## Seminar information archive

Seminar information archive ～01/18｜Today's seminar 01/19 | Future seminars 01/20～

### 2015/01/21

#### Number Theory Seminar

18:00-19:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Spreading-out of rigid-analytic families and observations on p-adic Hodge theory (English)

**Ofer Gabber**(CNRS, IHES)Spreading-out of rigid-analytic families and observations on p-adic Hodge theory (English)

[ Abstract ]

(Joint work with Brian Conrad.) Let $K$ be a complete rank 1 valued field with ring of integers $O_K$, $A$ an adic noetherian ring and $f:A\to O_K$ an adic morphism. If $g:X\to Y$ is a proper flat morphism between rigid analytic spaces over $K$ then locally on $Y$ a flat formal model of $g$ spreads out to a proper flat morphism between formal schemes topologically of finite type over $A$. As an application one can prove that for proper smooth $g$ and $K$ of characteristic 0, the Hodge to de Rham spectral sequence for $g$ degenerates and the $R^q g_* \Omega^p_{X/Y}$ are locally free.

(Joint work with Brian Conrad.) Let $K$ be a complete rank 1 valued field with ring of integers $O_K$, $A$ an adic noetherian ring and $f:A\to O_K$ an adic morphism. If $g:X\to Y$ is a proper flat morphism between rigid analytic spaces over $K$ then locally on $Y$ a flat formal model of $g$ spreads out to a proper flat morphism between formal schemes topologically of finite type over $A$. As an application one can prove that for proper smooth $g$ and $K$ of characteristic 0, the Hodge to de Rham spectral sequence for $g$ degenerates and the $R^q g_* \Omega^p_{X/Y}$ are locally free.

#### Classical Analysis

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Remarks on the number of accessory parameters (JAPANESE)

**Shingo Kamimoto**(Kyoto University)Remarks on the number of accessory parameters (JAPANESE)

### 2015/01/20

#### PDE Real Analysis Seminar

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Maximum Principle and generalized principal eigenvalue for degenerate elliptic operators (English)

**Italo Capuzzo Dolcetta**(Università degli Studi di Roma "La Sapienza")Maximum Principle and generalized principal eigenvalue for degenerate elliptic operators (English)

[ Abstract ]

In my presentation I will report on a joint paper with H. Berestycki, A. Porretta and L. Rossi to appear shortly on JMPA.

We characterize the validity of the Maximum Principle in bounded domains for fully nonlinear degenerate elliptic operators in terms of the sign of a suitably defined generalized principal eigenvalue. Here, the maximum principle refers to the property of non-positivity of viscosity subsolutions of the Dirichlet problem.

The new notion of generalized principal eigenvalue that we introduce here allows us to deal with arbitrary type of degeneracy of the elliptic operators.

We further discuss the relations between this notion and other natural generalizations of the classical notion of principal eigenvalue, some of which have been previously introduced for particular classes of operators.

In my presentation I will report on a joint paper with H. Berestycki, A. Porretta and L. Rossi to appear shortly on JMPA.

We characterize the validity of the Maximum Principle in bounded domains for fully nonlinear degenerate elliptic operators in terms of the sign of a suitably defined generalized principal eigenvalue. Here, the maximum principle refers to the property of non-positivity of viscosity subsolutions of the Dirichlet problem.

The new notion of generalized principal eigenvalue that we introduce here allows us to deal with arbitrary type of degeneracy of the elliptic operators.

We further discuss the relations between this notion and other natural generalizations of the classical notion of principal eigenvalue, some of which have been previously introduced for particular classes of operators.

#### Tuesday Seminar on Topology

16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

On Lagrangian caps and their applications (JAPANESE)

**Toru Yoshiyasu**(The University of Tokyo)On Lagrangian caps and their applications (JAPANESE)

[ Abstract ]

In 2013, Y. Eliashberg and E. Murphy established the $h$-principle for

exact Lagrangian embeddings with a concave Legendrian boundary. In this

talk, I will explain a modification of their $h$-principle and show

applications to Lagrangian submanifolds in the complex projective spaces.

In 2013, Y. Eliashberg and E. Murphy established the $h$-principle for

exact Lagrangian embeddings with a concave Legendrian boundary. In this

talk, I will explain a modification of their $h$-principle and show

applications to Lagrangian submanifolds in the complex projective spaces.

### 2015/01/19

#### Seminar on Geometric Complex Analysis

10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Hyperbolic span and pseudoconvexity (Japanese)

**Hiroshi Yamaguchi**(Shia University, Prof. emeritus)Hyperbolic span and pseudoconvexity (Japanese)

[ Abstract ]

We show that the hyperbolic span for open torus (which is introduced by M. Shiba in 1993) has the intimate relation with the pseudoconvexity.

We show that the hyperbolic span for open torus (which is introduced by M. Shiba in 1993) has the intimate relation with the pseudoconvexity.

#### Numerical Analysis Seminar

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Between error and residual in numerical computations (日本語)

**Yoshitaka Watanabe**(Kyushu University)Between error and residual in numerical computations (日本語)

#### Algebraic Geometry Seminar

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

Crepant resolutions of Slodowy slice in nilpotent orbit closure in sl_N(C) (JAPANESE)

**Ryo Yamagishi**(Kyoto University)Crepant resolutions of Slodowy slice in nilpotent orbit closure in sl_N(C) (JAPANESE)

[ Abstract ]

Nilpotent orbit closures and their intersections with Slodowy slices are typical examples of symplectic varieties. It is known that every crepant resolution of a nilpotent orbit closure is obtained as a Springer resolution. In this talk, we show that every crepant resolution of a Slodowy slice in nilpotent orbit closure in sl_N(C) is obtained as the restriction of a Springer resolution and explain how to count the number of crepant resolutions. The proof of the main results is based on the fact that Slodowy slices can be described as quiver varieties.

Nilpotent orbit closures and their intersections with Slodowy slices are typical examples of symplectic varieties. It is known that every crepant resolution of a nilpotent orbit closure is obtained as a Springer resolution. In this talk, we show that every crepant resolution of a Slodowy slice in nilpotent orbit closure in sl_N(C) is obtained as the restriction of a Springer resolution and explain how to count the number of crepant resolutions. The proof of the main results is based on the fact that Slodowy slices can be described as quiver varieties.

### 2015/01/16

#### Geometry Colloquium

10:00-11:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Degeneration and curves on K3 surfaces (Japanese)

**Takeo Nishinou**(Rikkyo University)Degeneration and curves on K3 surfaces (Japanese)

[ Abstract ]

There is a well-known conjecture which states that all projective K3 surfaces contain infinitely many rational curves. By calculating obstructions in deformation theory through degeneration, we give a new approach to this problem. In particular, we show that there is a Zariski open subset in the moduli space of quartic K3 surfaces whose members fulfil the conjecture.

There is a well-known conjecture which states that all projective K3 surfaces contain infinitely many rational curves. By calculating obstructions in deformation theory through degeneration, we give a new approach to this problem. In particular, we show that there is a Zariski open subset in the moduli space of quartic K3 surfaces whose members fulfil the conjecture.

#### Seminar on Probability and Statistics

14:00-15:30 Room #052 (Graduate School of Math. Sci. Bldg.)

A stable particle filter in high-dimensions

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2014/06.html

**Ajay Jasra**(National University of Singapore)A stable particle filter in high-dimensions

[ Abstract ]

We consider the numerical approximation of the filtering problem in high dimensions, that is, when the hidden state lies in $\mathbb{R}^d$ with $d$ large. For low dimensional problems, one of the most popular numerical procedures for consistent inference is the class of approximations termed as particle filters or sequential Monte Carlo methods. However, in high dimensions, standard particle filters (e.g. the bootstrap particle filter) can have a cost that is exponential in $d$ for the algorithm to be stable in an appropriate sense. We develop a new particle filter, called the space-time particle filter, for a specific family of state-space models in discrete time. This new class of particle filters provide consistent Monte Carlo estimates for any fixed $d$, as do standard particle filters. Moreover, under a simple i.i.d. model structure, we show that in order to achieve some stability properties this new filter has cost $\mathcal{O}(nNd^2)$, where $n$ is the time parameter and $N$ is the number of Monte Carlo samples, that are fixed and independent of $d$. Similar results hold, under a more general structure than the i.i.d. one. Here we show that, under additional assumptions and with the same cost, the asymptotic variance of the relative estimate of the normalizing constant grows at most linearly in time and independently of the dimension. Our theoretical results are supported by numerical simulations. The results suggest that it is possible to tackle some high dimensional filtering problems using the space-time particle filter that standard particle filters cannot.

