5th Geometry Day

Schedule

• TBA

Title & Abstract

• Jihyeon Lee (IBS-CGP)

Title : Hamiltonian Stationary Twisted Lagrangian Tori in $\mathbb{C}^n$

Abstract : Chekanov's exotic tori play an important role in symplectic geometry as examples of Lagrangian tori that are not Hamiltonian isotopic to the standard product torus. A useful class of such Lagrangian tori can be constructed by twisting a simple closed planar curve, producing what are known as twisted Lagrangian tori. In a recent work, Chen and Coulibaly studied the Hamiltonian stationary condition for twisted Lagrangian tori in $\mathbb{C}^2$ and proved that the only Hamiltonian stationary twisted tori arise from circles centered at the origin, i.e., the Clifford product torus. 

In this talk, we generalize their framework to higher-dimensional complex space $\mathbb{C}^n$, and derive explicit geometric formulas for Hamiltonian stationary equation for twisted tori generated by planar curves. In particular, we show that the Hamiltonian stationary condition imposes strong restrictions on the generating curve and that, under natural assumptions, the only Hamiltonian stationary twisted tori in $\mathbb{C}^n$ are the product tori. These results provide a higher-dimensional perspective on the geometry of twisted Lagrangian tori and clarify the role of Chekanov-type constructions in Hamiltonian stationary geometry. 

• Jungwoo Moon (Chung-Ang University) 

Title : TBA

Abstract : TBA

• Sanghun Lee (Pusan National University) 

Title : TBA

Abstract: TBA

• NAME (POSTECH) 

Title : TBA

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• NAME (POSTECH) 

Title : TBA

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• Yunhee Euh (Sungkyunkwan University) 

Title : TBA

Abstract: TBA

• Shinjin Woo (Sookmyung Women's University) 

Title : TBA

Abstract: TBA

• NAME (Affiliation) 

Title : TBA

Abstract: TBA