## 過去の記録

### 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

#### トポロジー火曜セミナー

17:00-18:00   オンライン開催

Epimorphism between knot groups and isomorphisms on character varieties (JAPANESE)
[ 講演概要 ]
A partial order on the set of prime knots is given by the existence of an epimorphism between the fundamental groups of the knot complements. In this talk we will survey some basic properties of this order, and discuss some results and questions in connection with the SL(2,C)-character variety. In particular we study to what extend the SL(2,C)-character variety to determine the knot. This talk will be based on joint works with Michel Boileau(Univ. Aix-Marseille), Steven Sivek(Imperial College London), and Raphael Zentner(Univ. Regensburg).
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

### 2022年11月21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

Resolution of singularities for $C^{\infty}$ functions and meromorphy of local zeta functions (Japanese)
[ 講演概要 ]
In this talk, we attempt to resolve the singularities of the zero variety of a $C^{\infty}$ function of two variables as much as possible by using ordinary blowings up. As a result, we formulate an algorithm to locally express the zero variety in the “almost” normal crossings form, which is close to the normal crossings form but may include flat functions. As an application, we investigate analytic continuation of local zeta functions associated with  $C^{\infty}$ functions of two variables.
[ 参考URL ]
https://forms.gle/hYT2hVhDE3q1wDSh6

### 2022年11月17日(木)

#### 講演会

11:00-12:30   オンライン開催
Professor O. Emanouilov (Colorado State Univ.) による連続セミナー
Professor O. Emanouilov 氏 (Colorado State Univ.)
Inverse problems for partial differential equations: past and future works (English)
[ 参考URL ]
https://u-tokyo-ac-jp.zoom.us/j/88649482949?pwd=Yk9sNzJDNmNmZlRDeXAvcFFtcUkzUT09

#### 情報数学セミナー

16:50-18:20   数理科学研究科棟(駒場) 123号室

[ 講演概要 ]

### 2022年11月16日(水)

#### 代数学コロキウム

17:00-18:00   ハイブリッド開催
Zijian Yao 氏 (University of Chicago)
The eigencurve over the boundary of the weight space (English)
[ 講演概要 ]
The eigencurve is a geometric object that p-adically interpolates eigenforms of finite slope. The global geometry of the eigencurve is somewhat mysterious, except that over the boundary, it is predicted to behave rather nicely (by the so-called Halo conjecture). This conjecture has been studied by Liu--Wan--Xiao for definite quaternion algebras. In this talk, we will report on some work in progress on this conjecture in the case of GL2. If time permits, we will discuss some generalizations towards groups beyond GL2. This is partially joint with H. Diao.

### 2022年11月15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

Ring isomorphisms of locally measurable operator algebras
[ 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

Arthur Soulié 氏 (IBS Center for Geometry and Physics, POSTECH)
Stable cohomology of mapping class groups with some particular twisted contravariant coefficients (ENGLISH)
[ 講演概要 ]
The twisted cohomology of mapping class groups of compact orientable surfaces (with one boundary) is very difficult to compute generally speaking. In this talk, I will describe the computation of the stable cohomology algebra of these mapping class groups with twisted coefficients given by the first homology of the unit tangent bundle of the surface. This type of computation is out of the scope of the traditional framework for homological stability. Indeed, these twisted coefficients define a contravariant functor over the classical category associated to mapping class groups to study homological stability, rather than a covariant one. I will also present the computation of the stable cohomology algebras with with twisted coefficients given by the exterior powers and tensor powers of the first homology of the unit tangent bundle of the surface. All this represents a joint work with Nariya Kawazumi.
[ 参考URL ]
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html

#### 代数幾何学セミナー

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

Positivity of anticanonical divisors in algebraic fibre spaces (日本語)
[ 講演概要 ]
It is known that the positivity of the anti-canonical divisor is an important property that is closely related to the geometric structure of a variety. Given an algebraic fibre space f : X → Y between normal projective varieties with mild singularities, and let F be a general fibre of f. In this talk, we will introduce results relating the positivity of −KX and −KY under some conditions on the asymptotic base loci of −KX. In particular, we will obtain an inequality between the anti-canonical Iitaka dimensions κ(X, −KX) ≤ κ(F, −KF ) + κ(Y, −KY ) under the assumption that the stable base locus B(−KX) does not dominant over Y .

### 2022年11月14日(月)

#### 複素解析幾何セミナー

15:00-16:30   オンライン開催
オンラインのみで、開始時間が15:00からとなっておりますのでご注意ください。参加の際は参考URLからご登録ください。

The double holomorphic tangent space of the Teichmueller spaces (Japanese)
[ 講演概要 ]
The double holomorphic tangent space of a complex manifold is the holomorphic tangent space of the holomorphic tangent bundle of the complex manifold. In this talk, we will give an intrinsic description of the double tangent spaces of the Teichmueller spaces of closed Riemann surfaces of genus at least 2.
[ 参考URL ]
https://forms.gle/hYT2hVhDE3q1wDSh6

### 2022年11月10日(木)

#### 講演会

11:00-12:30   オンライン開催
Professor O. Emanouilov (Colorado State Univ.) による連続セミナー
Professor O. Emanouilov 氏 (Colorado State Univ.)
Inverse problems for partial differential equations: past and future works (English)
[ 参考URL ]
https://u-tokyo-ac-jp.zoom.us/j/88649482949?pwd=Yk9sNzJDNmNmZlRDeXAvcFFtcUkzUT09

### 2022年11月08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

On the type of the von Neumann algebra of an open subgroup of the Neretin group
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm