Zoom Link for the Fall Semester 2024
Join Zoom Meeting
https://osu.zoom.us/j/99158238170?pwd=S1I0MCsrczcrRW1qUUF1SmRaZVV2UT09
Meeting ID: 991 5823 8170
Password: 314159
Date |
Speaker |
Title |
Host |
| August 14 | Edriss Titi | On Recent Advances of the 3D Euler Equations by Means of Examples |
Holmes |
| August 22
(Applied Math/MathBiol) |
Daozhou Gao | Effects of Human Movement on Disease Spread: Persistence versus Prevalence | Lam |
| August 27 | |||
| September 3 | Vlad Kobzar | PDE-Based Analysis of Prediction with Expert Advice and Two-Armed Bandit | OSU |
| September 10 | Timur Akhunov | Modified energy method for illposedness of dispersive equations | Holmes |
| September 17 | |||
| September 24 | Chang-Hong Wu | Spreading fronts arising from the singular limit of reaction-diffusion systems | Lam |
| October 1 | |||
| October 8 | |||
| October 15 | |||
| October 22 | |||
| October 29 | |||
| November 5 | |||
| November 12 | |||
| November 19 | |||
| November 26 | |||
| December 3 | |||
| December 10 | |||
| December 17 | |||
Abstracts
Edriss Titi
Title: On Recent Advances of the 3D Euler Equations by Means of Examples
Abstract: Euler-Loss-Regularity
Daozhou Gao
Title: Effects of Human Movement on Disease Spread: Persistence versus Prevalence
Abstract: Human movement not only facilitates disease spread but also poses a serious challenge to disease control and eradication. It is common to use patch models to describe the spatial spread of infectious diseases in a discrete space. The basic reproduction number R0 usually serves as a threshold for disease extinction and persistence. Thus, it is desirable to control population dispersal such that R0 is reduced to less than 1 to achieve disease eradication. However, in reality, disease eradication is extremely difficult or even impossible for most infectious diseases. Reducing disease prevalence (proportion of people being infected) to a low level is a more feasible and cost-effective goal. In this talk, based on an SIS patch model initially proposed and analyzed by Allen et al. (SIAM J Appl Math, 2007), I will explore the influence of dispersal intensity and dispersal asymmetry on the disease persistence and disease prevalence. Our study highlights the necessity of evaluating control measures with other quantities besides the basic reproduction number.
Timur Akhunov
Title: Modified energy method for illposedness of dispersive equations
Abstract: Korteweg and de Vries in 1890s derived an equation that bears their name to elucidate unusual behavior of water waves. They discovered solitons that behave like billiard balls when interacting. Can solitons be made compactly supported? Rosenau-Hyman in 93 proposed partial differential equations with such solutions that they dubbed “compactons”. Wellposedness of compacton equations is poorly understood. A plausible avenue to prove illposedness results is a modified energy method.
Vlad Kobzar
Title: PDE-Based Analysis of Prediction with Expert Advice and Two-Armed Bandit
Abstract: This talk addresses the classic online learning problem of prediction with expert advice (the expert problem): at each round until the final time, the predictor (player) uses guidance from a collection of experts with the goal of minimizing the difference (regret) between the player’s loss and that of the best performing expert in hindsight. The experts’ losses are determined by the environment (adversary). Using verification arguments from optimal control theory, we view the task of finding lower and upper bounds on the value of the expert problem (regret) as the problem of finding sub- and supersolutions of certain partial differential equations (PDEs). These sub- and supersolutions serve as the potentials for player and adversary strategies, which lead to the corresponding bounds. To get explicit bounds, we use closed-form solutions of specific PDEs. In certain regimes, these bounds improve upon the previous state of the art. We will also briefly discuss our subsequent work generalizing this analysis to the two-armed bandit problem, which is a partial information counterpart of the corresponding expert problem. This talk is based on joint work with Robert Kohn and Zhilei Wang.
Chang-Hong Wu
Title: Spreading fronts arising from the singular limit of reaction-diffusion systems
Abstract:
In this talk, we will focus on the singular limit of reaction-diffusion systems to gain insight into the formation of spreading fronts of invasive species. We will derive some free boundary problems and provide interpretations for spreading fronts from a modeling perspective. Additionally, numerical examples will be presented to facilitate discussion on invasion speed. This talk is based on joint works with Hirofumi Izuhara and Harunori Monobe.
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