Registration

Martin Guest

Title: Geometry versus analysis:  noncompact real forms of the Toda equations 

Abstract: The sinh-Gordon equation and Tzitzeica/Bullough-Dodd equations appear in both geometry and analysis in various ways.  They are special cases of the (2-dimensional, real, affine) Toda equations. We shall describe a new Lie-theoretic classification of real forms obtained recently by Ian McIntosh (arXiv:2406.02323), which was motivated by the various choices of sign in the Toda equations, and by the influence of these signs on the solvability of the equations.  Radial solutions (on the domain C - {0}) of the Toda equations can be interpreted as isomonodromic deformations of a meromorphic o.d.e., and here again the influence of the signs is significant.  We shall discuss some examples related to the tt*-Toda equations and quantum cohomology. 

 Lunch break

Yat-Hin Marco Suen 孫逸軒

Title: Realization problems in toric equivariant mirror symmetry

Abstract: In this talk, I will introduce two realization problems in toric equivariant mirror symmetry. Given a tropical Lagrangian multi-section $L^{trop}$ over a complete rational fan $\Sigma$, the A-realization problem asks if there exists an exact embedded Lagrangian in the cotangent bundle of a vector space whose asymptotics are prescribed by $L^{trop}$. On the other hand, the B-realization problem asks if there exists a toric equivariant vector bundle over the toric variety $X_{\Sigma}$ whose tropicalization is $L^{trop}$. We will give an affirmative answer to both realization problems when $X_{\Sigma}$ is a toric surface and $L^{trop}$ is of degree 2.

Tea break

Tzu-Mo Kuo 郭子模

Title: Two Topics in Conformal Geometry: Extrinsic GJMS Operators and Conformal Boundary Conditions

Abstract: The GJMS operators are a family of conformally covariant differential operators on Riemannian manifolds. In the first part of this talk, I will briefly describe the construction and properties of an analogous family of operators on a submanifold of a Riemannian manifold. These are differential operators that depend on the extrinsic geometry of the submanifold. This is joint work with Jeffrey Case and Robin Graham.

There are extrinsic conformal invariants, called conformal fundamental forms, on the boundary of a Riemannian manifold. These invariants determine whether the Riemannian manifold is conformal to an asymptotically Poincaré-Einstein manifold. The second part of the talk addresses an analogous problem: there are extrinsic conformal invariants on the boundary of a submanifold in a Riemannian manifold. These invariants determine whether the submanifold is conformal to an asymptotically minimal submanifold in a conformally compact manifold. If time permits, I will briefly describe the construction of these invariants. This is joint work with Jeffrey Case, Jarosław Kopiński, Aaron Tyrrell, and Andrew Waldron. 

Break

forum

Symposium Banquet (The expense will be covered by NCTS)

Place: 豐盛食堂(台北市大安區麗水街1之3號)