinates for such a representation. We will discuss the set of positive representations as a subset of framed representations and discuss connections to cluster mutations. Time permitting, we may mention Bonahon-Dreyer coordinates for closed surfaces, which build on Fock-Goncharov's work.

Wednesday October 05, 2022

Departmental Tea Time
C is for cookie, and shorthand for C[0,1] w/the sup norm
Time: 3: Room: 204 LOV

Computational Methods for Stochastic Optimization and Control
Stochastic computing and optimization
- Students in ACM and Math Fin, FSU
Time: 3:05pm Room: 231

Biomathematics Journal Club [url]
A Programmable Dual-RNA-Guided DNA Endonuclease in Adaptive Bacterial Immunity
- Nicole Bruce, FSU
Time: 5:00 Room: Dirac Library

Thursday October 06, 2022

Financial Mathematics Seminar [url]
Synchronization in a Kuramoto Mean Field Game
- Mete Soner, Princeton University
Time: 3:05pm Room: LOV 231
Abstract/Desc: Originally motivated by systems of chemical and biological oscillators, the classical Kuramoto model has found an amazing range of applications from neuroscience to Josephson junctions in superconductors, and has become a key mathematical model to describe self organization in complex systems. These autonomous oscillators are coupled through a nonlinear interaction term which plays a central role in the long term behavior of the system. While the system is unsynchronized when this term is not sufficiently strong, fascinatingly, they exhibit an abrupt transition to a full synchronization above a critical value of the interaction parameter. We explore this system in the mean field formalism. We treat the system of oscillators as an infinite particle system, but instead of positing the dynamics of the particles, we let the individual particles determine endogenously their behaviors by minimizing a cost functional and eventually, settling in a Nash equilibrium. The mean field game also exhibits a bifurcation from unsynhcronization to self-organization. This approach has found interesting applications including circadian rhythms and jet-lag recovery. This is joint work with Rene Carmona and Quentin Cormier of Princeton University.

Friday October 07, 2022

FSU Mathematics Distinguished Lecture [url]
Recent computational methods for stochastic optimal control
- Mete Soner, Princeton University
Time: 3:05pm Room: 101
More Information
Abstract/Desc: Stochastic optimal control has been an effective tool for many problems in quantitative finance and financial economics. Although, they provide the much needed quantitative modeling for such problems, until recently they have been numerically intractable in high-dimensional settings. However, readily available and computationally highly effective optimization libraries now make regression type algorithms over hypothesis spaces with large number of parameters computationally feasible. In the context of stochastic optimal control, these exciting advances allow efficient approximations of the feedback controls. An algorithm, proposed by E, Jentzen & Han, uses deep artificial neural networks to approximate the feedback actions which are then trained by empirical risk minimization. This methodology and hybrid methods combined with dynamic programming have been explored and developed by many authors, including, Bachouch, Becker, Cheridito, Fecamp, Jentzen, Germain, Gonon, Hure, Langrene, Mikael, Pham, Teichmann, Warin, Welti, Wood. In this talk, I will outline this highly effective methodology and discuss it through representative examples from financial economics. This is based on joint works with Max Reppen of Boston University and Valentin Tissot-Daguette of Princeton University.

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