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日時：2024年4月23日（火），15:00-16:30
場所：理学部A201号室
講師：石原 海 氏 (広島大学)
題目：結び目と絡み目における局所変形とその応用
結び目や絡み目における交差交換は、DNAのトポロジーを変えるトポイソメラーゼの作用として知られています。また、バンド手術は、DNAの組換えや渦の結び目における変形の数学的モデル化として知られています。この講演では、結び目や絡み目における局所変形、特に交差交換やバンド手術のトポロジーを用いた特長付けとその応用についてお話しします。
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日時：2024年5月7日（火），15:00-16:30
場所：理学部A201号室
講師：Víctor Pérez-Valdés 氏 (龍谷大学)
題目：Construction and classification of vector-valued differential symmetry breaking operators from $S^3$ to $S^2$
Any equivariant irreducible vector bundle for the conformal group $SO_0(4,1)$ on the $3$-sphere $S^3$ is parametrized by an odd number ($=2N+1$) and a complex number $\lambda$. On the other hand, any equivariant irreducible vector bundle for the conformal group $SO_0(3,1)$ on the $2$-sphere $S^2$ is a line bundle,
and is parametrized by an integer number $m$ and a complex number $\nu$.
In the present talk, we consider the problems of construction and classification of all the differential operators,
that are symmetry breaking operators with respect to the conformal pair $(SO_0(4,1), SO_0(3,1))$ between the spaces of smooth sections of a vector bundle $V_\lambda^{2N+1}$ over the $3$-sphere $S^3$ and a line bundle $L_{m, \nu}$ over the $2$-sphere $S^2$.
In particular, we solve these problems when the rank of the vector bundle is less than or equal to $7$ (i.e., for $N = 1,2,3$), and for $|m| > N$, and propose a strategy to solve them for $N > 3$. The method we use is the F-method of T. Kobayashi, which in our setting allows us to reduce the problem of constructing differential symmetry breaking operators to the problem of solving an overdetermined system of $2(2N+1)$ ordinary differential equations on $2N+1$ unknown polynomials.
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日時：2024年5月28日（火），15:00-16:30
場所：理学部A201号室
講師：Thomas Raujouan 氏 (神戸大学)
題目：The Loop Weierstrass Representation
We will talk about two classes of surfaces.
On the one hand, minimal surfaces, such as the catenoid, are critical points of the area functional. They can be constructed with the help of holomorphic functions via the Weierstrass representation (1866). On the other hand, constant mean curvature (CMC) surfaces, such as the cylinder, are critical points of the area functional under volume constraint. They can be constructed with the help of loop groups via the method of Dorfmeister, Pedit and Wu (DPW, 1998).
Recently, several achievements in the theory of CMC surfaces have been made using DPW. Inspired by them, we will re-interpret the Weierstrass representation and introduce a new framework for the construction of minimal surfaces: the Loop-Weierstrass Representation (LWR). We will then show that some methods of the DPW method can be applied to the study of minimal surfaces, shedding a new light on ancient results. This talk is based on a joint work with N. Schmitt and J. Ziefle.
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日時：2024年6月4日（火），15:00-16:30
場所：理学部A201号室
講師：Luis Pedro Castellanos 氏 (広島大学)
題目：Classification of symplectic Structures on Almost Abelian Lie algebras
We are interested in the classification or finding conditions for the existence of left-
invariant symplectic structures on Lie groups. Only some classifications are know,
specially in low dimensions. In this talk we consider this problem in the case of almost
Abelian Lie algebras, that is Lie algebras that contain a codimension 1 Abelian subalgebra.
We show that, in this setting, the problem of existence and classification can be reduced to
a known matrix equation and a corresponding equivalence relation, respectively. We then solve
this equations and give a complete classification of symplectic structures on almost Abelian Lie algebras .
In fact, using the same ideas we give a complete classification of presymplectic structures on
almost Abelian lie algebras. We state sufficient and necessary conditions for the existence of these structures.
