Seminar information archive

Seminar information archive ~03/28Today's seminar 03/29 | Future seminars 03/30~

2023/02/06

Applied Analysis

16:00-18:10   Room #126 (Graduate School of Math. Sci. Bldg.)
Marek Fila (Comenius University) 16:00-17:00
Solutions with moving singularities for nonlinear diffusion equations (ENGLISH)
[ Abstract ]
We give a survey of results on solutions with singularities moving along a prescribed curve for equations of fast diffusion or porous medium type. These results were obtained in collaboration with J.R. King, P. Mackova, J. Takahashi and E. Yanagida.
Petra Mackova (Comenius University) 17:10-18:10
Fast diffusion equation: uniqueness of solutions with a moving singularity (ENGLISH)
[ Abstract ]
This talk focuses on open questions in the area of the uniqueness of distributional solutions of the fast diffusion equation with a given source term. The existence of different sets of such solutions is known from previous research, and the natural next issue is to examine their uniqueness. Assuming that the source term is a measure, the existence of different classes of solutions is known, however, their uniqueness is an open problem. The existence of a class of asymptotically radially symmetric solutions with a singularity that moves along a prescribed curve was proved by M. Fila, J. Takahashi, and E. Yanagida. More recently, it has been established by M. Fila, P. M., J. Takahashi, and E. Yanagida that these solutions solve the corresponding problem with a moving Dirac source term. In this talk, we discuss the uniqueness of these solutions. This is a joint work with M. Fila.
[ Reference URL ]
https://forms.gle/nKa4XATuuGPwZWbUA

Algebraic Geometry Seminar

13:00-14:30   Room #123 (Graduate School of Math. Sci. Bldg.)
The 2nd lecture of series talks.
Chenyang Xu (Princeton University)
K-stability of Fano varieties. (English)
[ Abstract ]
The notion of K-stability of Fano varieties was first introduced to characterize the existence of Kahler-Einstein metric. Recently, a purely algebro-geometric theory has been developed and it has yielded many striking results, such as the solution of the Yau-Tian-Donaldson Conjecture for all Fano varieties, as well as the construction of a projective moduli scheme, called K-moduli, parametrizing K-polystable Fano varieties.

In this lecture series, I will survey the recent progress. The first two lectures will be devoted to explain the evolution of algebraic geometer’s understanding of various aspects of the notion of K-stability. The Lecture 3 and 4 will be devoted to discuss the construction of the K-moduli space.

2023/01/31

Algebraic Geometry Seminar

14:30-16:00   Room #ハイブリッド開催/002 (Graduate School of Math. Sci. Bldg.)
Shiji Lyu (Princeton University)
Some properties of splinters via ultrapower (English)
[ Abstract ]
A Noetherian (reduced) ring is called a splinter if it is a direct summand of every finite ring extension of it. This notion is related to various interesting notions of singularities, but far less properties are known about splinters.
In this talk, we will discuss the question of "regular ascent"; in the simplest (but already essential) form, we ask, for a Noetherian splinter R, is the polynomial ring R[X] always a splinter. We will see how ultrapower, a construction mainly belonging to model theory, is involved.

2023/01/27

Algebraic Geometry Seminar

13:00-14:30   Room #056 (Graduate School of Math. Sci. Bldg.)
4 lectures; 1/27: 13:00―14:30 Room056, 2/6: 13:00―14:30, Room 123, 2/17: 10:00―11:30,Room 123室 2/20 10:00ー11:30, Room:056室
Chenyang Xu (Princeton University)
K-stability of Fano varieties (English)
[ Abstract ]
The notion of K-stability of Fano varieties was first introduced to characterize the existence of Kahler-Einstein metric. Recently, a purely algebro-geometric theory has been developed and it has yielded many striking results, such as the solution of the Yau-Tian-Donaldson Conjecture for all Fano varieties, as well as the construction of a projective moduli scheme, called K-moduli, parametrizing K-polystable Fano varieties.

