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Language：English   Publisher：Warsaw, 2000, Abstracts,  

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Language：English  

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Language：English   Publisher：Universit'e Montpellier II  

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Language：English   Publisher：GEOMERIC STUDY OF FOLIATIONS  

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Language：English   Publisher：BRAZIL数学会  

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Language：English   Publisher：the American Mathematical Society  

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Language：English   Publisher：葉層構造国際会議及び日本数学会  

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Language：English   Publisher：葉層構造国際会議及び日本数学会  

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Language：English   Publisher：Indiana University  

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Language：English   Publisher：LODZ URVIVERSITY (POLAND)  

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Language：English   Publisher：紀伊國屋書店  

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Language：English   Publisher：JAGIELLONSKI University (POLAND)  

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Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

葉向複素構造をもつ Reeb 成分の自己同型群の構造を、境界葉のホロノミーが恒等写像に平坦である場合に、関係する関数方程式を完全に解くことにより決定した。

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Abstract: I will try to explain some construction of some strange|rn|symplectic structures on some non-Kahler manifolds or b-symplectic|rn|structures. It is an application of the method that I developed in|rn|constructing leafwise symplectic foliations. It is work in progress, so|rn|that the talk will be quite casual.

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

abstract:|rn| We recreate an unpublished proof of Thurston's h-principle |rn|for 2-dimensional foliations which says that any smooth 2-plane fieeld |rn|on a manifold of dimension at least 4 is homotopic to the tangent plane |rn|fieeld of a foliation. We learned a simplest proof for 4 and 5 |rn|dimensional |rn|case from Andre Haefliger via Takashi Tsuboi and it is completed |rn|along its line by using a result by Haller-Rybicki-Teichmann. |rn| As an issue, the (q+1)-connectivity of F\Gamma_q(=B\overline\Gamma_q) |rn|is concluded without passing through the Mather-Thurston theory but |rn|only by using Haefliger's original argument for q-connectivity proof. |rn| This is a joint work with Elmar Vogt.

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Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Levi 平坦実超曲面を境界に持つ Stein 多様体の基本的な例の紹介と構成。|rn|3次元代数的 Anosov 流・葉層が本質的にかかわる

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Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Abstract.|rn|We recreate an unpublished proof of William Thurston from the|rn|early 1970's that any smooth 2-plane field on a manifold of dimension|rn|at least 4 is homotopic to the tangent plane field of a foliation.

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Abstract:|rn| Even though analytical foundations for the fluid mechanics is still very hard to establish and |rn|not yet enough developed, it is still a tempting idea to look at |rn|fluids how they flow on manifolds for understanding the topology and geometry of manifolds. |rn|Moreover in the case of foliated manifolds, we even encounter a difficulty in writing down |rn|a proper Euler equation, the equation of motion for ideal foliated fluids.|rn| This talk is concerning a more primitive stage than the genuine fluid mechanics, namely,|rn|trying to understand, in the case of codimension 1 foliations on closed oriented 3-manifolds, |rn|the space of velocity fields of foliated ideal fluids. One of the main tools is the asymptotic linking. |rn||rn| For a volume form dvol on a closed oriented manifold M, X denotes the set of smooth vector |rn|fields on M, Xd the set of divergence free vector fields, and Xh the kernel of |rn|the asymptotic cycle: Xd \to H1(M). The asymptotic linking lk is a symmetric bi-linear form on Xh. |rn| Under the presence of a codimension 1 foliation F on M X(M;F) = {X \in X ; X//F} and |rn|X*(M;F) = X(M;F) \cup X* for * = d, h. Also Xloc(M;F) denotes the span