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日時：2024年7月9日（火），15:00-16:30
場所：理学部A201号室
講師：村尾 智 氏 (高知大学)
題目：ハンドル体結び目の彩色不変量とconstituentハンドル体絡み目
3次元球面に埋め込まれたハンドル体をハンドル体結び目と呼び，ハンドル体結び目を何枚かの本質的円板で切り開いて得られるいくつかのハンドル体の非交和を元のハンドル体結び目のconstituentハンドル体絡み目と呼ぶ．
本講演では，与えられたハンドル体結び目のconstituentハンドル体絡み目が満たす条件について，彩色不変量の観点から考察する．
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日時：2024年7月18日（木），14:15-15:45
場所：理学部E209号室 (普段と曜日場所などが異なっているのでご注意ください)
講師：Olivia Dumitrescu (University of North Carolina, Chapel Hill)
題目：Interplay between opers, Higgs bundles and quantum curves
I will present an algebraic correspondence between opers
a la Beilinson-Drinfeld and Higgs fields on the Hitchin section.
In rank 1 and rank 2 I will illustrate some differences between two
diffeomorphic moduli spaces, the Hitchin and the de Rham moduli spaces,
in terms of lagrangians filling up the entire space.
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日時：2024年7月18日（木），16:00-17:30
場所：理学部E209号室 (普段と曜日場所などが異なっているのでご注意ください)
講師：Motohico Mulase (University of California, Davis)
題目：From Enumeration to Moduli Spaces: Another Story of Categorification
The first part of the talk is aimed at presenting a simple
counting problem and its solution, i.e., the generating function F.
A surprise is that a special value of F gives topological information of
moduli spaces of stable curves. An elementary combinatorial identity of
the original counting problem translates into nonlinear PDEs for F,
which are directly related to the celebrated KP equations,
and reproduce the resultsof Witten, Kontsevich, and Mirzakhani.
The second part is about an open-ended story of a currently ongoing
project on finding the geometry that represents the irrationality of Zeta(3).
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日時：2024年11月22日（金），15:00-16:00 (普段と曜日と部屋が異なりますのでご注意ください)
場所：理学部A２１０号室
講師：陳 浩 氏 (上海科技大学)
題目：Gluing construction of maxfaces
The gluing method has been a powerful tool for constructing minimal surfaces. Recently, we applied this method to construct maxfaces in Lorentz space that look like space-like planes connected by Lorentzian catenoids. We obtained a large amount of examples, including (but not limited to) the first CHM-type maxface. We also analyzed singularities on our examples. It seems that this progress is only a beginning: In view of its power on minimal surfaces, the method may produce many more maxfaces in the future.
This is a joint work with Pradip Kumar et al.
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日時：2025年12月17日（火），15:00-16:30
場所：理学部A201号室
講師：久保利久氏 (龍谷大学)
題目：On the projectively covariant differential operators from a line bundle to a vector bundle over a real projective space
Construction and classification of covariant differential operators are classical problems in parabolic geometry. In 1976, Fegan accomplished to classify and construct conformally covariant differential operators of first order. Since then, the results of Fegan have been generalized by Cap-Slovak-Soucek, Slovak-Soucek, Ørsted, Koranyi-Reimann, among others. The first order case is now settled.
Higher order case is in contrast still a work in progress. In 2015, Kobayashi-Ørsted-Somberg-Soucek obtained, among many other things, explicit formulas of differential symmetry breaking operators and conformally covariant differential operators on a natural line bundle over a conformal sphere. In this talk, we shall classify and construct projectvely covariant differential operators on real projective spaces. If time permits, we would also like to discuss such operators in a symmetry breaking setting. This talk is partially based on joint work with Bent Ørsted.
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日時：2025年1月14日（火），15:00-16:30
場所：理学部A201号室
講師：石塚慶太氏 (三菱電機株式会社 情報技術総合研究所)
題目：Linear complementary dual codes and its applications
Linear complementary dual
codes（以下、LCD符号）は共通鍵暗号や量子誤り訂正符号への応用が知られた2010年代後半以降、盛んに研究されている符号である。
本講演では、線形符号の導入から始めて、LCD符号の主要な先行研究や応用を紹介する。