## 今後の予定

### 2017年03月06日(月)

#### 複素解析幾何セミナー

10:00-11:30   数理科学研究科棟(駒場) 128号室
いつもと時間が異なります。
Vladimir Matveev 氏 (University of Jena)
Projective and c-projective metric geometries: why they are so similar (ENGLISH)
[ 講演概要 ]
I will show an unexpected application of the standard techniques of integrable systems in projective and c-projective geometry (I will explain what they are and why they were studied). I will show that c-projectively equivalent metrics on a closed manifold generate a commutative isometric $\mathbb{R}^k$-action on the manifold. The quotients of the metrics w.r.t. this action are projectively equivalent, and the initial metrics can be uniquely reconstructed by the quotients. This gives an almost algorithmic way to obtain results in c-projective geometry starting with results in much better developed projective geometry. I will give many application of this algorithmic way including local description, proof of Yano-Obata conjecture for metrics of arbitrary signature, and describe the topology of closed manifolds admitting strictly nonproportional c-projectively equivalent metrics.
Most results are parts of two projects: one is joint with D. Calderbank, M. Eastwood and K. Neusser, and another is joint with A. Bolsinov and S. Rosemann.

### 2017年03月08日(水)

#### トポロジー火曜セミナー

17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
Arthur Soulié 氏 (Université de Strasbourg)
Action of the Long-Moody Construction on Polynomial Functors (ENGLISH)
[ 講演概要 ]
In 2016, Randal-Williams and Wahl proved homological stability with certain twisted coefficients for different families of groups, in particular the one of braid groups. In fact, they obtain the stability for coefficients given by functors satisfying polynomial conditions. We only know few examples of such functors. Among them, we have the functor given by the unreduced Burau representations. In 1994, Long and Moody gave a construction on representations of braid groups which associates a representation of Bn with a representation of Bn+1. This construction complexifies in a sense the initial representation: for instance, starting from a dimension one representation, one obtains the unreduced Burau representation. In this talk, I will present this construction from a functorial point of view. I will explain that the construction of Long and Moody defines an endofunctor, called the Long-Moody functor, between a suitable category of functors. Then, after defining strong polynomial functors in this context, I will prove that the Long-Moody functor increases by one the degree of strong polynomiality of a strong polynomial functor. Thus, the Long-Moody construction will provide new examples of twisted coefficients entering in the framework of Randal-Williams and Wahl.

### 2017年03月10日(金)

#### トポロジー火曜セミナー

17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00, Lie群論・表現論セミナーと合同
Lizhen Ji 氏 (University of Michigan)
Satake compactifications and metric Schottky problems (ENGLISH)
[ 講演概要 ]
The quotient of the Poincare upper half plane by the modular group SL(2, Z) is a basic locally symmetric space and also the moduli space of compact Riemann surfaces of genus 1, and it admits two important classes of generalization:

(1) Moduli spaces M_g of compact Riemann surfaces of genus g>1,

(2) Arithmetic locally symmetric spaces Γ \ G/K such as the Siegel modular variety A_g, which is also the moduli of principally polarized abelian varieties of dimension g.

There have been a lot of fruitful work to explore the similarity between these two classes of spaces, and there is also a direct interaction between them through the Jacobian (or period) map J: M_g --> A_g. In this talk, I will discuss some results along these lines related to the Stake compactifications and the Schottky problems on understanding the image J(M_g) in A_g from the metric perspective.

#### Lie群論・表現論セミナー

17:00-18:30   数理科学研究科棟(駒場) 056号室
トポロジー火曜セミナーと合同．場所がいつもと異なりますので，ご注意ください．
Lizhen Ji 氏 (University of Michigan, USA)
Satake compactifications and metric Schottky problems (English)
[ 講演概要 ]
The quotient of the Poincare upper half plane by the modular group SL(2, Z) is a basic locally symmetric space and also the moduli space of compact Riemann surfaces of genus 1, and it admits two important classes of generalization:

(1) Moduli spaces M_g of compact Riemann surfaces of genus g>1,

(2) Arithmetic locally symmetric spaces \Gamma \ G/K such as the Siegel modular variety A_g, which is also the moduli of principally polarized abelian varieties of dimension g.

There have been a lot of fruitful work to explore the similarity between these two classes of spaces, and there is also a direct interaction between them through the Jacobian (or period) map J: M_g --> A_g.
In this talk, I will discuss some results along these lines related to the Stake compactifications and the Schottky problems on understanding the image J(M_g) in A_g from the metric perspective.

### 2017年03月30日(木)

#### 代数学コロキウム

16:40-17:40   数理科学研究科棟(駒場) 056号室
いつもと曜日が異なりますのでご注意ください．
Haoyu Hu 氏 (東京大学数理科学研究科)
Logarithmic ramifications via pull-back to curves (English)
[ 講演概要 ]
Let X be a smooth variety over a perfect field of characteristic p>0, D a strict normal crossing divisor of X, U the complement of D in X, j:U—>X the canonical injection, and F a locally constant and constructible sheaf of F_l-modules on U (l is a prime number different from p). Using Abbes and Saito’s logarithmic ramification theory, we define a Swan divisor SW(j_!F), which supported on D. Let i:C-->X be a quasi-finite morphism from a smooth curve C to X. Following T. Saito’s idea, we compare the pull-back of SW(j_!F) to C with the Swan divisor of the pull-back of j_!F to C. It answers an expectation of Esnault and Kerz and generalizes the same result of Barrientos for rank 1 sheaves. As an application, we obtain a lower semi-continuity property for Swan divisors of an l-adic sheaf on a smooth fibration, which gives a generalization of Deligne and Laumon’s lower semi-continuity property of Swan conductors of l-adic sheaves on relative curves to higher relative dimensions. This application is a supplement of the semi-continuity of total dimension of vanishing cycles due to T. Saito and the lower semi-continuity of total dimension divisors due to myself and E. Yang.

### 2017年10月17日(火)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Hoài-Minh Nguyên 氏 (École Polytechnique Fédérale de Lausanne)