| Speaker | Sachiko Hamano (Osaka City University) |
| Title | On rigidity of pseudoconvex domains fibered by open Riemann surfaces according to directional moduli |
| Date | March 23 (Wed.) 2022, 17:00～18:00 |
| Place | Dept. of Mathematics, Faculty of Science Bldg., E408 & Zoom Registration （Please register by 9:00 on March 22th.） |
| Abstract | I will talk about the contents of my paper: Sachiko Hamano, On rigidity of pseudoconvex domains fibered by open Riemann surfaces according to directional moduli. Math. Z. (2022). In this paper, for a marked open Riemann surface $R$ of finite genus $g$ and a real $g$-vector $a$, we define the $a$-span of $R$. From the viewpoint of several complex variables, we show that if a smooth family $\cal{R}$ is a two-dimensional pseudoconvex domain fibered by open Riemann surfaces of the same topological type, then the diameter of the $a$-directional moduli disk is subharmonic. |
| Speaker | Tatsuya Horiguchi (OCAMI) |
| Title | Schubert calculus on Peterson variety |
| Date | March 23 (Wed.) 2022, 15:45～16:45 |
| Place | Dept. of Mathematics, Faculty of Science Bldg., E408 & Zoom |
| Abstract | Peterson varieties are subvarieties of flag varieties which are related to the quantum cohomology of flag varieties. In this talk, I will explain Schubert calculus on the Peterson variety in type A. More specifically, we consider the intersections of the Peterson variety and Schubert varieties, and construct an additive basis for the integral cohomology of the Peterson variety which reflects the geometry of the intersections. Moreover, I will also explain a combinatorial game which yields an effective computation of the structure constants with respect to our basis. This is joint work with Hiraku Abe, Hideya Kuwata, and Haozhi Zeng. |
| Speaker | Megumi Sano (Hiroshima University) |
| Title | Harmonic transplantation and its application to functional inequalities |
| Date | February 9 (Wed.) 2022, 17:00～18:00 |
| Place | Dept. of Mathematics, Faculty of Science Bldg., E408 & Zoom Registration （Please register by 9:00 on February 8th.） |
| Abstract | First, we will introduce harmonic transplantation proposed by Hersch in 1969. Also, we will explain the difference between harmonic transplantation and M\'obius transformation. We will point out that various transformations can be understood as a special case or a general case of harmonic transplantation. As an application, we will derive several improvements and several limiting forms of functional inequalities via harmonic transplantation. In the half-space, we cannot apply harmonic transplantation to these inequalities directly due to the lack of the explicit form of the $p$-Green function. Therefore, we will consider a modification of the original harmonic transplantation. By using that, we derive the improved Hardy inequality in the half-space and the critical Hardy inequality as the limiting form. A part of this work is based on a joint work with Prof. F. Takahashi (Osaka City University). |
| Speaker | Futoshi Takahashi (Osaka City University) |
| Title | Asymptotic behavior of least energy solutions to the Finsler Lane-Emden problem with large exponents |
| Date | February 9 (Wed.) 2022, 15:45～16:45 |
| Place | Dept. of Mathematics, Faculty of Science Bldg., E408 & Zoom |
| Abstract | In this talk, we are concerned with the least energy solutions to the Lane-Emden problem driven by an anisotropic operator, so-called the Finsler $N$-Laplacian, on a bounded domain in $\re^N$. Nonlinearity in the equation is of polynomial type, and we prove several asymptotic formulae as the nonlinear exponent $p$ gets large. This talk is based on a joint work with Sadaf Habibi (OCU, D2). |
| Speaker | Professor Yukio Tsushima (Emeritus Professor of Osaka City University) |
| Title | Recalling my 39 years experience as an Osaka City University faculty member |
| Date | January 19 (Wed.) 2022, Delivery of the order of the Sacred Treasure by Vice-president Hiroyuki Sakuragi 16:45 Commemorative lecture 17:00～18:00 |
| Place | Dept. of Mathematics, Faculty of Science Bldg., E408 & Zoom |
| Abstract | Being consolidated with Osaka prefecture university, Osaka city university will disappear at least on the name term. On this occasion, as a person who has worked for/at Osaka city university for 39 years (from 1966 to 2005) as a faculty member, to the present faculty members, I’d like to talk about my own experience that could be useful for managing the new math department. That was the main reason I accepted the invitation. |
| Speaker | Yuta Wakasugi (Hiroshima University) |
| Title | Energy decay of solutions to the wave equation with space-dependent damping |
| Date | December 8 (Wed.) 2021, 17:00～18:00 |
| Place | Dept. of Mathematics, Faculty of Science Bldg., E408 & Zoom Registration （Please register by 9:00 on December 7th.） |
| Abstract | We consider the wave equation with space-dependent damping. This equation has a particular property that the energy of solutions monotonically decreases due to the damping effect. Problems such as whether the energy decays to zero as time goes to infinity, and in that case, how fast the energy decays to zero, have been studied for a long time. In this talk, we present some recent results on the problem of how the magnitude of damping and initial data at the spatial infinity determine the decay rate of the energy. In particular, it has recently been found that the energy method, which uses an appropriate super solution of the corresponding heat equation as a weight function, is effective for this problem, and we would like to introduce this method. This talk is based on joint work with Dr. Motohiro Sobajima (Tokyo University of Science). |
| Speaker | Tadashi Ochiai (Osaka University) |
| Title | Artin L-function and its p-adic analog |
| Date | December 1 (Wed.) 2021, 17:00～18:00 |
| Place | Dept. of Mathematics, Faculty of Science Bldg., E408 & Zoom Registration （Please register by 9:00 on November 30th.） |
| Abstract | We first explain Riemann zeta function and Dirichlet L-function, as well as Dedekind zeta function and Hecke L-function. Then we explain the Artin L-function associated to a finite dimensional complex representation of the absolute Galois group of an algebraic number field is a natural generalization of these L-functions. After we review these classical L-functions, we discuss the p-adic analog of these L-functions. We present Greenberg's work on the p-adic Artin L-function over a totally real field and our work (joint with Takashi Hara) on the p-adic Artin L-function over a CM field. |
| Speaker | Hiroshi Iriyeh (Ibaraki University) |
| Title | On Mahler's conjecture for convex bodies |
| Date | October 27 (Wed.) 2021, 17:00～18:00 |
| Place | Dept. of Mathematics, Faculty of Science Bldg., E408 & Zoom Registration （Please register by 9:00 on October 26th.） |
| Abstract | The product of volume of a centrally symmetric convex body in R^n and
its polar body is called Mahler volume (volume product),
which was first introduced in his work on "the geometry of numbers".
