Colloquium (2019)

List of colloquium by year
Speaker Mikiya Masuda (Osaka City University)
Title Mathematics and Eula
Date FEBRUARY 5 (Wed.) 2020, 17:00～18:00
Place Dept. of Mathematics, Faculty of Science Bldg., E408
Abstract I will talk about people I met and what impressed me through mathematics.
Speaker Ryo Kanda (Osaka City University)
Title Noncommutative regular algebras and Feigin-Odesskii's elliptic algebras
Date JANUARY 29 (Wed.) 2020, 17:00～18:00
Place Dept. of Mathematics, Faculty of Science Bldg., E408
Abstract The study of noncommutative regular algebras is one of the main topics in noncommutative algebraic geometry. Feigin and Odesskii introduced a family of graded algebras called elliptic algebras, using certain elliptic solutions of the Yang-Baxter equation. The family contains an important class of algebras called Sklyanin algebras, which are known to be a typical example of higher-dimensional regular algebras. In this talk, I will state some of the important results and conjectures in noncommutative algebraic geometry, and present our recent results on Feigin-Odesskii's elliptic algebras.
Speaker Yukihiro Seki (OCAMI)
Title On singularity mechanisms in harmonic map heat flow with values in a sphere.
Date JANUARY 22 (Wed.) 2020, 17:00～18:00
Place Dept. of Mathematics, Faculty of Science Bldg., E408
Abstract Harmonic map heat flow is one of the classical research topics in geometric analysis. Harmonic maps between general Riemannian manifolds have been studied by many researchers since a pioneering work by Eells--Sampson in 1960s appeared. In this talk, we will discuss heat flows from an Euclidean space to a unit sphere, which may be apparently the simplest setting. Even in this simple situation, the classical Eells--Sampson's theory cannot be applied. Indeed, singularity formation can arise in finite-time. Focusing on possible singularity mechanisms in view of asymptotic analysis, I will introduce my recent results on local-in-space estimates of blow-up solutions that can be regarded as typical ones.
Speaker Takayuki Koike (Osaka City University)
Title Gluing construction of K3 surfaces
Date DECEMBER 4 (Wed.) 2019, 17:00～18:00
Place Dept. of Mathematics, Faculty of Science Bldg., E408
Abstract We explain our recent study on the complex analytic structure of a small tubular neighborhood of a complex submanifold, which is based on T. Ueda's classification theory. We also explain how to apply them to a study on non-projective and non-Kummer K3 surfaces. This talk is based on a joint work with T. Uehara.
Speaker Tomoyuki Arakawa (Kyoto University, RIMS)
Title 4d/2d duality and representation therory
Date NOVEMBER 20 (Wed.) 2019, 17:00～18:00
Place Dept. of Mathematics, Faculty of Science Bldg., E408
Abstract The 4D / 2D correspondence recently discovered in physics constructs representation theoretical objects, such as representations of an affine Lie algebra, as an invariant of the 4 dimensional superconformal field theory with N = 2 supersymmetry. Furthermore, it is predicted that a remarkable duality exists between the representation theoretical objects constructed in this way and the geometric invariant of the original 4 dimensional theory. In this talk, I will explain this duality between representation theoretical objects and geometric objects conjectured in the 4D / 2D correspondence from a mathematical perspective.
Speaker Hideyuki Ishi (Osaka City University／JST PRESTO)
Title Matrix integrals and Cholesky decomposition
Date OCTOBER 16 (Wed.) 2019, 17:00～18:00
Place Dept. of Mathematics, Faculty of Science Bldg., E408
Abstract The set of positive definite real symmetric matrices forms a convex cone.
This cone can be regarded as a natural multi-dimensional analogue of the half line, and it appears everywhere in mathematics. Especially, the Gamma integral formula on the half line is generalized as the so-called Siegel integral formula, which played important roles in statistics (Wishart), analytic number theory (Siegel), and theory of partial differential equations (Garding). After that, Gindikin generalized the integral formula to any homogeneous cone, that is, a regular convex cone on which a linear Lie group acts transitively. On the other hand, analogous integral formulas for cones of real symmetric matrices with prescribed zero components have been utilized in statistics. In this talk, we present a frame work unifying these formulas, focusing on a special role of Cholesky decomposition. Actually, if a vector space of symmetric matrices is closed under a certain non-associative bilinear product arising from Cholesky decomposition, we have an integral formula on the associated convex cone.
Speaker Tetsuo Ueda（Kyoto University）
Title On the structure of parabolic fixed points of holomorphic maps
Date SEPTEMBER 25 (Wed.) 2019, 17:00～18:00
Place Dept. of Mathematics, Faculty of Science Bldg., E408
Abstract We review the Ecalle-Voronin theory that describe the subtle structure of parabolic fixed points of holomorphic maps.
We can cover the neighborhood of such a fixed point by two domains, and define Fatou coordinate on each of the two domains, which linearizes the mapping. The parabolic map can be intrinsically characterized by the transformation map between these two Fatou coordinates.
Conversely, it is known that, when a transformation map is prescribed, we can construct a parabolic map with the given transformation map. We give a new proof this fact based on the Koebe uniformization theorem.
Speaker J. Scott Carter (University of South Alabama / OCAMI, Osaka City University / George Washington University)
Title Diagrammatic Algebra
Date MAY 29 (Wed.) 2019, 17:00～18:00
Place Dept. of Mathematics, Faculty of Science Bldg., E408
Abstract This talk is based upon on-going work with Seiichi Kamada. We will begin with the abstract tensor definition of the Jones Polynomial, and discuss it from a categorical perspective. The main idea there is that the category of tangles is the free braided tortile category on one self dual object generator. Then we turn to play with algebraic structures and to give them categorical descriptions.
Our main result for this talk is a new interpretation of a result that has been mostly understood since the early 1990s. A multi-category that two objects, a reflexive weakly invertible $1$-arrow, whose triple arrows satisfy some mild conditions, coincides with the multi-category of surfaces that are smoothly and properly embedded in $3$-space.
Speaker Mitsuyasu Hashimoto (Osaka City University)
Title Ring theoretic properties of invariant subrings
Date APRIL 24 (Wed.) 2019, 17:00～18:00
Place Dept. of Mathematics, Faculty of Science Bldg., E408
Abstract Hochster, Kei-ichi Watanabe and others started to study homological properties of invariant subrings from 1970's, when the commutative algebra from the viewpoint of homological algebra started to grow as an independent area of mathematics. In this talk, we review these histories, and then introduce the results on the F-singularities of the rings of invariants by the researchers including the speaker.
Speaker Shunsuke Yamana (Osaka City University)
Title Modular forms from various angles
Date APRIL 17 (Wed.) 2019, 17:00～18:00
Place Dept. of Mathematics, Faculty of Science Bldg., E408
Abstract Modular forms are supersymmetric complex analytic functions on symmetric spaces. They look analytic objects at a first glance, but they can be viewed as sections of vector bundles on a moduli space of abelian varieties and possess rich algebraic and geometric structures. A generating function of an arithmetically interesting sequence may be a modular form, and analytic properties of geometric L-series such as Hasse-Weil L-series are proved only when they are identified with an L-series of a modular form. The modular form is a subject in which diverse areas of mathematics are fused together. In this talk I start with a concept of modular forms and summarize its theory and applications with various examples, and close my talk by touching on my current research project.
Last Modified on 2020. 1. 15