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Abstract: A closed 2-form of rank two on a 3-manifold|rn|is called 2-calibration of the 3-manifold.|rn|This is equivalent to having a non-singular|rn|divergence free vector field on the 3-manifold.|rn|Typical examples are contact 3-manifolds with a fixed contact form|rn|\alpha. Then d\alpha is the calibration.|rn||rn|David Martinez Torres studied codimension 1 foliations on|rn|(2n+1)-dimensional manifolds with 2-calibrations,|rn|namely, a closed 2-form of rank 2n which restricts to|rn|a symplectic structure on each leaf.|rn|If we find a Lagrangian n-sphere L on a leaf,|rn|we can consider the generalized Dehn twist along L|rn|which produces a new calibrated foliation.|rn|It is also interpreted as a generalized Dehn twist|rn|of the manifold and also interpreted as a surgery|rn|described by attaching a symplectic handle of dimension|rn|2n+2. He also developed a Donaldson theory|rn|(approximate holomorphic geometry) to analyze|rn|the dynamical structure of 2-calibrated foliations.|rn||rn|This talk is an introduction to the surgery part|rn|in his paper restricted to dimension 3.|rn|As a corollary we show|rn|that on most closed oriented 3-manifolds|rn|any 2nd real cohomology class is r

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

In this talk, we present a framework for the existence of leafwise symplectic |rn|structures on a codimension 1 foliation associated with a Milnor fibrationv|rn|or with an open book decomposition supporting a contact structure. |rn||rn|Definition 1.1. A leafwise symplectic structure on a foliatited manifold |rn|(M;F) is a smooth 2-form \omega which restricts to a symplectic form on each |rn|leaf.|rn||rn| Our previous result was the following. |rn|Theorem 1.2 ([Mi]). |rn|The natural codimension 1 spinnable foliation Fk on |rn|S5 associated with the simple elliptic hypersurface singularity \tilde Ek |rn|admits a leafwise symplectic structure for k = 6, 7, 8. |rn|Corollary 1.3. |rn|There exist regular Poisson stuctures on S^5 whose symplectic dimension is 4.|rn||rn||rn| Now our main result is stated as follows.|rn||rn|Theorem 1.4. |rn|In the above situation, supppose the following conditions |rn|are satisfied. Then M admits a natural `spinnable' codimension 1 foliation F |rn|with a leafwise symplectic structure and an isotopic family of contact |rn|structures starting from the given one \xi on M which converges to F as a |rn|family of almost contact structures.|rn|(1) The link K^2n-

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

This talk has the following purposes: |rn||rn|- By presenting some applications |rn|of Thurston's $h$-principle for foliations of codimension $q>1$, |rn|we would like to draw attentions and to provide motivations |rn|for the homotopy theory of foliations. |rn||rn|- By explaining a special proof of the principle |rn|for the case of 2dimensional foliations on 4-manifolds, |rn|which is due to Haefliger and Thurston, |rn|the talk serves as an introduction to especially |rn|Ga\"el Meigniez's minicourse and also presents an |rn|interesting application of the simplicity |rn|of some group of diffeomorphisms. |rn||rn||rn|Section 1. |rn||rn|Fisrt we recall the statement of Thurston's $h$-principle and |rn|specialize it to the case of 2-dimensional foliations. |rn|It turns out to be that if we have a plane field on a manifold, |rn|then it is homotopically deformed as plane fields |rn|into an integrable one, {\i.e.}, a 2-dim foliation. |rn|This specialization stands on the $(q+1)$-connectedness of |rn|$B\overline{\Gamma}_q$ which is due to Haefliger |rn|(up to $q$-connnectedness) and Mather-Thurston. |rn|Some parts of this connectivity might be presented |rn|as exercises which are common to t

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Abstract: |rn| In order to understand the topology and geometry of manifolds or geometric structures |rn|on them, it might be a natural idea to look at how fluids flow on them. |rn|Unfortunately, the analytical foundations for the fluid mechanics is very hard to establish |rn|and not yet enough to employ this idea. |rn|However, it is still tempting the author, even to investigate foliations on manifolds. |rn| We have already a difficulty in writing down the proper Euler equation, |rn|namely, the equation of motion for incompressible fluids without viscosity whose |rn|flow lines are contained in leaves. |rn|If the time allows, we will discuss on this difficulty in the talk. |rn| The main topic of this talk is concerning a more primitive stage than the genuine |rn|fluid mechanics. We try to understand in the case of codimension 1 foliations on closed oriented |rn|3-manifolds the space of velocity fields of such fluids by using an interpretation of the notion |rn|of helicity as a symmetric bi-linear form on the space (not of velocity fields but) of volticity |rn|fields, which is so called the asymptotic linking.|rn| Fix a volume form dvol on a closed oriented manifold M. Let X de

