## Seminar information archive

Seminar information archive ～02/23｜Today's seminar 02/24 | Future seminars 02/25～

#### Algebraic Geometry Seminar

15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

On the Picard number of Fano 6-folds with a non-small contraction (English)

**Taku Suzuki**(Waseda University)On the Picard number of Fano 6-folds with a non-small contraction (English)

[ Abstract ]

A generalization of S. Mukai's conjecture says that $\rho(i-1) \leq n$ holds for any Fano $n$-fold with Picard number $\rho$ and pseudo-index $i$, with equality if and only if it is isomorphic to $(\mathbb{P}^{i-1})^{\rho}$. In this talk, we consider this conjecture for $n=6$, which is an open problem, and give a proof of some special cases.

A generalization of S. Mukai's conjecture says that $\rho(i-1) \leq n$ holds for any Fano $n$-fold with Picard number $\rho$ and pseudo-index $i$, with equality if and only if it is isomorphic to $(\mathbb{P}^{i-1})^{\rho}$. In this talk, we consider this conjecture for $n=6$, which is an open problem, and give a proof of some special cases.

#### Numerical Analysis Seminar

16:50-18:20 Room #002 (Graduate School of Math. Sci. Bldg.)

Theory and application of the method of fundamental solutions (日本語)

**Koya Sakakibara**(University of Tokyo)Theory and application of the method of fundamental solutions (日本語)

### 2017/04/24

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Lagrangian Mean Curvature Flows and Moment maps

**Hiroshi Konno**(Meiji University)Lagrangian Mean Curvature Flows and Moment maps

[ Abstract ]

In this talk, we construct various examples of Lagrangian mean curvature flows in Calabi-Yau manifolds, using moment maps for actions of abelian Lie groups on them. The examples include Lagrangian self-shrinkers and translating solitons in the Euclid spaces. We also construct Lagrangian mean curvature flows in non-flat Calabi-Yau manifolds. In particular, we describe Lagrangian mean curvature flows in 4-dimensional Ricci-flat ALE spaces in detail and investigate their singularities.

In this talk, we construct various examples of Lagrangian mean curvature flows in Calabi-Yau manifolds, using moment maps for actions of abelian Lie groups on them. The examples include Lagrangian self-shrinkers and translating solitons in the Euclid spaces. We also construct Lagrangian mean curvature flows in non-flat Calabi-Yau manifolds. In particular, we describe Lagrangian mean curvature flows in 4-dimensional Ricci-flat ALE spaces in detail and investigate their singularities.

#### Operator Algebra Seminars

16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Bass-Serre trees of amalgamated free product $C^*$-algebras (English)

**Kei Hasegawa**(Kyushu Univ.)Bass-Serre trees of amalgamated free product $C^*$-algebras (English)

#### Tokyo Probability Seminar

16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Rough differential equations containing path-dependent bounded variation terms (JAPANESE)

**Shigeki Aida**(Graduate School of Mathematical Science, the University of Tokyo)Rough differential equations containing path-dependent bounded variation terms (JAPANESE)

### 2017/04/20

#### Seminar on Probability and Statistics

15:00- Room #117 (Graduate School of Math. Sci. Bldg.)

Central limit theorem for symmetric integrals

Stochastic heat equation with rough multiplicative noise

**David Nualart**(Kansas University) -Central limit theorem for symmetric integrals

**David Nualart**(Kansas University) -Stochastic heat equation with rough multiplicative noise

[ Abstract ]

The aim of this talk is to present some results on the existence and uniqueness of a solution for the one-dimensional heat equation driven by a Gaussian noise which is white in time and it has the covariance of a fractional Brownian motion with Hurst parameter less than 1/2 in the space variable. In the linear case we establish a Feynman-Kac formula for the moments of the solution and discuss intermittency properties.

The aim of this talk is to present some results on the existence and uniqueness of a solution for the one-dimensional heat equation driven by a Gaussian noise which is white in time and it has the covariance of a fractional Brownian motion with Hurst parameter less than 1/2 in the space variable. In the linear case we establish a Feynman-Kac formula for the moments of the solution and discuss intermittency properties.