This is joint work with: Alex Beskos (UCL), Dan Crisan (Imperial), Kengo Kamatani (Osaka) and Yan Zhou (NUS).

[ Reference URL ]We consider the numerical approximation of the filtering problem in high dimensions, that is, when the hidden state lies in $\mathbb{R}^d$ with $d$ large. For low dimensional problems, one of the most popular numerical procedures for consistent inference is the class of approximations termed as particle filters or sequential Monte Carlo methods. However, in high dimensions, standard particle filters (e.g. the bootstrap particle filter) can have a cost that is exponential in $d$ for the algorithm to be stable in an appropriate sense. We develop a new particle filter, called the space-time particle filter, for a specific family of state-space models in discrete time. This new class of particle filters provide consistent Monte Carlo estimates for any fixed $d$, as do standard particle filters. Moreover, under a simple i.i.d. model structure, we show that in order to achieve some stability properties this new filter has cost $\mathcal{O}(nNd^2)$, where $n$ is the time parameter and $N$ is the number of Monte Carlo samples, that are fixed and independent of $d$. Similar results hold, under a more general structure than the i.i.d. one. Here we show that, under additional assumptions and with the same cost, the asymptotic variance of the relative estimate of the normalizing constant grows at most linearly in time and independently of the dimension. Our theoretical results are supported by numerical simulations. The results suggest that it is possible to tackle some high dimensional filtering problems using the space-time particle filter that standard particle filters cannot.

This is joint work with: Alex Beskos (UCL), Dan Crisan (Imperial), Kengo Kamatani (Osaka) and Yan Zhou (NUS).

http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2014/06.html

### 2015/01/15

#### Infinite Analysis Seminar Tokyo

15:00-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)

On Gram matrices of the Shapovalov form of a basic representation of a

quantum affine group (ENGLISH)

Continuous and Infinitesimal Hecke algebras (ENGLISH)

**Shunsuke Tsuchioka**(Graduate School of Mathematical Sciences, the University of Tokyo) 15:00-16:30On Gram matrices of the Shapovalov form of a basic representation of a

quantum affine group (ENGLISH)

[ Abstract ]

We consider Gram matrices of the Shapovalov form of a basic

representation

of a quantum affine group. We present a conjecture predicting the

invariant

factors of these matrices and proving that it gives the correct

invariants

when one specializes or localizes the ring $\mathbb{Z}[v,v^{-1}]$ in

certain ways.

This generalizes Evseev's theorem which settled affirmatively

the K\"{u}lshammer-Olsson-Robinson conjecture that predicts

the generalized Cartan invariants of the symmetric groups.

This is a joint work with Anton Evseev.

We consider Gram matrices of the Shapovalov form of a basic

representation

of a quantum affine group. We present a conjecture predicting the

invariant

factors of these matrices and proving that it gives the correct

invariants

when one specializes or localizes the ring $\mathbb{Z}[v,v^{-1}]$ in

certain ways.

This generalizes Evseev's theorem which settled affirmatively

the K\"{u}lshammer-Olsson-Robinson conjecture that predicts

the generalized Cartan invariants of the symmetric groups.

This is a joint work with Anton Evseev.

**Alexander Tsymbaliuk**(SCGP (Simons Center for Geometry and Physics)) 17:00-18:30Continuous and Infinitesimal Hecke algebras (ENGLISH)

[ Abstract ]

In the late 80's V. Drinfeld introduced the notion of the

degenerate affine Hecke algebras. The particular class of those, called

symplectic reflection algebras, has been rediscovered 15 years later by

[Etingof and Ginzburg]. The theory of those algebras (which include also

the rational Cherednik algebras) has attracted a lot of attention in the

last 15 years.

In this talk we will discuss their continuous and infinitesimal versions,

introduced by [Etingof, Gan, and Ginzburg]. Our key result relates those

classical algebras to the simplest 1-block finite W-algebras.

In the late 80's V. Drinfeld introduced the notion of the

degenerate affine Hecke algebras. The particular class of those, called

symplectic reflection algebras, has been rediscovered 15 years later by

[Etingof and Ginzburg]. The theory of those algebras (which include also

the rational Cherednik algebras) has attracted a lot of attention in the

last 15 years.

