This is an international research meeting for Professor Martin Guest's retirement from Waseda University.

Registration Form Here  (Please registrate by June 7 (Fri) if you want to attend the Party on June 19 Wednesday evening.)

Dates: June 18 (Tue) - June 20 (Thu), 2024

Place :  The 2nd Meeting Room (55N-1-01), 1F Building 55, Nishi-Waseda campus, Waseda University  

Invited Speakers:

River Chiang (National Cheng Kung University, Taiwan)

Martin A. Guest (Waseda University, Japan)

Atsushi Kanazawa (Waseda University, Japan)

Hui Ma (Tsinghua University, China)

Yoshiaki Maeda (Tohoku University, Japan)

Kenta Miyahara (Indiana University - Purdue University Indianapolis, USA)

Wayne Rossman (Kobe University, Japan)

Makiko Sumi Tanaka (Tokyo University of Science, Japan)

Kohei Yamaguchi (The University of Electro-Communications, Japan)

Program (provisional):

June 18 (Tue):

14:00 - 15:00  Atsushi Kanazawa 

15:15 - 16:15  Hui Ma 

June 19 (Wed):

10:30-11:30  Makiko Sumi Tanaka

 Lunch

13:30-14:30  Kohei Yamaguchi 

14:45-15:45  Yoshiaki Maeda 

16:00-17:00  Martin A. Guest 

Group Photo

18:00-   Party 

June 20 (Thu)

10:30-11:30  Kenta Miyahara 

Lunch

13:30-14:30  River Chiang 

14:45-15:45  Wayne Rossman  

Title & Abstract of Talks:

Atsushi Kanazawa:

"BCOV cusp forms of lattice polarized K3 surfaces"

In 1993, Bershadsky, Ceccoti, Ooguri and Vafa introduced the so-called BCOV potential which gives the generating functions of g=1 Gromov-Witten invariants of Calabi-Yau 3-folds generalizing mirror symmetry at g=0 due to Candelas et al. It involves an interesting interplay between the variation of Hodge structures and the Kähler geometry on moduli spaces of Calabi-Yau 3-folds. In fact, it originates from the tt^*-geometry on the moduli space of N=2 SQFT in 2 dimensions. Recently, we found an analogue of BCOV potential for lattice polarized K3 surfaces  (https://arxiv.org/abs/2303.04383 joint work with Shinobu Hosono). In this talk, I will give an overview of our work.

Hui Ma:

"Symmetry of hypersurfaces with symmetric boundary"

Let $G$ be a compact connected subgroup of $SO(n+1)$. In $\mathbb{R}^{n+1}$, we gain interior $G$-symmetry for minimal hypersurfaces and hypersurfaces of constant mean curvature (CMC) which have  $G$-invariant boundaries and $G$-invariant contact angles along boundaries. The main ingredients of the proof are to build an associated Cauchy problem based on infinitesimal Lie group actions, and to apply Morrey’s regularity theory and the Cauchy-Kovalevskaya Theorem. Moreover, we also investigate the same kind of symmetry inheritance from boundaries for hypersurfaces of constant higher order mean curvature and Helfrich-type hypersurfaces in $\mathbb{R}^{n+1}$. This talk is based on the recent joint work with Chao Qian, Jing Wu and Yongsheng Zhang.

Makiko Sumi Tanaka:

"Antipodal sets of compact symmetric spaces"

A subset S of a symmetric space M is called an antipodal set if s_x(y)=y holds for any x, y in S, where s_x denotes the symmetry at x. When M is compact, there is the maximum of the cardinalities of antipodal sets of M, called the 2-number of M, which has certain bearings on the topology of M. In our joint research with Hiroyuki Tasaki, we have been studying classification of maximal antipodal sets of compact symmetric spaces. When there is a covering map \pi from a compact symmetric space M onto a compact symmetric space M', in some cases, there is a simple relation between maximal antipodal sets of M and those of M' when the covering degree of \pi is odd. We gave a theoretical proof of this fact when M and M' are compact Lie groups, which are not necessarily connected, and \pi is a covering homomorphism with odd degree.

Kohei Yamaguchi:

"Spaces of rational curves on a toric variety and their homotopy stability"

abstract (PDF) 

Yoshiaki Maeda:

"The fundamental groups of isometry groups of metrics on a Sasakian manifold"

abstract (PDF) 

Martin A. Guest:

"The Toda equations revisited, revisited"

The Toda equations are a never-ending source of inspiration in the theory of integrable systems, with many applications in differential geometry and physics.  We shall describe some Lie-theoretic aspects of the "noncompact case", i.e. where the Lie group is noncompact.  This is joint work with Ian McIntosh.

Kenta Miyahara: 

"Connection formulae for the radial Toda equations"

Since the invention of the 1D Toda lattice equation in 1967, many types of Toda equations have been considered. In this presentation, we will talk about the global asymptotic behavior of the radial solutions of the 2D periodic Toda lattice equation of type $A_n$. The principal issue is the connection formulae between the asymptotic parameters describing the behavior of the general solution at zero and infinity. To reach this goal we use a fusion of the Iwasawa factorization in the loop group theory and the Riemann-Hilbert nonlinear steepest descent method of Deift and Zhou which applies to 2D Toda in view of its Lax integrability. A principal technical challenge is the extension of the nonlinear steepest descent analysis to Riemann-Hilbert problems of matrix rank greater than $2$. As a first nontrivial example, we meet this challenge for the case $n=2$ (the rank $3$ case) and it already captures the principal features of the general $n$ case. This is a joint work with Martin Guest, Alexander Its, Maksim Kosmakov, and Ryosuke Odoi.

River Chiang: 

"From symplectic deformation to isotopy, equivariantly"

Wayne Rossman:

"Gauging, dressing and transforming surfaces both smooth and discrete"

I will start with discussing the role of gauging and dressing in the theory of constant mean surfaces, based in part on work with Martin Guest and Sepp Dorfmeister, followed by a description of how this leads to elements of transformation theory for smooth surfaces and subsequently discrete surfaces. Then, in the discrete case I will describe some recent joint work with Thomas Raujouan and Naoya Suda on transforming discrete surfaces, extending the class of examples that work by Tim Hoffmann and Andrew Sagemann-Furnas can be applied to. 

Organizers:  Yasushi Homma (Waseda University.),  Yoshihiro Ohnita (Waseda University & OCAMI), Takashi Sakai (Tokyo Metropolitan University) , Saki Okuhara (OCAMI)

Scientific Advisors:  Martin Guest (Waseda University)

Contact:    Yoshihiro Ohnita    yohnita@aoni.waseda.jp   ohnita@omu.ac.jp