幾何構造と可積分系セミナー: Evolution of space curves and the Pohlmeyer–Lund–Regge equation: explicit solutions via Riemann theta functions（古郷 優平）, On minimal Lagrangian surfaces in the complex hyperquadric Q_2 （曾 思浩）

Time： 15:00–15:45 （古郷）および15:45–16:30 （曾） 

Place：Faculty of Science Building  #3, Room 204

Speaker：古郷優平（北海道大学，D2），曾 思浩 （北海道大学，D1）

Title（古郷）: Evolution of space curves and the Pohlmeyer–Lund–Regge equation: explicit solutions via Riemann theta functions

Abstract（古郷）:  In this talk, we report the time evolution of a space curve governed by the Lund–Regge condition within the framework of integrable systems. By considering the SU(2)-valued Frenet frame through its Frenet-Serret and time evolution relations, we identify the associated su(2)-valued coefficient matrices with a Lax pair, and we derive the Pohlmeyer–Lund–Regge (PLR) equation for a complex function. Then following the result of Date and the Sym fomrula,  we give an explicit parametrization of the associated surfaces in terms of the Riemann theta-functions. The first part of this talk is based on joint work with Shimpei Kobayashi (Hokkaido University) and Nozomu Matsuura (Fukuoka University).

Title（曾）: On minimal Lagrangian surfaces in the complex hyperquadric Q_2 （曾）

Abstract（曾）:  In this talk, we present our results on minimal Lagrangian surfaces in the 2 dimensional complex hyperquadric Q_2. We will introduce the relation between minimality and the family of flat connections, and talk about how to characterize it. After choosing the appropriate lift and the gauge transformation, we will provide the key techniques for constructing new examples, which related to the theory of CMC surfaces in space forms. This talk is based on joint works with Shimpei Kobayashi (Hokkaido University)

Organizer： 井ノ口順一、小林真平