In this talk we will discuss their continuous and infinitesimal versions,

introduced by [Etingof, Gan, and Ginzburg]. Our key result relates those

classical algebras to the simplest 1-block finite W-algebras.

### 2015/01/14

#### Number Theory Seminar

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

Iterate extensions and relative Lubin-Tate groups

**Laurent Berger**(ENS de Lyon)Iterate extensions and relative Lubin-Tate groups

[ Abstract ]

Let K be a p-adic field, let P(T) be a polynomial with coefficients in K, and let {$u_n$} be a sequence such that $P(u_{n+1}) = u_n$ for all n and $u_0$ belongs to K. The extension of K generated by the $u_n$ is called an iterate extension. I will discuss these extensions, show that under certain favorable conditions there is a theory of Coleman power series, and explain the relationship with relative Lubin-Tate groups.

Let K be a p-adic field, let P(T) be a polynomial with coefficients in K, and let {$u_n$} be a sequence such that $P(u_{n+1}) = u_n$ for all n and $u_0$ belongs to K. The extension of K generated by the $u_n$ is called an iterate extension. I will discuss these extensions, show that under certain favorable conditions there is a theory of Coleman power series, and explain the relationship with relative Lubin-Tate groups.

#### Operator Algebra Seminars

16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Canonical cyclic group actions on noncommutative tori

**Zhuofeng He**(Univ. Tokyo)Canonical cyclic group actions on noncommutative tori

### 2015/01/13

#### Tuesday Seminar on Topology

16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Stable presentation length of 3-manifold groups (JAPANESE)

**Ken'ichi Yoshida**(The University of Tokyo)Stable presentation length of 3-manifold groups (JAPANESE)

[ Abstract ]

We will introduce the stable presentation length

of a finitely presented group, which is defined

by stabilizing the presentation length for the

finite index subgroups. The stable presentation

length of the fundamental group of a 3-manifold

is an analogue of the simplicial volume and the

stable complexity introduced by Francaviglia,

Frigerio and Martelli. We will explain some

similarities of stable presentation length with

simplicial volume and stable complexity.

We will introduce the stable presentation length

of a finitely presented group, which is defined

by stabilizing the presentation length for the

finite index subgroups. The stable presentation

length of the fundamental group of a 3-manifold

is an analogue of the simplicial volume and the

stable complexity introduced by Francaviglia,

Frigerio and Martelli. We will explain some

similarities of stable presentation length with

simplicial volume and stable complexity.

#### PDE Real Analysis Seminar

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Global regular solutions to the Navier-Stokes equations which remain close to the two-dimensional solutions (English)

**Wojciech Zajączkowski**(Institute of Mathematics Polish Academy of Sciences)Global regular solutions to the Navier-Stokes equations which remain close to the two-dimensional solutions (English)

[ Abstract ]

We consider the motion of the Navier-Stokes equations in a cylinder with the Navier-boundary conditions. First we prove global existence of regular two-dimensional solutions non-decaying in time. Next we show stability of these solutions. In this way we have existence of global regular solutions which remain close to the two-dimensional solutions. We prove the results for nonvanishing external force in time.

We consider the motion of the Navier-Stokes equations in a cylinder with the Navier-boundary conditions. First we prove global existence of regular two-dimensional solutions non-decaying in time. Next we show stability of these solutions. In this way we have existence of global regular solutions which remain close to the two-dimensional solutions. We prove the results for nonvanishing external force in time.

### 2015/01/10

#### Harmonic Analysis Komaba Seminar

13:00-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Scattering theory for the Laplacian on symmetric spaces of noncompact type and its application (JAPANESE)

スケール不変性を持つ臨界Hardyの不等式について (JAPANESE)

**Koichi Kaizuka**(Gakushuin University) 13:30-15:00Scattering theory for the Laplacian on symmetric spaces of noncompact type and its application (JAPANESE)

**Norisuke Ioku**(Ehime University) 15:30-17:00スケール不変性を持つ臨界Hardyの不等式について (JAPANESE)

### 2015/01/07

#### Number Theory Seminar

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

Congruences of modular forms modulo p and a variant of the Breuil-Mézard conjecture (English)

**Sandra Rozensztajn**(ENS de Lyon)Congruences of modular forms modulo p and a variant of the Breuil-Mézard conjecture (English)

[ Abstract ]

In this talk I will explain how a problem of congruences modulo p in the space of modular forms $S_k(\Gamma_0(p))$ is related to the geometry of some deformation spaces of Galois representations and can be solved by using a variant of the Breuil-Mézard conjecture.

