Events
Department of Mathematics and Statistics
Texas Tech University
We establish the precise asymptotic behavior, as time $t$ tends to infinity, for nontrivial, decaying solutions of genuinely nonlinear systems of ordinary differential equations. The lowest order term in these systems, when the spatial variables are small, is not linear, but rather positively homogeneous of a degree greater than one. We prove that the solution behaves like $\xi t^{-p}$, as $t\to\infty$, for a nonzero vector $\xi$ and an explicit number $p>0$.
This week's Analysis seminar may be attended at 4:00 PM CST (UT-6) in MA 115.
No abstract.
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 | Wednesday
Jan. 25
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| Algebra and Number Theory
No Seminar
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This week's PDGMP seminar may be attended at 3:00 PM CDT (UT-5) via this Zoom link.
Meeting ID: 933 4646 9342
Humans have been discussing the benefits and drawbacks of democratic vs. authoritarian governance for millennia, with perhaps the earliest and most famous discussion favoring enlightened authoritarian rule contained in Plato's 'Republic'. The commonly cited benefits of an enlightened dictatorial regime are the efficiency of governance and long-term horizon in planning due to the independence of frequent election cycles. To analyze the claims of potential superiority of an authoritarian rule, we develop a simple mathematical theory of a dictatorship in the ideal case of a dictator wanting the best outcome for the country, with the additional external noise describing external and internal challenges in the country's path.
We assume the linear proportional feedback control based on the information provided by the output from the advisors. The resulting stochastic differential equations (SDEs) describe the evolution of both the trajectory of a country's well-being and the accuracy of advisors' information. We show the system's inherent instability due to the corruption of the advisor's information provided to the dictator. While the system without noise does possess a large amount of phase space with stable solutions, the noise pushes all solutions to the unstable regime. We show that there is a typical unstable time scale, and describe the long-term evolution of the system using asymptotic solutions, some results from the theory of SDEs and phase space analysis. We also discuss the application of the theory to historical data on grain harvest in the Soviet Union. No previous knowledge of Ito's calculus or theory of SDEs is assumed; I will provide all necessary background from that theory during the lecture.
When: 4:00 pm (Lubbock's local time is GMT -6)
Where: room MATH 011 (basement)
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* Meeting ID: 940 7062 3025
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I will continue to talk about stacks and simplicial presheaves in the context of prequantum field theories.