In this lecture series, I will survey the recent progress. The first two lectures will be devoted to explain the evolution of algebraic geometer’s understanding of various aspects of the notion of K-stability. The Lecture 3 and 4 will be devoted to discuss the construction of the K-moduli space.

thesis presentations

9:15-10:30   Room #118 (Graduate School of Math. Sci. Bldg.)
MATSUMOTO Keiho (Graduate School of Mathematical Sciences University of Tokyo)
Integral Derived Invariants and Motives
(整数導来不変量とモチーフ)

thesis presentations

9:15-10:30   Room #122 (Graduate School of Math. Sci. Bldg.)
YABE Takahiro (Graduate School of Mathematical Sciences University of Tokyo)
On classification of 2-generated axial algebras of Jordan and Majorana type
(Jordan型及びMajorana型の二元生成軸代数の分類について)

thesis presentations

9:15-10:30   Room #126 (Graduate School of Math. Sci. Bldg.)
TSURUHASHI Tomonori (Graduate School of Mathematical Sciences University of Tokyo)
On microscopic interpretation for convex integration and self- similar structure of vortices in turbulence
(凸積分法に関する微視的表現と乱流渦の自己相似構造について)

thesis presentations

11:00-12:15   Room #118 (Graduate School of Math. Sci. Bldg.)
SATO Ken (Graduate School of Mathematical Sciences University of Tokyo)
A group action on higher Chow cycles on a family of Kummer surfaces
(あるクンマー曲面族の上の高次チャウサイクルへの群作用について)

thesis presentations

11:00-12:15   Room #122 (Graduate School of Math. Sci. Bldg.)
HARAKO Shuichi (Graduate School of Mathematical Sciences University of Tokyo)
Manifolds Graded by an Arbitrary Abelian Group
(任意のアーベル群で次数付けられた多様体)

thesis presentations

11:00-12:15   Room #126 (Graduate School of Math. Sci. Bldg.)
SATO Shoichi (Graduate School of Mathematical Sciences University of Tokyo)
Various problems for properties of solutions to fractional partial differential equations
(非整数階偏微分方程式の解の性質に関する諸問題)

thesis presentations

13:00-14:15   Room #118 (Graduate School of Math. Sci. Bldg.)
ZHA Chenghan (Graduate School of Mathematical Sciences University of Tokyo)
Integral Structures in the Local Algebra of a Singularity
(特異点の局所代数の整構造について)

thesis presentations

13:00-14:15   Room #122 (Graduate School of Math. Sci. Bldg.)
SATOMI Takashi (Graduate School of Mathematical Sciences University of Tokyo)
Refinement of Young’s convolution inequality on locally compact groups and generalizations of related inequalities
(局所コンパクト群上のYoung の畳み込み不等式の精密化と関連の不等式の拡張)

2023/01/26

thesis presentations

9:15-10:30   Room #122号室 (Graduate School of Math. Sci. Bldg.)
OKUDA Nobuki (Graduate School of Mathematical Sciences University of Tokyo)
Fourier-Mukai transforms for non-commutative complex tori
(非可換複素トーラスのフーリエ・向井変換)

thesis presentations

11:00-12:15   Room #122 (Graduate School of Math. Sci. Bldg.)
ASAKA Takeru (Graduate School of Mathematical Sciences University of Tokyo)
Earthquake theorem and cluster algebras
(地震定理とクラスター代数)

thesis presentations

11:00-12:15   Room #126 (Graduate School of Math. Sci. Bldg.)
HAYASHI Kohei (Graduate School of Mathematical Sciences University of Tokyo)
On universality of the Kardar-Parisi-Zhang equation in high temperature regime
(高温相におけるKardar-Parisi-Zhang 方程式の普遍性について)

thesis presentations

13:00-14:15   Room #118 (Graduate School of Math. Sci. Bldg.)
WANG LONG (Graduate School of Mathematical Sciences University of Tokyo)
Studies on the Cone Conjecture, Automorphisms, and Arithmetic Degrees
(錐予想, 自己同型と算術次数の研究)

thesis presentations

13:00-14:15   Room #122 (Graduate School of Math. Sci. Bldg.)
KIM Minkyu (Graduate School of Mathematical Sciences University of Tokyo)
Finite path integral model and toric code based on homological algebra
(ホモロジー代数に基づく有限経路積分モデルとトーリックコード)

thesis presentations

14:45-16:00   Room #118 (Graduate School of Math. Sci. Bldg.)
TSURUSAKI Hisanori (Graduate School of Mathematical Sciences University of Tokyo)
Irreducible module decompositions of rank 2 symmetric hyperbolic Kac-Moody Lie algebras by sl2 subalgebras which are generalizations of principal sl2 subalgebras
(主sl2部分代数の一般化であるsl2部分代数によるrank2対称双曲型Kac-Moody Lie 代数の既約分解)