In this talk I will explain how a problem of congruences modulo p in the space of modular forms $S_k(\Gamma_0(p))$ is related to the geometry of some deformation spaces of Galois representations and can be solved by using a variant of the Breuil-Mézard conjecture.

#### Operator Algebra Seminars

16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)

De Finetti theorems related to Boolean independence (English)

**Tomohiro Hayase**(Univ. Tokyo)De Finetti theorems related to Boolean independence (English)

### 2015/01/06

#### PDE Real Analysis Seminar

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Global existence and asymptotic behavior for some Keller-Segel systems coupled with Navier-Stokes equations (英語)

**Elio Eduardo Espejo**(National University of Colombia / Osaka University)Global existence and asymptotic behavior for some Keller-Segel systems coupled with Navier-Stokes equations (英語)

[ Abstract ]

There are plenty of examples in nature, where cells move in response to some chemical signal in the environment. Biologists call this phenomenon chemotaxis. In my talk I will approach the problem of describing mathematically the phenomenon of chemotaxis when it happens surrounded by a fluid. This is a new research topic bringing the attention of many scientists because it has given rise to many interesting questions having relevance in both biology and mathematics. In particular, I will present some new mathematical models arising from my current research that have given rise to Keller-Segel type systems coupled with Navier-Stokes systems. I will present some results of global existence and asymptotic behavior. Finally I will discuss some open problems.

There are plenty of examples in nature, where cells move in response to some chemical signal in the environment. Biologists call this phenomenon chemotaxis. In my talk I will approach the problem of describing mathematically the phenomenon of chemotaxis when it happens surrounded by a fluid. This is a new research topic bringing the attention of many scientists because it has given rise to many interesting questions having relevance in both biology and mathematics. In particular, I will present some new mathematical models arising from my current research that have given rise to Keller-Segel type systems coupled with Navier-Stokes systems. I will present some results of global existence and asymptotic behavior. Finally I will discuss some open problems.

### 2014/12/22

#### Mathematical Biology Seminar

15:00-16:20 Room #122 (Graduate School of Math. Sci. Bldg.)

Estimating the seroincidence of pertussis in Japan

**Don Yueping**(Department of Global Health Policy, Graduate School of Medicine, The University of Tokyo)Estimating the seroincidence of pertussis in Japan

[ Abstract ]

Despite relatively high vaccination coverage of pertussis for decades, the disease keeps circulating among both vaccinated and unvaccinated individuals and a periodic large epidemic is observed every 4 years. To understand the transmission dynamics, specific immunoglobulin G (IgG) antibodies against pertussis toxin (PT) have been routinely measured in Japan. Using the cross-sectional serological survey data with a known decay rate of antibody titres as a function of time since infection, we estimate the age-dependent seroincidence of pertussis. The estimated incidence of pertussis declined with age, the shape of which will be extremely useful for reconstructing the transmission dynamics and considering effective countermeasures.

Despite relatively high vaccination coverage of pertussis for decades, the disease keeps circulating among both vaccinated and unvaccinated individuals and a periodic large epidemic is observed every 4 years. To understand the transmission dynamics, specific immunoglobulin G (IgG) antibodies against pertussis toxin (PT) have been routinely measured in Japan. Using the cross-sectional serological survey data with a known decay rate of antibody titres as a function of time since infection, we estimate the age-dependent seroincidence of pertussis. The estimated incidence of pertussis declined with age, the shape of which will be extremely useful for reconstructing the transmission dynamics and considering effective countermeasures.

### 2014/12/19

#### Geometry Colloquium

10:00-11:30 Room #126 (Graduate School of Math. Sci. Bldg.)

Exotic components in linear slices of quasi-Fuchsian groups

**Yuichi KABAYA**(Kyoto University)Exotic components in linear slices of quasi-Fuchsian groups

[ Abstract ]

The linear slice of quasi-Fuchsian punctured torus groups is defined by fixing the length of some simple closed curve to be a fixed positive real number. It is known that the linear slice is a union of disks, and it has one `standard' component containing Fuchsian groups. Komori-Yamashita proved that there exist non-standard components if the length is sufficiently large. In this talk, I give another proof based on the theory of complex projective structures. If time permits, I will talk about a refined statement and a generalization to other surfaces.

