## 過去の記録

### 2022年12月20日(火)

#### 代数幾何学セミナー

9:30-10:30   数理科学研究科棟(駒場) オンラインZoom号室
Takumi Murayama 氏 (パーデュー大学)
The relative minimal model program for excellent algebraic spaces and analytic spaces in equal characteristic zero (English)
[ 講演概要 ]
In 2010, Birkar, Cascini, Hacon, and McKernan proved a relative version of the minimal model program for projective morphisms of complex quasi-projective varieties, called the relative minimal model program with scaling. Their result is now fundamental to our understanding of the birational classification of quasi-projective varieties and has numerous applications.
In this talk, I will discuss recent joint work with Shiji Lyu that establishes the relative minimal model program with scaling for excellent schemes, excellent algebraic spaces, and analytic spaces simultaneously in equal characteristic zero. This not only recovers previous results for complex varieties, complex algebraic spaces, and complex analytic spaces, but also greatly extends the scope of the relative minimal model program with scaling to a broader class of geometric spaces, including formal schemes, rigid analytic spaces, and Berkovich spaces, all in equal characteristic zero. Our results for (non-algebraic) schemes and rigid analytic spaces were previously only known in dimensions ≤3 and ≤2, respectively, and our results for formal schemes and Berkovich spaces are completely new.

#### 解析学火曜セミナー

16:00-17:30   数理科学研究科棟(駒場) 126号室

[ 講演概要 ]
Jan Boman's (Stockholm Univ.) recent two papers:
[1], Regularity of a distribution and of the boundary of its support, The Journal of Geometric Analysis vol.32, Article number: 300 (2022).
[2], A hypersurface containing the support of a Radon transform must be an ellipsoid. II: The general case; J. Inverse Ill-Posed Probl. 2021; 29(3): 351–367.
In [1] he proved "Let $f(x_1,…,x_n,y)$ be a non-zero distribution with support in a $C^1$ surface $N=\{y=F(x)\}$. If $f(x,y)$ is depending real analytically on x-variables, then $F(x)$ is analytic". As an application, he reinforced the main result of [2]. These results are obtained essentially by means of matrix algebra and a number theoretic method.
[ 参考URL ]
https://forms.gle/BpciRTzKh9FPUV8D7

#### 作用素環セミナー

16:45-18:15   オンライン開催

Band width and the Rosenberg index
[ 講演概要 ]
Band width is a concept recently proposed by Gromov. It is based on the idea that when a certain band (i.e., manifold with two boundaries) is openly immersed to a target manifold M with positive scalar curvature metric, then its width is bounded by a uniform constant called the band width of M. A qualitative consequence is that infiniteness of the band width of M obstructs to positive scalar curvature.
In this talk, infiniteness of a version of the band width, Zeidler's KO-band width, is dominated as a PSC obstruction by an existing obstruction, the Rosenberg index. This answers to a conjecture by Zeidler.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

### 2022年12月13日(火)

#### 代数幾何学セミナー

10:30-11:30   数理科学研究科棟(駒場) ハイブリッド開催/002号室

Moduli of G-constellations and crepant resolutions (日本語)
[ 講演概要 ]
For a finite subgroup G of SL_n(C), a moduli space of G-constellations is a generalization of the G-Hilbert scheme and is important from the viewpoint of McKay correspondence. In this talk I will explain its basic properties and show that every projective crepant resolution of C^3/G is isomorphic to such a moduli space.

