【談話会】Boris Shakarov 氏（1月27日）

下記要領で談話会を開催します。

日程：2025年1月27日 (月) 16:30〜17:30
場所：津田塾大学小平キャンパス新館談話会室M320
講演者：Boris Shakarov 氏（University of Toulouse, France）
題目：Nonlinear Schrodinger Equations on Quantum Graphs
概要：
Quantum graphs, frequently modeled as one-dimensional networks, serve as powerful approximations of higher-dimensional domains. They can feature a variety of shapes—such as loops, branching structures, and interconnected segments—and can accommodate diverse boundary conditions at their vertices. These properties make quantum graphs an appealing framework for studying wave phenomena across a broad range of settings. In the first part of this talk, we will present a broad overview of the nonlinear Schrödinger equation (NLS) on quantum graphs, focusing on essential concepts like well-posedness, vertex conditions, and the existence of ground states. The second part will discuss the passage from two-dimensional fractured strips to one-dimensional graphs. Specifically, we will analyze how ground states—whether in the attractive or repulsive regime—converge to one-dimensional solutions as the width of the strip approaches zero. This sheds light on the dimensional reduction process that underpins many quantum graph models, helping to bridge the gap between higher-dimensional quantum structures and their graph-like counterparts. By highlighting the role of different topologies in shaping wave behavior, our study provides insights that can inform future applications in quantum networks and related fields.

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