AIMR Math Group Seminar2025/5/29
Date: May. 29th (Thu) 2025 15:00-18:00
Venue: AIMR, Combination Room on the 5th floor
1.
Speaker: Dr.Naoki Sakata (WPI-AIMR, Tohoku University)
Title: Topological Modeling of Structures in Soft Matter
Abstract:
This talk introduces topological modeling approaches for mathematically describing and understanding the characteristic structures observed in soft matter.
In the first part, I will present a method of describing microphase separation structures, such as those in block copolymers, using the concept of handlebody decomposition of three-dimensional manifolds. This model can describe complex phase separation structures with three or more phases. I will also introduce mathematically defined structural transformation operations that can relate these structures to each other. These operations enable a hierarchical description of the structures.
In the second part, I will focus on the phenomenon of "transient entanglement" in ring polymer chains and introduce a topological model to characterize this state of entanglement. Specifically, I will consider a situation in which a pair of topologically unlinked ring polymers cannot be separated by pulling them at certain positions. I will present how these states can be modeled using tangles from knot theory, and how they can be mathematically determined given specific pulling positions.
2.
Speaker: Dr.Xiao Dongyuan (WPI-AIMR, Tohoku University)
Title: Propagation Phenomena in Reaction-Diffusion Equations and Their Applications
Abstract:
In this talk, I will begin by introducing the propagation phenomena of solutions to reaction-diffusion equations, a central topic in the study of pattern formation and wavefront dynamics. I will briefly present some of my previous research in this area, including results on the Fisher-KPP equation and the Lotka–Volterra competition system. In the second part of the talk, I will discuss ongoing and future research directions, with a particular focus on problems inspired by applications in materials science.
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