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Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

We have constructed a leafwise symplectic structure for a foliation on the 5 sphere which is associated to the Milnor fibration of a simple elliptic hypersurface singularity in 3 complex variables. The foliation associated with x^3+y^3+z^3=0 is nothing but Lawson’s foliation which was constructed as the 1st codimension one foliation on the 5-sphere in 1970. In this talk we abstract the essence of the construction as a framework to produce a leafwise symplectic foliation or a family of almost contact structure converging to a symplectic foliation from an exact symplectic open book decomposition supporting a contact structure.|rn| |rn|As a by-product of the framework, we can show that a similar construction works also for the cusp singularities in 3 variables. If the time allows we discuss about the possibility of further applicability of the framework as well as the impossibility.

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Abstract: |rn||rn||rn|The helicity plays many intresting roles in 3-dimensinal diffential topology. One of its earliest appearences in was the question by Dennis Sullivan, asking to express the Godbilon-Vey invariant in terms of linking of fluids. Here the Godbillon-Vey is an invariant for codimension1 foliations which lives in the 3rd de Rham cohomology. The question is well-understood and we know which fluid motion should be taken. If we think of helicity as a quadratic function on the space of incompressible fluids, namely the space of divergence free vector fields, it goes down to a symmetric bilinear form. Some ideas concerning this bilinear form for studies of foliations and contact structures are introduced. For example, in the case of codimmension one foliations the 1st foliated cohomology will appear. If the foliation is deofrmed to contact structures, unexpectedly phenomena which might be related to a quatization procedure is found.

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Abstract: Lawson's foliation is, among other codimension 1 foliations, the first one which was found on S^5 (around 1970). Later on, Alberto Verjovsky posed questions (around 2000) whether if Lawson's one or some modified ones admit leafwise complex structures or leafwise symplectic structures. In this talk, we show that Lawson's foliation, without any modification, admits a leafwise symplectic structure. The results can be paraphrased that the 5-sphere admits a regular Poisson structure whose symplectic leaves form Lawson's foliation. The heart is to show the existence of an end-periodic symplectic structure on the Fermat cubic surface X^3+Y^3+Z^3=1, while it seems fairy rare for Stein manifolds to admit end-periodic symplectic structures. The argument also applies with minor modifications to two other cases of simple elliptic hypersurface singularities. If the time allows, end-periodic symplectic structures on globally convex symplectic manifolds are discussed.

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Abstract:|rn||rn|Featuring Lawson's foliation on the 5-sphere, |rn|codimension 1 foliation associated with |rn|open book decompositions are discussed, |rn|especially for the possibilty for the existence |rn|of leafwise symplectic structures. |rn|A relation with the theory of singularities |rn|are commented, |rn|especially on simple elliptic ones |rn|given as hypersurface ones are of |rn|the most interest. |rn| |rn|The case where a global closed 2-form |rn|restricts to symplectic forms on each leaf |rn|is called as 2-calibrated, on which we will |rn|make a further discussion, if the time allows, |rn|as well as |rn|on the existence of leafwise complex structure.

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Le résumé:L'enlacement asymptotique défine |rn|un pairing bi-linéaire symétrique |rn|non-dégénéré. Donc on est tenté de |rn|définir sa signature qui donnerait |rn|l'invariant de la variété. |rn|Cette idée directe ne marche pas |rn|mais la présence d'un feuilletage |rn|parfois admet la situation non-triviale. |rn| Nous expliquons les relations |rn|entre la première cohomologie feuilleté |rn|et l'invariant exotique et |rn|surtout à la presence d'un flot d'Anosov |rn|algébrique et une application potentielle |rn|à la topologie des structures de contact.