### 2017/04/18

#### Algebraic Geometry Seminar

15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

On the existence of almost Fano threefolds with del Pezzo fibrations (English)

**Takeru Fukuoka**(The University of Tokyo)On the existence of almost Fano threefolds with del Pezzo fibrations (English)

[ Abstract ]

We say that a smooth projective 3-fold is almost Fano if its anti-canonical divisor is nef and big but not ample. By Jahnke-Peternell-Radloff and Takeuchi, the numerical classification of such 3-folds was given. Among the classification results, there exists precisely 10 cases such that it was yet to be known whether these have an example or not. The main result of this talk shows the existence of examples of each of 10 cases. In 9 cases of the 10 cases, the degree of del Pezzo fibrations are 6. We will discuss one of the reason of difficulty constructing del Pezzo fibrations of degree 6. After that, we will show that every almost Fano del Pezzo fibration of degree 6 with specific anti-canonical volume can be embedded into some higher dimensional del Pezzo fibration as a relative linear section.

We say that a smooth projective 3-fold is almost Fano if its anti-canonical divisor is nef and big but not ample. By Jahnke-Peternell-Radloff and Takeuchi, the numerical classification of such 3-folds was given. Among the classification results, there exists precisely 10 cases such that it was yet to be known whether these have an example or not. The main result of this talk shows the existence of examples of each of 10 cases. In 9 cases of the 10 cases, the degree of del Pezzo fibrations are 6. We will discuss one of the reason of difficulty constructing del Pezzo fibrations of degree 6. After that, we will show that every almost Fano del Pezzo fibration of degree 6 with specific anti-canonical volume can be embedded into some higher dimensional del Pezzo fibration as a relative linear section.

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Milnor invariants via unipotent Magnus embeddings (JAPANESE)

**Takefumi Nosaka**(Tokyo institute of Technology)Milnor invariants via unipotent Magnus embeddings (JAPANESE)

[ Abstract ]

We reconfigured the Milnor invariant, in terms of central group extensions and unipotent Magnus embeddings, and develop a diagrammatic computation of the invariant. In this talk, we explain the reconfiguration and the computation with mentioning some examples. I also introduce some properties of the unipotent embeddings. This is a joint work with Hisatoshi Kodani.

We reconfigured the Milnor invariant, in terms of central group extensions and unipotent Magnus embeddings, and develop a diagrammatic computation of the invariant. In this talk, we explain the reconfiguration and the computation with mentioning some examples. I also introduce some properties of the unipotent embeddings. This is a joint work with Hisatoshi Kodani.

### 2017/04/17

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Dense holomorphic curves in spaces of holomorphic maps

**Yuta Kusakabe**(Osaka University)Dense holomorphic curves in spaces of holomorphic maps

[ Abstract ]

We study when there exists a dense holomorphic curve in a space of holomorphic maps from a Stein space. Our results state that for any bounded convex domain $\Omega \Subset \mathbb{C}^n$ and any connected complex manifold $Y$, the space $\mathcal{O}(\Omega,Y)$ contains a dense holomorphic disc, and that $Y$ is an Oka manifold if and only if for any Stein space $X$ there exists a dense entire curve in every path component of $\mathcal{O}(X,Y)$. The latter gives a new characterization of Oka manifolds. As an application of the former, we construct universal maps from bounded convex domains to any connected complex manifold.

We study when there exists a dense holomorphic curve in a space of holomorphic maps from a Stein space. Our results state that for any bounded convex domain $\Omega \Subset \mathbb{C}^n$ and any connected complex manifold $Y$, the space $\mathcal{O}(\Omega,Y)$ contains a dense holomorphic disc, and that $Y$ is an Oka manifold if and only if for any Stein space $X$ there exists a dense entire curve in every path component of $\mathcal{O}(X,Y)$. The latter gives a new characterization of Oka manifolds. As an application of the former, we construct universal maps from bounded convex domains to any connected complex manifold.