The linear slice of quasi-Fuchsian punctured torus groups is defined by fixing the length of some simple closed curve to be a fixed positive real number. It is known that the linear slice is a union of disks, and it has one `standard' component containing Fuchsian groups. Komori-Yamashita proved that there exist non-standard components if the length is sufficiently large. In this talk, I give another proof based on the theory of complex projective structures. If time permits, I will talk about a refined statement and a generalization to other surfaces.

### 2014/12/17

#### Number Theory Seminar

18:00-19:00 Room #117 (Graduate School of Math. Sci. Bldg.)

Equivariant $\wideparen{\mathcal{D}}$ modules on rigid analytic spaces

(English)

**Konstantin Ardakov**(University of Oxford)Equivariant $\wideparen{\mathcal{D}}$ modules on rigid analytic spaces

(English)

[ Abstract ]

Locally analytic representations of p-adic Lie groups are of interest in several branches of arithmetic algebraic geometry, notably the p-adic local Langlands program. I will discuss some work in progress towards a Beilinson-Bernstein style localisation theorem for admissible locally analytic representations of semisimple compact p-adic Lie groups using equivariant formal models of rigid analytic flag varieties.

Locally analytic representations of p-adic Lie groups are of interest in several branches of arithmetic algebraic geometry, notably the p-adic local Langlands program. I will discuss some work in progress towards a Beilinson-Bernstein style localisation theorem for admissible locally analytic representations of semisimple compact p-adic Lie groups using equivariant formal models of rigid analytic flag varieties.

#### Operator Algebra Seminars

16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)

Dynamics of an Open Quantum System with Repeated Harmonic Perturbation (with Hiroshi Tamura) (English)

**Valentin Zagrebnov**(Univ. d'Aix-Marseille)Dynamics of an Open Quantum System with Repeated Harmonic Perturbation (with Hiroshi Tamura) (English)

#### Mathematical Biology Seminar

14:50-16:20 Room #122 (Graduate School of Math. Sci. Bldg.)

A probabilistic interpretation of an evolution model of slime bacteria

(JAPANESE)

**Yumi YAHAGI**(Tokyo City University)A probabilistic interpretation of an evolution model of slime bacteria

(JAPANESE)

### 2014/12/16

#### Tuesday Seminar of Analysis

16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Global Strichartz estimates for Schr¥”odinger equations on

asymptotically conic manifolds (Japanese)

**Haruya Mizutani**(Graduate School of Science, Osaka University)Global Strichartz estimates for Schr¥”odinger equations on

asymptotically conic manifolds (Japanese)

#### Tuesday Seminar on Topology

17:10-18:10 Room #056 (Graduate School of Math. Sci. Bldg.)

Differential forms in diffeological spaces (JAPANESE)

**Norio Iwase**(Kyushu University)Differential forms in diffeological spaces (JAPANESE)

[ Abstract ]

The idea of a space with smooth structure is first introduced by K. T. Chen in his study of a loop space to employ the idea of iterated path integrals.

Following the pattern established by Chen, J. M. Souriau introduced his version of a space with smooth structure which is now called diffeology and become one of the most exciting topics in Algebraic Topology. Following Souriau, P. I.-Zenmour presented de Rham theory associated to a diffeology of a space. However, if one tries to show a version of de Rham theorem for a general diffeological space, he must encounter a difficulty to show the existence of a partition of unity and thus the exactness of the Mayer-Vietoris sequence. To resolve such difficulties, we introduce a new definition of differential forms.

The idea of a space with smooth structure is first introduced by K. T. Chen in his study of a loop space to employ the idea of iterated path integrals.

Following the pattern established by Chen, J. M. Souriau introduced his version of a space with smooth structure which is now called diffeology and become one of the most exciting topics in Algebraic Topology. Following Souriau, P. I.-Zenmour presented de Rham theory associated to a diffeology of a space. However, if one tries to show a version of de Rham theorem for a general diffeological space, he must encounter a difficulty to show the existence of a partition of unity and thus the exactness of the Mayer-Vietoris sequence. To resolve such difficulties, we introduce a new definition of differential forms.

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