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 128号室
Feng Xu 氏 (UC Riverside)
Entropy in QFT
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

#### トポロジー火曜セミナー

17:30-18:30   オンライン開催

Spectral convergence in geometric quantization on K3 surfaces (JAPANESE)
[ 講演概要 ]
In this talk I will explain the geometric quantization on K3 surfaces from the viewpoint of the spectral convergence. We take a special Lagrangian fibrations on the K3 surfaces and a family of hyper-Kähler structures tending to large complex structure limit and show a spectral convergence of the d-bar-Laplacians on the prequantum line bundle to the spectral structure related to the set of Bohr-Sommerfeld fibers.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

#### 解析学火曜セミナー

16:00-17:30   数理科学研究科棟(駒場) 126号室

Continuum limit problem of discrete Schrödinger operators on square lattices (Japanese)
[ 講演概要 ]
We consider discrete Schrödinger operators on the square lattice with its mesh size very small. The aim of this talk is to introduce the rigorous setting of continuum limit problems in the view point of operator theory and then to give its proof for the above operators, the one of which is defined on the vertices and the other of which is defined on the edges. This talk is based on joint works with Shu Nakamura (Gakushuin University) and Pavel Exner (Czech Academy of Science, Czech Technical University).
[ 参考URL ]
https://forms.gle/CRha8hydEuXzh71S7

### 2022年12月12日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

$L^2$-extension index and its applications (Japanese)
[ 講演概要 ]
In this talk, we introduce a new concept of $L^2$-extension indices. By using this notion, we propose a new way to study the positivity of curvature. We prove that there is an equivalence between how sharp the $L^2$-extension is and how positive the curvature is. As applications, we study Prekopa-type theorems and the positivity of a certain direct image sheaf.
[ 参考URL ]
https://forms.gle/hYT2hVhDE3q1wDSh6

### 2022年12月08日(木)

#### 情報数学セミナー

16:50-18:35   数理科学研究科棟(駒場) 123号室

Near-term 量子アルゴリズムと量子エラー抑制 (Japanese)
[ 講演概要 ]

### 2022年12月06日(火)

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 128号室

Equivariant covering spaces of quantum homogeneous spaces
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

#### トポロジー火曜セミナー

17:00-18:00   オンライン開催

Quentin Faes 氏 (東京大学大学院数理科学研究科)
Torsion in the abelianization of the Johnson kernel (ENGLISH)
[ 講演概要 ]
The Johnson kernel is the subgroup of the mapping class group of a closed oriented surface that is generated by Dehn twists along separating simple closed curves, and is also the second term of the so-called Johnson filtration of the mapping class group. The rational abelianization of this group is known, but it was recently proved by Nozaki, Sato and Suzuki, that the abelianization has torsion. They used the LMO homomorphism. In this talk, I will explain a purely two-dimensional proof of this result, which provides a lower bound for the cardinality of the torsion part of the abelianization. These results are also valid for the case of an open surface. This is joint work with Gwénaël Massuyeau.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

### 2022年12月05日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室

On sharper estimates of Ohsawa--Takegoshi $L^2$-extension theorem in higher dimensional case (Japanese)
[ 講演概要 ]
Hosono proposed an idea of getting an $L^2$-estimate sharper than the one of Berndtsson--Lempert type $L^2$-extension theorem by allowing constants depending on weight functions in $\mathbb{C}$.

In this talk, I explain the details of "sharper estimates" and the higher dimensional case of it. Also, I explain my recent studies related to it.
[ 参考URL ]
https://forms.gle/hYT2hVhDE3q1wDSh6

#### 統計数学セミナー

14:40-15:50   数理科学研究科棟(駒場) 号室

Michael Choi 氏 (National University of Singapore and Yale-NUS College)
A binary branching model with Moran-type interactions (English)
[ 講演概要 ]
Branching processes naturally arise as pertinent models in a variety of applications such as population size dynamics, neutron transport and cell proliferation kinetics. A key result for understanding the behaviour of such systems is the Perron Frobenius decomposition, which allows one to characterise the large time average behaviour of the branching process via its leading eigenvalue and corresponding left and right eigenfunctions. However, obtaining estimates of these quantities can be challenging, for example when the branching process is spatially dependent with inhomogeneous rates. In this talk, I will introduce a new interacting particle model that combines the natural branching behaviour of the underlying process with a selection and resampling mechanism, which allows one to maintain some control over the system and more efficiently estimate the eigenelements. I will then present the main result, which provides an explicit relation between the particle system and the branching process via a many-to-one formula and also quantifies the L^2 distance between the occupation measures of the two systems. Finally, I will discuss some examples in order to illustrate the scope and possible extensions of the model, and to provide some comparisons with the Fleming Viot interacting particle system. This is based on work with Alex Cox (University of Bath) and Denis Villemonais (Université de Lorraine).
[ 参考URL ]

