
12月演講

Colloquium, 國立中山大學應用數學系 許柏翰教授
Thursday, December 7, 15:10—16:00 數學系3174
Title: What is a Stochastic Differential Equation? Abstract: Stochastic differential equations (SDEs) are widely used in modeling phenomena in both social and natural sciences. In this talk, we will begin with some random phenomena and its underline SDEs. Then we will introduce Brownian motion, Ito integral, and the Ito formula. Lastly, if time permits, we will discuss a technique for solving an SDE called "martingale problem."

Colloquium, 國立成功大學性別平等教育委員會 吳怡靜行政專員
Thursday, December 7, 16:10—17:00 數學系3174
Title: 營造性別多元、平等的友善校園教學助理(TA)一定要知道的性別平等教育法規! Abstract:性平專題演講

Colloquium, 國家理論科學研究中心 陳世昕博士
Thursday, December 14, 16:10—17:00 數學系3174
Title: Synchronization of Heterogeneous Forced Kuramoto Oscillator Networks: A Differential Inequality Approach Abstract:Synchronization behaviors have been observed in various fields including power systems, biological oscillators, flash of fireflies, etc. To demonstrate such interesting phenomena, the Kuramoto model is proposed and investigated by many experts. In this talk, I shall introduce the forced Kuramoto model and briefly give a literature review. Then I will show the main results of frequency synchronization. If time permits, I will present the numerical simulations.

Colloquium, 國立中山大學應用數學系 王以晟教授
Thursday, December 21, 15:10—16:00 數學系3174
Title: Slice an Apple, and Glue the Pieces Back Together? Abstract:In this talk, we consider the application of the JSJ decomposition to handlebodyknot theory. The JSJ decomposition decomposes a 3manifold into simple pieces by cutting along some specially chosen annuli and tori. It turns out that, in the case of genus one and two handlebodyknots, the pieces in the decomposition are rather restricted and can be classified into finitely many types. On the other hand, how to glue these simple pieces back to recover the knot is a complex issue. The talk hopes to give a quick introduction to how the decomposition works, and how it is used to classify handlebodyknots, and how the gluing information may be recorded. I will also give some outline on the current classification program in this direction and some unsolved problems in this area.

Colloquium, 國立陽明交通大學應用數學系 薛名成教授
Thursday, December 21, 16:10—17:00 數學系3174
Title: Nonlinear Stokes Equations Applied to Ice Sheet Dynamics: Mathematical Modeling and Computation Abstract:In this presentation, we delve into the mathematical modeling and computation of ice sheet dynamics, exploring a novel approach necessitated by the crucial role played by the variable exponent in Glen's flow law, as indicated by numerical experiments in the literature. While the classic Glen's flow law typically considers the exponent as a positive constant, our study introduces a variable exponent. As an initial exploration of this mathematical model, we study the mathematical properties and propose relevant numerical methods for the nonlinear Stokes equations.

Colloquium, 國立清華大學數學系 邱聖夫博士
Thursday, December 28, 16:10—17:00 數學系3174
Title: Quantum Speed Limit and Relative Categorical Energy Abstract: Heisenberg's Uncertainty Principle is one of the most celebrated features of quantum mechanics, which states that one cannot simultaneously obtain the precise measurements of two conjugated physical quantities such as the pair of position and momentum or the pair of electric potential and charge density. Among the different formulations of this fundamental quantum property, the uncertainty between energy and time has a special place. This is because the time is rather a variable parametrizing the system evolution than a physical quantity waiting for determination. Physicists working in quantum information theory have understood this energytime relation by a universal bound of how fast any quantum system with given energy can evolve from one state to another in a distinguishable (orthogonal) way. Recently, there have been many arguing that this bound is not a pure quantum phenomenon but a general dynamical property of Hilbert space. In this talk, in contrast to the usual Hilbert space formalism, we will provide a dual viewpoint of this evolutional speed limit based on a persistencelike distance of the derived category of sheaves : during a fixed time period what is the minimal energy needed for a system to evolve from one sheaf to a status that is distinguishable from a given subcategory? As an application, we will show that such categorical energy with respect to open subsets gives rise to a nontrivial lower bound of Hofer displacement energy.