#### Operator Algebra Seminars

16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)

On diagonal actions whose full group is closed (English)

**Yoshikata Kida**(Univ. Tokyo)On diagonal actions whose full group is closed (English)

#### Tokyo Probability Seminar

16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Scaling limits of random walks via resistance forms (ENGLISH)

**David Croydon**(University of Warwick)Scaling limits of random walks via resistance forms (ENGLISH)

[ Abstract ]

In this talk, I will describe some recent work (partly joint with T. Kumagai, Kyoto University, and B. M. Hambly, University of Oxford) regarding scaling limits for random walks on spaces where the scaling limit of the associated resistance metric can be understood. This work is particularly applicable to "low-dimensional" graphs, whose scaling limits are trees and fractals, for example. It also gives a framework for understanding various time-changed processes on the spaces in question, such as those arising from Liouville Brownian motion, the Bouchaud trap model and the random conductance model.

In this talk, I will describe some recent work (partly joint with T. Kumagai, Kyoto University, and B. M. Hambly, University of Oxford) regarding scaling limits for random walks on spaces where the scaling limit of the associated resistance metric can be understood. This work is particularly applicable to "low-dimensional" graphs, whose scaling limits are trees and fractals, for example. It also gives a framework for understanding various time-changed processes on the spaces in question, such as those arising from Liouville Brownian motion, the Bouchaud trap model and the random conductance model.

### 2017/04/12

#### Number Theory Seminar

17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

A conjecture of Gross-Prasad and Rallis for metaplectic groups (JAPANESE)

**Hiraku Atobe**(University of Tokyo)A conjecture of Gross-Prasad and Rallis for metaplectic groups (JAPANESE)

### 2017/04/11

#### Number Theory Seminar

17:30-18:30 Room #117 (Graduate School of Math. Sci. Bldg.)

The geometric Satake equivalence in mixed characteristic (ENGLISH)

**Peter Scholze**(University of Bonn)The geometric Satake equivalence in mixed characteristic (ENGLISH)

[ Abstract ]

In order to apply V. Lafforgue's ideas to the study of representations of p-adic groups, one needs a version of the geometric Satake equivalence in that setting. For the affine Grassmannian defined using the Witt vectors, this has been proven by Zhu. However, one actually needs a version for the affine Grassmannian defined using Fontaine's ring B_dR, and related results on the Beilinson-Drinfeld Grassmannian over a self-product of Spa Q_p. These objects exist as diamonds, and in particular one can make sense of the fusion product in this situation; this is a priori surprising, as it entails colliding two distinct points of Spec Z. The focus of the talk will be on the geometry of the fusion product, and an analogue of the technically crucial ULA (Universally Locally Acyclic) condition that works in this non-algebraic setting.

In order to apply V. Lafforgue's ideas to the study of representations of p-adic groups, one needs a version of the geometric Satake equivalence in that setting. For the affine Grassmannian defined using the Witt vectors, this has been proven by Zhu. However, one actually needs a version for the affine Grassmannian defined using Fontaine's ring B_dR, and related results on the Beilinson-Drinfeld Grassmannian over a self-product of Spa Q_p. These objects exist as diamonds, and in particular one can make sense of the fusion product in this situation; this is a priori surprising, as it entails colliding two distinct points of Spec Z. The focus of the talk will be on the geometry of the fusion product, and an analogue of the technically crucial ULA (Universally Locally Acyclic) condition that works in this non-algebraic setting.

#### Numerical Analysis Seminar

16:50-18:20 Room #002 (Graduate School of Math. Sci. Bldg.)