### 2022年12月01日(木)

#### 情報数学セミナー

16:50-18:35   数理科学研究科棟(駒場) 123号室

[ 講演概要 ]

### 2022年11月30日(水)

#### 代数学コロキウム

17:00-18:00   ハイブリッド開催
Xinyao Zhang 氏 (東京大学大学院数理科学研究科)
The modularity of elliptic curves over some number fields (English)
[ 講演概要 ]
As a non-trivial case of the Langlands reciprocity conjecture, the modularity of elliptic curves always intrigues number theorists, and a famous result was proved for semistable elliptic curves over \mathbb{Q} by Andrew Wiles, implying Fermat's Last Theorem. In recent years, many new results have been proved using sufficiently powerful modularity lifting theorems. For instance, Thorne proved that elliptic curves over the cyclotomic \mathbb{Z}_p-extension of \mathbb{Q} are modular. In this talk, I will sketch some of these results and try to give a new one that elliptic curves over the cyclotomic \mathbb{Z}_p-extension of a real quadratic field are modular under some technical assumptions.

#### 離散数理モデリングセミナー

15:00-16:30   数理科学研究科棟(駒場) 128号室
Mikhail Bershtein 氏 (Skoltech・HSE / IPMU)
Folding transformations for q-Painleve equations (English)
[ 講演概要 ]
Folding transformation of the Painleve equations is an algebraic (of degree greater than 1) transformation between solutions of different equations. In 2005 Tsuda, Okamoto and Sakai classified folding transformations of differential Painleve equations. These transformations are in correspondence with automorphisms of affine Dynkin diagrams. We give a complete classification of folding transformations of the q-difference Painleve equations, these transformations are in correspondence with certain subdiagrams of the affine Dynkin diagrams (possibly with automorphism). The method is based on Sakai's approach to Painleve equations through rational surfaces.
Based on joint work with A. Shchechkin [arXiv:2110.15320]

### 2022年11月29日(火)

#### 解析学火曜セミナー

16:00-17:30   数理科学研究科棟(駒場) 126号室

Bernstein type theorem for the parabolic 2-Hessian equation under weaker assumptions (Japanese)
[ 講演概要 ]
In the early twentieth century, Bernstein proved that a minimal surface which can be expressed as the graph of a function defined in $\mathbb{R}^2$ must be a plane. For Monge-Ampère equation, it is known that a convex solution to $\det D^2 u=1$ in $\mathbb{R}^n$ must be a quadratic polynomial. Such kind of theorems, which we call Bernstein type theorems in this talk, have been extensively studied for various PDEs. For the parabolic $k$-Hessian equation, Bernstein type theorem has been proved by Nakamori and Takimoto (2015, 2016) under the convexity and some growth assumptions on the solution. In this talk, we shall obtain Bernstein type theorem for the parabolic 2-Hessian equation under weaker assumptions.
[ 参考URL ]
https://forms.gle/93YQ9C6DGYt5Vjuf7

#### トポロジー火曜セミナー

17:00-18:00   オンライン開催

GKM graph with legs and graph equivariant cohomology (JAPANESE)
[ 講演概要 ]
A GKM (Goresky-Kottiwicz-MacPherson) graph is a regular graph labeled on edges with some conditions. This notion has been introduced by Guillemin-Zara in 2001 to study the geometry of a nice class of manifolds with torus actions, called a GKM manifold, by a combinatorial way. In particular, we can define a ring on a GKM graph called a graph equivariant cohomology, and it is often isomorphic to the equivariant cohomology of a GKM manifold. In this talk, we introduce the GKM graph with legs (i.e., non-compact edges) related to non-compact manifolds with torus actions that may not satisfy the usual GKM conditions, and study the graph equivariant cohomology which is related to the GKM graph with legs. The talk is mainly based on the joint work with Grigory Solomadin (arXiv:2207.11380) and partially on the joint work with Vikraman Uma (arXiv:2106.11598).
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 128号室