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

http://www.lmba-math.fr/seminaires/algebre-et-geometrie.html

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

abstract:|rn|The Euler equation or the Navier-Stokes equation |rn|are the equations of motions of incompressible fluids |rn|with or without viscosity. |rn|On compact Riemannian maniflds the former one was |rn|established by Arnold in 60's and the latter by |rn|M. Taylor around 1990. |rn|In this talk, we review how they are deduced from |rn|geometric point of view. |rn||rn|If it were allowed to devide the mathematics into |rn|three major branches as algebra, analysis, and geometry, |rn|it might be possible to asign the tasks |rn|in mathematical sciences concerning `equations' |rn|to each branches as follows. |rn||rn|Analysis: existence of solutions |rn|Algebra: description of solutions |rn|Geometry: deduction of equations|rn||rn|Some of the key ideas for the Euler equation are |rn|symmetries and geodesics |rn|while for the Navier-Stokes equation |rn|Killing vector fields and viscous frictions |rn|might be central objects. |rn||rn|We begin with a theorem of Clairaut |rn|on geodesics of surfaces of revolutions |rn|featuring symmetries and try to present |rn|basic geometric problems behind |rn|the equation.

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Abstract: We are going to show that Lawson's foliation on the 5-sphere |rn|amits a smooth leafwise symplectic sturcture. This result can be |rn|paraphrased that the 5-sphere admits a regular Poisson structure |rn|with symplectic dimension 4. |rn| Historically, Lawson's foliation is the first one among foliations |rn|of codimension one which are constructed on the 5-sphere. |rn|It is obtained by modifying the Milnor fibration associated to |rn|the Fermat type cubic polynominal in three variables. |rn| Alberto Verjovsky proposed a question whether if Lawson's foliation |rn|or some codimension one foliation on the 5-sphere admit a leafwise |rn|symplectic (or complex) structure. As Lawson's one has a |rn|Kodaira-Thurston nil 4-manifold as a cmpact leaf, the question can not |rn|be solved simultaneously both for the symplectic and the complex cases. |rn| The main part of the construction is to show that the Fermat type |rn|cubic surface admits an `end-periodic' symplectic structure, while the |rn|natural one as an affine surface is conic and expanding at the end. |rn| While for the other two families of the simple elliptic hypersurface |rn|singularities almost the same construction

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Mercredi 7 mars 2012 : Yoshi Mitsumatsu|rn||rn|Structures symplectiques sur les feuilles du feuilletage de Lawson |rn||rn|H. Blaine Lawson, Jr. a construit un (peut-être le premier) feuilletage de codimension 1 sur la sphère de dimension 5 vers 1970. La construction repose sur la technique de tourbillonnement appliquée au fibré de Milnor associé au polynôme de Fermat de degree 3 en trois variables. Alberto Verjovsky a posé les questions suivantes: Existe-t-il une famille lisse de structures complexes définies sur les feuilles du feuilletage de Lawson? Même question pour n'importe quel feuilletage sur S^5? Et enfin, même question pour les structures symplectiques? |rn|On montre que le feuilletage de Lawson admet une telle structure symplectique. Il s'agit de chercher une structure symplectique qui est `périodique' à l'infini sur la surface affine de type Fermat X^3 + Y^3 + Z^3 = 1. Cependant sa structure symplectique naturelle est dilatante.

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Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Abstract: We are going to show that Lawson's foliation on the 5-sphere admits a smooth leafwise symplectic sturcture. Historically, Lawson's foliation is the first one among foliations of codimension one which are constructed on the 5-sphere. It is obtained by modifying the Milnor fibration associated with the Fermat type cubic polynominal in three variables. Alberto Verjovsky proposed a question whether if the Lawson's foliation or slighty modified ones admit a leafwise smooth symplectic structure and/or a leafwise complex structure. As Lawson's one has a Kodaira-Thurston nil 4-manifold as a compact leaf, the question can not be solved simultaneously both for the symplectic and the complex cases. The main part of the construction is to show that the Fermat type cubic surface admits an `end-periodic' symplectic structure, while the natural one as an affine surface is conic at the end. Even though for the other two families of the simple elliptic hypersurface singularities almost the same construction works, at present, it seems very limited where a Stein manifold admits an end-periodic symplectic structure. If the time allows, we also discuss the existence of such structures on glo

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Language：English   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

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We show that Lawson's foliation on the 5-sphere |rn|admits a smooth leafwise symplectic structure. |rn|The main part of the construction is |rn|to show that the Fermat type cubic surface |rn|admits an end-periodic symplectic structure. |rn||rn|If the time allows we will also discuss |rn|on the following two points. |rn| (1) This is related to a so called $\tilde{E}_6$ |rn|simple elliptic singularity. |rn|Almost the same construction works also for |rn|$\tilde{E}_7$ and $\tilde{E}_8$, |rn|which are, |rn|together with $\tilde{E}_6=$ the Fermat cubic, |rn|known to be the only isolated hypersurface |rn|simple elliptic singularities. |rn| (2) On the other hand, it seems to be a very rare case |rn|that a Stein surface (or even higher dimensional Stein |rn|manifold) admits a non-convex end-periodic |rn|symplectic structure. |rn|Recent solution of Taubes' conjecture |rn|by Friedl and Vidussi explains some part |rn|of this impossibility. |rn||rn| Our main result can be paraphrased that the 5-sphere |rn|admits a regular Poisson structure |rn|of symplectic dimension 4.

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Language：Japanese   Presentation type：Public lecture, seminar, tutorial, course, or other speech  

Aim|rn|• introduce modifications of 2-dimensional|rn|foliations on 4-manifolds|rn|• cohomological obstruction to turbulizations|rn|• how to geometrically realize?|rn|• geometric tautness of resultant foliations|rn|Key Behind|rn|• 3D (Geodisic) Anosov flow

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24.02.2009: Yoshihiko Mitsumatsu, Chuo University, Tokyo|rn||rn|On Geometric Backgrounds of Incompressible Fluid Dynamics on Riemannian Manifolds |rn| The equation of motion of perfect fluids on compact Riemannian manifolds, the Euler equation, has been deduced by Arnold, and the Navier-Stokes equation for incompressible fluids of uniform viscosity was obtained by Taylor. |rn| We explain these works and their geometric background and present and analyze some simple examples. |rn|Also we would like to propose a few problems from the geometric point of view. |rn|Dies ist eine gemeinsame Veranstaltung mit der Topologie (Prof. Dr. E. Vogt)

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"Harmonic Analysis and PDEs on Manifolds|rn|Department of Mathematics, Chuo University|rn|2013 April 19 Friday - 20 Saturday|rn|Organizers|rn|Tokio Matsuyama|rn|Yoshihiko Mitsumatsu|rn|Tsukasa Iwabuchi|rn|(Chuo University)|rn|Conference venue: Room No. 6701, 6th Building of Korakuen Campus, Chuo University"

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"Topics:|rn|Groups of diffeomorphisms, Moduli and classifying spaces, Mapping class groups, Characteristic classes, K-theory, Symplectic geometry, Foliations |rn||rn|Invited Speakers: |rn|Toshiyuki Akita Joan Birman Hisaaki Endo Sergio Fenley Koji Fujiwara Etienne Ghys Richard Hain Kiyoshi Igusa Nariya Kawazumi Teruaki Kitano Dieter Kotschick Yoshihiko Mitsumatsu Shigeyuki Morita Hitoshi Moriyoshi Kaoru Ono Robert Penner Leonid Polterovich Takuya Sakasai Ulrike Tillmann Takashi Tsuboi Karen Vogtmann"

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researchmap

researchmap

researchmap

researchmap

researchmap