## Future seminars

Seminar information archive ～04/27｜Today's seminar 04/28 | Future seminars 04/29～

### 2017/05/08

#### Seminar on Geometric Complex Analysis

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

Semipositivity theorems for a variation of Hodge structure

**Taro Fujisawa**(Tokyo Denki University)Semipositivity theorems for a variation of Hodge structure

[ Abstract ]

I will talk about my recent joint work with Osamu Fujino. The main purpose of our joint work is to generalize the Fujita-Zukcer-Kawamata semipositivity theorem from the analytic viewpoint. In this talk, I would like to illustrate the relation between the two objects, the asymptotic behavior of a variation of Hodge structure and good properties of the induced singular hermitian metric on an invertible subbundle of the Hodge bundle.

I will talk about my recent joint work with Osamu Fujino. The main purpose of our joint work is to generalize the Fujita-Zukcer-Kawamata semipositivity theorem from the analytic viewpoint. In this talk, I would like to illustrate the relation between the two objects, the asymptotic behavior of a variation of Hodge structure and good properties of the induced singular hermitian metric on an invertible subbundle of the Hodge bundle.

#### Geometry Colloquium

16:00-17:00 Room #056 (Graduate School of Math. Sci. Bldg.)

### 2017/05/09

#### Tuesday Seminar on Topology

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

Local and global coincidence homology classes (JAPANESE)

**Tatsuo Suwa**(Hokkaido University)Local and global coincidence homology classes (JAPANESE)

[ Abstract ]

We consider two differentiable maps between two oriented manifolds. In the case the manifolds are compact with the same dimension and the coincidence points are isolated, there is the Lefschetz coincidence point formula, which generalizes his fixed point formula. In this talk we discuss the case where the dimensions of the manifolds may possible be different so that the coincidence points are not isolated in general. In fact it seems that Lefschetz himself already considered this case (cf. [4]).

We introduce the local and global coincidence homology classes and state a general coincidence point theorem.

We then give some explicit expressions for the local class. We also take up the case of several maps as considered in [1] and perform similar tasks. These all together lead to a generalization of the aforementioned Lefschetz formula. The key ingredients are the Alexander duality in combinatorial topology, intersection theory with maps and the Thom class in Čech-de Rham cohomology. The contents of the talk are in [2] and [3].

References

[1] C. Biasi, A.K.M. Libardi and T.F.M. Monis,

[2] C. Bisi, F. Bracci, T. Izawa and T. Suwa,

[3] J.-P. Brasselet and T. Suwa,

[4] N.E. Steenrod,

We consider two differentiable maps between two oriented manifolds. In the case the manifolds are compact with the same dimension and the coincidence points are isolated, there is the Lefschetz coincidence point formula, which generalizes his fixed point formula. In this talk we discuss the case where the dimensions of the manifolds may possible be different so that the coincidence points are not isolated in general. In fact it seems that Lefschetz himself already considered this case (cf. [4]).

We introduce the local and global coincidence homology classes and state a general coincidence point theorem.

We then give some explicit expressions for the local class. We also take up the case of several maps as considered in [1] and perform similar tasks. These all together lead to a generalization of the aforementioned Lefschetz formula. The key ingredients are the Alexander duality in combinatorial topology, intersection theory with maps and the Thom class in Čech-de Rham cohomology. The contents of the talk are in [2] and [3].

References

[1] C. Biasi, A.K.M. Libardi and T.F.M. Monis,

*The Lefschetz coincidence class of p maps*, Forum Math. 27 (2015), 1717-1728.[2] C. Bisi, F. Bracci, T. Izawa and T. Suwa,

*Localized intersection of currents and the Lefschetz coincidence point theorem*, Annali di Mat. Pura ed Applicata 195 (2016), 601-621.[3] J.-P. Brasselet and T. Suwa,

*Local and global coincidence homology classes*, arXiv:1612.02105.[4] N.E. Steenrod,

*The work and influence of Professor Lefschetz in algebraic topology*, Algebraic Geometry and Topology: A Symposium in Honor of Solomon Lefschetz, Princeton Univ. Press 1957, 24-43.#### Algebraic Geometry Seminar

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

Upper bound of the multiplicity of locally complete intersection singularities (English)

**Kohsuke Shibata**(The University of Tokyo)Upper bound of the multiplicity of locally complete intersection singularities (English)

[ Abstract ]

The multiplicity of a point on a variety is a fundamental invariant to estimate how the singularity is bad. It is introduced in a purely algebraic context. On the other hand, we can also attach to the singularity the log canonical threshold and the minimal log discrepancy, which are introduced in a birational theoretic context. In this talk, we show bounds of the multiplicity by functions of these birational invariants for a singularity of locally a complete intersection. As an application, we obtain the affirmative answer to Watanabe’s conjecture on the multiplicity of canonical singularity of locally a complete intersection up to dimension 32.

The multiplicity of a point on a variety is a fundamental invariant to estimate how the singularity is bad. It is introduced in a purely algebraic context. On the other hand, we can also attach to the singularity the log canonical threshold and the minimal log discrepancy, which are introduced in a birational theoretic context. In this talk, we show bounds of the multiplicity by functions of these birational invariants for a singularity of locally a complete intersection. As an application, we obtain the affirmative answer to Watanabe’s conjecture on the multiplicity of canonical singularity of locally a complete intersection up to dimension 32.

### 2017/05/10

#### Number Theory Seminar

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

Wild ramification and restrictions to curves (JAPANESE)

**Hiroki Kato**(University of Tokyo)Wild ramification and restrictions to curves (JAPANESE)

### 2017/05/15

#### Seminar on Geometric Complex Analysis

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

On the moduli spaces of the tangent cones at infinity of some hyper-Kähler manifolds

**Kota Hattori**(Keio University)On the moduli spaces of the tangent cones at infinity of some hyper-Kähler manifolds

[ Abstract ]

For a metric space $(X,d)$, the Gromov-Hausdorff limit of $(X, a_n d)$ as $a_n \rightarrow 0$ is called the tangent cone at infinity of $(X,d)$. Although the tangent cone at infinity always exists if $(X,d)$ comes from a complete Riemannian metric with nonnegative Ricci curvature, the uniqueness does not hold in general. Colding and Minicozzi showed the uniqueness under the assumption that $(X,d)$ is a Ricci-flat manifold satisfying some additional conditions.

In this talk, I will explain a example of noncompact complete hyper-Kähler manifold who has several tangent cones at infinity, and determine the moduli space of them.

For a metric space $(X,d)$, the Gromov-Hausdorff limit of $(X, a_n d)$ as $a_n \rightarrow 0$ is called the tangent cone at infinity of $(X,d)$. Although the tangent cone at infinity always exists if $(X,d)$ comes from a complete Riemannian metric with nonnegative Ricci curvature, the uniqueness does not hold in general. Colding and Minicozzi showed the uniqueness under the assumption that $(X,d)$ is a Ricci-flat manifold satisfying some additional conditions.

In this talk, I will explain a example of noncompact complete hyper-Kähler manifold who has several tangent cones at infinity, and determine the moduli space of them.

### 2017/05/16

#### Algebraic Geometry Seminar

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

TBA (English)

**Katsuhisa Furukawa**(The University of Tokyo)TBA (English)

[ Abstract ]

TBA

TBA

#### Tuesday Seminar on Topology

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

Twisted Alexander invariants and Hyperbolic volume of knots (JAPANESE)

**Hiroshi Goda**(Tokyo University of Agriculture and Technology)Twisted Alexander invariants and Hyperbolic volume of knots (JAPANESE)

[ Abstract ]

In [1], Müller investigated the asymptotics of the Ray-Singer analytic torsion of hyperbolic 3-manifolds, and then Menal-Ferrer and Porti [2] have obtained a formula on the volume of a hyperbolic 3-manifold using the Higher-dimensional Reidemeister torsion.

On the other hand, Yoshikazu Yamaguchi has shown that a relationship between the twisted Alexander polynomial and the Reidemeister torsion associated with the adjoint representation of the holonomy representation of a hyperbolic 3-manifold in his thesis [3].

In this talk, we observe that Yamaguchi's idea is applicable to the Higher-dimensional Reidemeister torsion, then we give a volume formula of a hyperbolic knot using the twisted Alexander polynomial.

References

[1] Müller, W., The asymptotics of the Ray-Singer analytic torsion of hyperbolic 3-manifolds, Metric and differential geometry, 317--352, Progr. Math., 297, Birkhäuser/Springer, Basel, 2012.

[2] Menal-Ferrer, P. and Porti, J., Higher-dimensional Reidemeister torsion invariants for cusped hyperbolic 3-manifolds. J. Topol., 7 (2014), no. 1, 69--119.

[3] Yamaguchi, Y., On the non-acyclic Reidemeister torsion for knots, Dissertation at the University of Tokyo, 2007.

In [1], Müller investigated the asymptotics of the Ray-Singer analytic torsion of hyperbolic 3-manifolds, and then Menal-Ferrer and Porti [2] have obtained a formula on the volume of a hyperbolic 3-manifold using the Higher-dimensional Reidemeister torsion.

On the other hand, Yoshikazu Yamaguchi has shown that a relationship between the twisted Alexander polynomial and the Reidemeister torsion associated with the adjoint representation of the holonomy representation of a hyperbolic 3-manifold in his thesis [3].

In this talk, we observe that Yamaguchi's idea is applicable to the Higher-dimensional Reidemeister torsion, then we give a volume formula of a hyperbolic knot using the twisted Alexander polynomial.

References

[1] Müller, W., The asymptotics of the Ray-Singer analytic torsion of hyperbolic 3-manifolds, Metric and differential geometry, 317--352, Progr. Math., 297, Birkhäuser/Springer, Basel, 2012.

[2] Menal-Ferrer, P. and Porti, J., Higher-dimensional Reidemeister torsion invariants for cusped hyperbolic 3-manifolds. J. Topol., 7 (2014), no. 1, 69--119.

[3] Yamaguchi, Y., On the non-acyclic Reidemeister torsion for knots, Dissertation at the University of Tokyo, 2007.

### 2017/05/22

#### Seminar on Geometric Complex Analysis

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

Complex K3 surfaces containing Levi-flat hypersurfaces

**Takayuki Koike**(Kyoto University)Complex K3 surfaces containing Levi-flat hypersurfaces

[ Abstract ]

We show the existence of a complex K3 surface $X$ which is not a Kummer surface and has a one-parameter family of Levi-flat hypersurfaces in which all the leaves are dense. We construct such $X$ by patching two open complex surfaces obtained as the complements of tubular neighborhoods of elliptic curves embedded in blow-ups of the projective planes at general nine points.

We show the existence of a complex K3 surface $X$ which is not a Kummer surface and has a one-parameter family of Levi-flat hypersurfaces in which all the leaves are dense. We construct such $X$ by patching two open complex surfaces obtained as the complements of tubular neighborhoods of elliptic curves embedded in blow-ups of the projective planes at general nine points.

#### Operator Algebra Seminars

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

(English)

**Toshihiko Masuda**(Kyushu Univ.)(English)

#### Tokyo Probability Seminar

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

TBA (JAPANESE)

**Yoshihiro Tawara**(National Institute of Technology, Nagaoka College)TBA (JAPANESE)

### 2017/05/23

#### Tuesday Seminar on Topology

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

Johnson homomorphisms, stable and unstable (ENGLISH)

**Richard Hain**(Duke University)Johnson homomorphisms, stable and unstable (ENGLISH)

[ Abstract ]

In this talk I will recall how motivic structures (Hodge and/or Galois) on the relative completions of mapping class groups yield non-trivial information about Johnson homomorphisms. I will explain how these motivic structures can be pasted, and why I believe that the genus 1 case is of fundamental importance in studying the higher genus (stable) case.

In this talk I will recall how motivic structures (Hodge and/or Galois) on the relative completions of mapping class groups yield non-trivial information about Johnson homomorphisms. I will explain how these motivic structures can be pasted, and why I believe that the genus 1 case is of fundamental importance in studying the higher genus (stable) case.

### 2017/05/26

#### Colloquium

15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)

ループ空間上のスペクトルギャップの漸近挙動について (JAPANESE)

**Shigeki Aida**(Graduate School of Mathematical Sciences, The University of Tokyo)ループ空間上のスペクトルギャップの漸近挙動について (JAPANESE)

### 2017/05/29

#### Seminar on Geometric Complex Analysis

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

LCK structures on compact solvmanifolds

**Hiroshi Sawai**(National Institute of Technology, Numazu College)LCK structures on compact solvmanifolds

[ Abstract ]

A locally conformal Kähler (in short LCK) manifold is said to be Vaisman if Lee form is parallel with respect to Levi-Civita connection. In this talk, we prove that a Vaisman structure on a compact solvmanifolds depends only on the form of the fundamental 2-form, and it do not depends on a complex structure. As an application, we give the structure theorem for Vaisman (completely solvable) solvmanifolds and LCK nilmanifolds. Moreover, we show the existence of LCK solvmanifolds without Vaisman structures.