Actions of tensor categories on $C^*$-algebras
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

#### 代数幾何学セミナー

10:30-11:30   数理科学研究科棟(駒場) ハイブリッド開催/002号室
Thomas Hall 氏 (University of Nottingham)
The behaviour of Kahler-Einstein polygons under combinatorial mutation
(English)
[ 講演概要 ]
Combinatorial mutations play an important role in the mirror symmetry approach to the classification of Fano varieties. Another important notion for Fano varieties is that of K-polystability, which turns out to have a nice combinatorial characterisation in the toric case. In this talk, I will give an overview of how mutations work and sketch the key ideas used to explore its interaction with Kahler-Einstein polygons (i.e. the Fano polygons whose associated toric variety is K-polystable).

### 2022年11月25日(金)

#### 談話会・数理科学講演会

15:30-16:30   ハイブリッド開催

Shane Kelly 氏 (東京大学大学院数理科学研究科)
Motivic cohomology: theory and applications
(ENGLISH)
[ 講演概要 ]
The motive of a smooth projective algebraic variety was originally envisaged by Grothendieck in the 60's as a generalisation of the Jacobian of a curve, and formed part of a strategy to prove the Weil conjectures. In the 90s, following conjectures of Beilinson on special values of L-functions, Voevodsky, together with Friedlander, Morel, Suslin, and others, generalised this to the A^1-homotopy type of a general algebraic variety. This A^1-homotopy theory lead to a proof of the Block-Kato conjecture (and a Fields Medal for Voevodsky).
One consequence of making things A^1-invariant is that unipotent groups (as well as wild ramification, irregular singularities, nilpotents including higher nilpotents in the sense of derived algebraic geometry, certain parts of K-theory, etc) become invisible and the last decade has seen a number of candidates for a non-A^1-invariant theory.
In this talk I will give an introduction to the classical theory and discuss some current and future research directions.
[ 参考URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZErcumupjouGdXpOac2j3rcFFN545yAuoSb

### 2022年11月24日(木)

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 370号室

シュタルク・シュレディンガー作用素に対する放射条件評価と定常散乱理論 (Japanese)
[ 講演概要 ]

[ 参考URL ]

#### 情報数学セミナー

16:50-18:35   数理科学研究科棟(駒場) 123号室

[ 講演概要 ]

### 2022年11月22日(火)

#### 代数幾何学セミナー

10:30-12:00   数理科学研究科棟(駒場) 002号室
90分ハイブリッド開催です。

Non-free sections of Fano fibrations (日本語)
[ 講演概要 ]
Manin’s Conjecture predicts the asymptotic formula for the counting function of rational points over number fields or global function fields. In the late 80’s, Batyrev developed a heuristic argument for Manin’s Conjecture over global function fields, and the assumptions underlying Batyrev’s heuristics are refined and formulated as Geometric Manin’s Conjecture. Geometric Manin’s Conjecture is a set of conjectures regarding properties of the space of sections of Fano fibrations, and it consists of three conjectures: (i) Pathological components are controlled by Fujita invariants; (ii) For each nef algebraic class, a non-pathological component which should be counted in Manin’s Conjecture is unique (This component is called as Manin components); (iii) Manin components exhibit homological or motivic stability. In this talk we discuss our proofs of GMC (i) over complex numbers using theory of foliations and the minimal model program. Using this result, we prove that these pathological components are coming from a bounded family of accumulating maps. This is joint work in progress with Brian Lehmann and Eric Riedl.

#### 作用素環セミナー

16:45-18:15   数理科学研究科棟(駒場) 128号室

Multiplicative characters and Gaussian fluctuation limits
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm