
4月演講

Analysis Seminar, Prof. Tomoyuki Tanaka, Faculty of Science and Engineering, Doshisha University
Wednesday, April 3, 16:10—17:00 數學系3174
Title: Unconditional WellPosedness for Generalized KdV Type Equations on the Torus Abstract: We will motivate and introduce the notion of Grothendieck ring of varieties in algebraic geometry, and explain how we obtain new results on Cremona groups through it in recent joint works with E. Shinder. (We assume zero background in algebraic geometry.)

Colloquium, 台灣大學海洋研究所 謝志豪教授
Thursday, April 11, 16:10—17:00 理學教學大樓 1F36102演講廳
Title: Empirical Dynamic Modeling for Nonlinear Dynamical Systems Application and Extension of Takens’ Embedding Theorem Abstract:Mechanistic understanding and forecasting are important for effective policy and management recommendations for ecosystems. However, these tasks are challenging, because real world is complex, where correlation does not necessarily imply causation. In this seminar, I aim to introduce a timeseries analytical framework, known as Empirical Dynamic Modeling (EDM). EDM is rooted in Takens’ Embedding theorem for state space reconstruction. EDM enables detecting causality among interacting components in nonlinear dynamical systems, constructing timevarying interaction networks, forecasting effects of external forcing, and serving as early warning signal for critical transition. I will demonstrate the efficacy of EDM in various systems. The information can shed light on identifying drivers of ecosystem stability and translating this science into policyrelevant information.

Algebraic Geometry Seminar, 國家理論中心 Pedro Nunez, Postdoc
Thursday, April 18, 13:30—14:30 數學系館 3F會議室
Title: Indecomposability of Derived Categories of Threefolds on the Noether Line Abstract: Minimal smooth projective varieties of nonzero geometric genus are conjectured to have indecomposable derived categories. Particularly interesting from a birational point of view are minimal varieties with extremal birational invariants. In this talk we discuss the case of threefolds sitting on the Noether line, i.e., those for which the volume of the canonical divisor is as low as possible in relation to their geometric genus. This is joint work in progress with Jungkai Alfred Chen.

Colloquium, 義守大學資料科學與大數據分析學系 黃宏財教授
Thursday, April 18, 16:10—17:00 數學系3174
Title: The Method of Fundamental Solutions: Theory and Applications Abstract:演講摘要

Colloquium, 日本明治大學 Toshiyuki Ogawa 教授
Thursday, April 25, 15:10—16:00 數學系3174
Title: Traveling Wave Solutions in ThreeComponent CompetitionDiffusion Systems Abstract: Segregation is one of the important issues in ecology. Several simple situations have been proposed that enable segregation by using mathematical model approach. In particular, the LotkaVolterra type competition reactiondiffusion model is often studied, and here we are going to focus on the case that we have three competing species. Moreover, we consider the situation where an exotic species invades to the buffer zone between the native two strong species. Since we already know the existence and stability of traveling wave solution connecting two stable constant states in 2componet strong competition reaction diffusion system, we consider 3component extended competition system. The original 2component traveling wave with no third species is again a trivial solution for the 3component system as well. We focus on the stability change of this trivial traveling wave solution with respect to the intrinsic growth rate for the third species and study the bifurcation structure around it. We are also going to discuss further global bifurcation structure relating to this problem.
This talk is based on the joint works between ChiunChuan Chen, ChuehHsin Chang, Shinichiro Ei, Hideo Ikeda, and Masayasu Mimura.

Colloquium, 嘉義大學應用數學系 李信儀 教授
Thursday, April 25, 16:10—17:00 數學系3174
Title: Global Classical Solutions for Nonisentropic Gas in the Nozzle Flows Abstract: In this talk, we investigate the global existence of classical solutions for nonisentropic gas flows through a duct. This problem can be described as an initialboundary value problem for the full compressible Euler equations with the geometric source in Lagrangian coordinates, which can be viewed as a hyperbolic system of balance laws when the Riemann invariants are applied. We prove the global existence theorem for classical solutions under appropriate conditions on entropies, ducts, and initial and boundary data. This leads to an essential identity related to the entropy and crosssectional area of the duct. Our analysis mainly depends on the local existence theorem and uniform a priori estimates, which can be obtained by using the method of characteristics and introducing generalized Lax transformations. Furthermore, the longtime behavior of global classical solutions along all characteristic curves and vertical lines is also determined completely.
This is joint work with ShihWei Chou, John M. Hong, and ShihMing Wang.