A locally conformal Kähler (in short LCK) manifold is said to be Vaisman if Lee form is parallel with respect to Levi-Civita connection. In this talk, we prove that a Vaisman structure on a compact solvmanifolds depends only on the form of the fundamental 2-form, and it do not depends on a complex structure. As an application, we give the structure theorem for Vaisman (completely solvable) solvmanifolds and LCK nilmanifolds. Moreover, we show the existence of LCK solvmanifolds without Vaisman structures.

#### Operator Algebra Seminars

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

On fundamental groups of tensor product II$_1$ factors (English)

**Yusuke Isono**(RIMS, Kyoto Univ.)On fundamental groups of tensor product II$_1$ factors (English)

### 2017/05/30

#### Tuesday Seminar on Topology

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

On a conjecture of Dunfield, Friedl and Jackson for hyperbolic knots (JAPANESE)

**Takayuki Morifuji**(Keio University)On a conjecture of Dunfield, Friedl and Jackson for hyperbolic knots (JAPANESE)

[ Abstract ]

The hyperbolic torsion polynomial is defined to be the twisted Alexander polynomial associated to the holonomy representation of a hyperbolic knot. Dunfield, Friedl and Jackson conjecture that the hyperbolic torsion polynomial determines the genus and fiberedness of a hyperbolic knot. In this talk we will survey recent results on the conjecture and explain its generalization to hyperbolic links.

The hyperbolic torsion polynomial is defined to be the twisted Alexander polynomial associated to the holonomy representation of a hyperbolic knot. Dunfield, Friedl and Jackson conjecture that the hyperbolic torsion polynomial determines the genus and fiberedness of a hyperbolic knot. In this talk we will survey recent results on the conjecture and explain its generalization to hyperbolic links.

#### Infinite Analysis Seminar Tokyo

17:30-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)

$Q$-functions associated to the root system of type $C$ (JAPANESE)

**Soichi Okada**(Graduate School of Mathematics, Nagoya University)$Q$-functions associated to the root system of type $C$ (JAPANESE)

[ Abstract ]

Schur $Q$-functions are a family of symmetric functions introduced

by Schur in his study of projective representations of symmetric

groups. They are obtained by putting $t=-1$ in the Hall-Littlewood

functions associated to the root system of type $A$. (Schur

functions are the $t=0$ specialization.) This talk concerns

symplectic $Q$-functions, which are obtained by putting $t=-1$

in the Hall-Littlewood functions associated to the root system

of type $C$. We discuss several Pfaffian identities as well

as a combinatorial description for them. Also we present some

positivity conjectures.

Schur $Q$-functions are a family of symmetric functions introduced

by Schur in his study of projective representations of symmetric

groups. They are obtained by putting $t=-1$ in the Hall-Littlewood

functions associated to the root system of type $A$. (Schur

functions are the $t=0$ specialization.) This talk concerns

symplectic $Q$-functions, which are obtained by putting $t=-1$

in the Hall-Littlewood functions associated to the root system

of type $C$. We discuss several Pfaffian identities as well

as a combinatorial description for them. Also we present some

positivity conjectures.

### 2017/06/06

#### Algebraic Geometry Seminar

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

TBA (English)

https://sites.google.com/site/chenjiangmath/

**Chen Jiang**(IPMU)TBA (English)

[ Abstract ]

TBA

[ Reference URL ]TBA

https://sites.google.com/site/chenjiangmath/

### 2017/06/12

#### Seminar on Geometric Complex Analysis

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

TBA

**Yoshihiko Matsumoto**(Osaka University)TBA

[ Abstract ]

TBA

TBA

#### Algebraic Geometry Seminar

15:30-17:00 Room #056 (Graduate School of Math. Sci. Bldg.)

TBA (English)

**Ivan Cheltsov**(The University of Edinburgh)TBA (English)

[ Abstract ]

TBA

TBA

### 2017/06/19

#### Seminar on Geometric Complex Analysis

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

TBA

**Yuya Takeuchi**(The University of Tokyo)TBA

[ Abstract ]

TBA

TBA

### 2017/06/26

#### Seminar on Geometric Complex Analysis

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

TBA

**Akito Futaki**(The University of Tokyo)TBA

[ Abstract ]

TBA

TBA

#### Operator Algebra Seminars

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

TBA (English)

**David Kerr**(Texas A & M Univ.)TBA (English)

### 2017/07/03

#### Seminar on Geometric Complex Analysis

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

TBA

**Yasuyuki Nagatomo**(Meiji University)TBA

[ Abstract ]

TBA

TBA

### 2017/07/10

#### Tokyo Probability Seminar

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

TBA (ENGLISH)

**Mei Yin**(University of Denver)TBA (ENGLISH)