Some issues in the Lagrange-Galerkin method and solutions: computability, dependence on the viscosity and inflow boundary conditions (日本語)

**Shinya Uchiumi**(Waseda University)Some issues in the Lagrange-Galerkin method and solutions: computability, dependence on the viscosity and inflow boundary conditions (日本語)

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Homotopy Lie algebroids (ENGLISH)

**Alexander Voronov**(University of Minnesota)Homotopy Lie algebroids (ENGLISH)

[ Abstract ]

A well-known result of A. Vaintrob [Vai97] characterizes Lie algebroids and their morphisms in terms of homological vector fields on supermanifolds. We give an interpretation of Lie bialgebroids and their morphisms in terms of odd symplectic dg-manifolds, building on the approach of D. Roytenberg [Roy99]. This extends naturally to the homotopy Lie case and leads to the notion of L

A well-known result of A. Vaintrob [Vai97] characterizes Lie algebroids and their morphisms in terms of homological vector fields on supermanifolds. We give an interpretation of Lie bialgebroids and their morphisms in terms of odd symplectic dg-manifolds, building on the approach of D. Roytenberg [Roy99]. This extends naturally to the homotopy Lie case and leads to the notion of L

_{∞}-bialgebroids and L_{∞}-morphisms between them.### 2017/04/10

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Slice theorem for CR structures near the sphere and its applications

**Kengo Hirachi**(The University of Tokyo)Slice theorem for CR structures near the sphere and its applications

[ Abstract ]

We formulate a slice theorem for CR structures by following Bland-Duchamp and give some applications to the rigidity theorems.

We formulate a slice theorem for CR structures by following Bland-Duchamp and give some applications to the rigidity theorems.

#### Operator Algebra Seminars

16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)

Reconstruction of the Bost-Connes groupoid from K-theoretic data (English)

**Yosuke Kubota**(Riken)Reconstruction of the Bost-Connes groupoid from K-theoretic data (English)

### 2017/04/06

#### Mathematical Biology Seminar

16:00-17:00 Room #126 (Graduate School of Math. Sci. Bldg.)

(JAPANESE)

**Shinji Nakaoka**(JAPANESE)

#### Mathematical Biology Seminar

17:00-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

#### Colloquium of mathematical sciences and society

15:00-16:00 Room #002 (Graduate School of Math. Sci. Bldg.)

### 2017/03/30

#### Number Theory Seminar

16:40-17:40 Room #056 (Graduate School of Math. Sci. Bldg.)

Logarithmic ramifications via pull-back to curves (English)

**Haoyu Hu**(University of Tokyo)Logarithmic ramifications via pull-back to curves (English)

[ Abstract ]

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.

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.

### 2017/03/22

#### FMSP Lectures

13:00- Room #117 (Graduate School of Math. Sci. Bldg.)

Lecture 1: Derived symplectic varieties and the Darboux theorem.

Lecture 2: The moduli of anti-canonically marked del Pezzo surfaces. (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Grojnowski.pdf

**Ian Grojnowski**(University of Cambridge)Lecture 1: Derived symplectic varieties and the Darboux theorem.

Lecture 2: The moduli of anti-canonically marked del Pezzo surfaces. (ENGLISH)

[ Reference URL ]

http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Grojnowski.pdf

### 2017/03/21

#### Colloquium

14:40-15:40 Room #大講義室 (Graduate School of Math. Sci. Bldg.)

A tour around microlocal analysis and algebraic analysis (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~kiyoomi/index.html

**Kiyoomi Kataoka**(Graduate School of Mathematical Sciences, The University of Tokyo)A tour around microlocal analysis and algebraic analysis (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~kiyoomi/index.html

#### Colloquium

16:00-17:00 Room #大講義室 (Graduate School of Math. Sci. Bldg.)

40 years along with stochastic analysis --- Motivated by statistical physics problems --- (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~funaki/

**Tadahisa Funaki**(Graduate School of Mathematical Sciences, The University of Tokyo)40 years along with stochastic analysis --- Motivated by statistical physics problems --- (JAPANESE)

[ Reference URL ]

http://www.ms.u-tokyo.ac.jp/~funaki/

### 2017/03/10

#### Tuesday Seminar on Topology

17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Satake compactifications and metric Schottky problems (ENGLISH)

**Lizhen Ji**(University of Michigan)Satake compactifications and metric Schottky problems (ENGLISH)

[ Abstract ]

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.

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.

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