2023/01/20

Colloquium

15:30-16:30   Hybrid
If you do not belong to Graduate School of Mathematical Sciences, the University of Tokyo, please take part online [Reference URL].
Mikhail Bershtein (HSE University, Skoltech)
Kyiv formula and its applications (ENGLISH)
[ Abstract ]
The Kyiv formula gives the generic tau function of Painleve' equation (and more generally isomonodromy deformation equations) in terms of conformal blocks or Nekrasov partition function. I will explain the statement, examples and different approaches to the proof. If time permits, I will discuss some applications of this formula.
[ Reference URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZUrduioqjouG9wBfhl35VPxN_K92oa1wB4P

Tokyo-Nagoya Algebra Seminar

10:30-12:00   Online
Please see the reference URL for details on the online seminar.
Shunsuke Kano (Tohoku University)
Tropical cluster transformations and train track splittings (Japanese)
[ Reference URL ]
http://www.math.nagoya-u.ac.jp/~aaron.chan/TNAseminar.html

2023/01/19

Information Mathematics Seminar

16:50-18:35   Room #123 (Graduate School of Math. Sci. Bldg.)
Shintaro Narisada (KDDI Research, Inc.)
Code-based cryptography and its decoding algorithm (Japanese)
[ Abstract ]
This talk overviews code-based cryptography and its decoding algorithm called Information Set Decoding (ISD). All lectures will be given in Japanese.

2023/01/18

Number Theory Seminar

17:00-18:00   Hybrid
Kestutis Cesnavicius (Paris-Saclay University)
The affine Grassmannian as a presheaf quotient (English)
[ Abstract ]
The affine Grassmannian of a reductive group G is usually defined as the étale sheafification of the quotient of the loop group LG by the positive loop subgroup. I will discuss various triviality results for G-torsors which imply that this sheafification is often not necessary.

2023/01/17

Tuesday Seminar on Topology

17:00-18:00   Online
Pre-registration required. See our seminar webpage.
Chenghan Zha (The Univesity of Tokyo)
Integral structures in the local algebra of a singularity (ENGLISH)
[ Abstract ]
We compute the image of the Milnor lattice of an ADE singularity under a period map. We also prove that the Milnor lattice can be identified with an appropriate relative K-group defined through the Berglund-Huebsch dual of the corresponding singularity. Furthermore, we figure out the image of the Milnor lattice of the singularity of an invertible polynomial of chain type using the basis of middle homology constructed by Otani-Takahashi. We calculated the Seifert form of the basis as well.
[ Reference URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

2023/01/16

Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Takayuki Koike (Osaka Metropolitan University)
Holomorphic foliation associated with a semi-positive class of numerical dimension one (Japanese)
[ Abstract ]
Let $X$ be a compact Kähler manifold and $\alpha$ be a Dolbeault cohomology class of bidegree $(1,1)$ on $X$.
When the numerical dimension of $\alpha$ is one and $\alpha$ admits at least two smooth semi-positive representatives, we show the existence of a family of real analytic Levi-flat hypersurfaces in $X$ and a holomorphic foliation on a suitable domain of $X$ along whose leaves any semi-positive representative of $\alpha$ is zero.

As an application, we give the affirmative answer to a conjecture on the relation between the semi-positivity of the line bundle $[Y]$ and the analytic structure of a neighborhood of $Y$ for a smooth connected hypersurface $Y$ of $X$.

As an application, we give the affirmative answer to a conjecture on the relation between the semi-positivity of the line bundle $[Y]$ and the analytic structure of a neighborhood of $Y$ for a smooth connected hypersurface $Y$ of $X$.
[ Reference URL ]
https://forms.gle/hYT2hVhDE3q1wDSh6

2023/01/13

Discrete mathematical modelling seminar

13:15-14:45   Room #126 (Graduate School of Math. Sci. Bldg.)
Andy Hone (University of Kent)
An infinite sequence of Heron triangles with two rational medians (English)
[ Abstract ]
Triangles with integer length sides and integer area are known as Heron triangles. Taking rescaling freedom into account, one can apply the same name when all sides and the area are rational numbers. A perfect triangle is a Heron triangle with all three medians being rational, and it is a longstanding conjecture that no such triangle exists. However, despite an assertion by Schubert that even two rational medians are impossible, Buchholz and Rathbun showed that there are infinitely many Heron triangles with two rational medians, an infinite subset of which are associated with rational points on an elliptic curve E(Q) with Mordell-Weil group Z x Z/2Z, and they observed a connection with a pair of Somos-5 sequences. Here we make the latter connection more precise by providing explicit formulae for the integer side lengths, the two rational medians, and the area in this infinite family of Heron triangles. The proof uses a combined approach to Somos-5 sequences and associated Quispel-Roberts-Thompson (QRT) maps in the plane, from several different viewpoints: complex analysis, real dynamics, and reduction modulo a prime.

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