The upper bound estimate of Mahler volume is well-known as the Blaschke-Santal\'o inequality,
and the bound is attained only for ellipsoids.
In contrast, the problem for the sharp lower bound estimate is called Mahler conjecture(1939)
and it remains as one of the longstanding open problems in the field of convex geometry. In this talk, we explain the outline of the proof of the conjecture in the 3-dimensional case. If time permits, we also explain a weaker result of its higher dimensional case, and the relation between the Mahler conjecture and the Viterbo conjecture in the area of symplectic geometry. This talk is based on joint work with Masataka Shibata. |
| Speaker | Hiroyuki Minamoto (Osaka Prefecture University) |
| Title | On quiver Heisenberg algebras |
| Date | September 29 (Wed.) 2021, 17:00～18:00 |
| Place | Zoom Registration （Please register by 18:00 on the 27th in advance.） |
| Abstract | Recall that the preprojective algebra P(Q) of a quiver Q is the path algebra of the double quiver of Q with the mesh relations.
It is an important mathematical object having rich representation theory and plenty of applications. In this joint work with M. Herschend, we study a central extension H(Q) of P(Q) under the name ``quiver Heisenberg algebras''.
We note that our algebra H(Q) is a special case of central extensions of the preprojective algebras introduced by Etingof-Rains, which is a special case of N=1 quiver algebras introduced by Cachazo-Katz-Vafa,
which is a special family of the deformation of preprojective algebras introduced by Crawley-Boevey-Holland.
However, our algebra H(Q) of very special case has intriguing properties, among other things it provides an exact sequence of KQ-bimodules which can be called the universal Auslander-Reiten triangle. We construct an algebra B(Q) as an upper triangular matrix algebra from H(Q). Together with previous results about H(Q) by Etingof-Rains, Etingof-Latour-Rains and Eu-Schedler, our results show that H(Q) and B(Q) posses properties that can be looked as one-dimension higher versions of that of the preprojective algebras P(Q) and the path algebras KQ. |
| Speaker | Takamichi Sano (Osaka City University) |
| Title | On derivatives of Kato’s Euler system |
| Date | July 15 (Thurs.) 2021, 17:05～18:05 |
| Place | Dept. of Mathematics, Faculty of Science Bldg., E408 & Zoom Registration （Please register at least 2 days in advance.） |
| Abstract | The notion of Euler systems was introduced by Kolyvagin and Rubin around 1990. It has important applications to the Birch-Swinnerton-Dyer conjecture and Iwasawa main conjectures. Constructing an Euler system is regarded as a difficult problem, but Kazuya Kato constructed a new Euler system for elliptic curves in 2004. In this talk, we formulate a new conjecture on “derivatives” of Kato’s Euler system and explain that it generalizes the Perrin-Riou conjecture, the Mazur-Tate-Teitelbaum conjecture, and the Mazur-Tate conjecture. As an application, we give a partial solution to the Mazur-Tate conjecture. This talk is based on joint work with David Burns and Masato Kurihara. |
| Speaker | Yuichiro Taketomi (OCAMI) |
| Title | Maximal elements of moduli spaces of Riemannian metrics |
| Date | May 12 (Wed.) 2021, 17:00～18:00 |
| Place | Zoom Registration （Please register at least 2 days in advance.） |
| Abstract | For a given smooth manifold, we consider the moduli space of smooth Riemannian metrics up to isometry and scaling.
One can define a pre-order on the moduli space by the size of the conjugacy classes of the isometry groups in the diffeomorphism group.
We call a Riemannian metric that gives a maximal element with respect to the pre-order a maximal metric. The maximal metrics give nice examples of self-similar solutions for various metric evolution equations such as the Ricci flow. In this talk, we construct many examples of maximal metrics on the Euclidean spaces. |
