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Seminar information archive
Seminar information archive ～04/30｜Today's seminar 05/01 | Future seminars 05/02～
2016/05/31
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Benoît Guerville-Ballé (Tokyo Gakugei University)
A linking invariant for algebraic curves (ENGLISH)
Benoît Guerville-Ballé (Tokyo Gakugei University)
A linking invariant for algebraic curves (ENGLISH)
[ Abstract ]
We construct a topological invariant of algebraic plane curves, which is in some sense an adaptation of the linking number of knot theory. As an application, we show that this invariant distinguishes a new Zariski pair of curves (ie a pair of curves having same combinatorics, yet different topology).
We construct a topological invariant of algebraic plane curves, which is in some sense an adaptation of the linking number of knot theory. As an application, we show that this invariant distinguishes a new Zariski pair of curves (ie a pair of curves having same combinatorics, yet different topology).
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Kiwamu Watanabe (Saitama University)
A Characterization of Symplectic Grassmannians (JAPANESE)
Kiwamu Watanabe (Saitama University)
A Characterization of Symplectic Grassmannians (JAPANESE)
[ Abstract ]
In the series of their works, J. M. Hwang and N. Mok have been developing the theory of Varieties of Minimal Rational Tangents (VMRT for short). In this direction, the results of Mok and J. Hong-Hwang allow us to recognize a homogeneous Fano manifold X of Picard number one by looking at its VMRT at a general point. This characterization works for all rational homogeneous manifolds of Picard number one whenever the VMRT is rational homogeneous, which is always the case except for the short root cases; namely for symplectic Grassmannians, and for two varieties of type F*4*.
In this talk we show that, if we impose that the VMRT is the expected one at every point of the variety, we may still characterize symplectic Grassmannians. This is a joint work with G. Occhetta and L. E. Sola Conde (arXiv:1604.06867).
In the series of their works, J. M. Hwang and N. Mok have been developing the theory of Varieties of Minimal Rational Tangents (VMRT for short). In this direction, the results of Mok and J. Hong-Hwang allow us to recognize a homogeneous Fano manifold X of Picard number one by looking at its VMRT at a general point. This characterization works for all rational homogeneous manifolds of Picard number one whenever the VMRT is rational homogeneous, which is always the case except for the short root cases; namely for symplectic Grassmannians, and for two varieties of type F*4*.
In this talk we show that, if we impose that the VMRT is the expected one at every point of the variety, we may still characterize symplectic Grassmannians. This is a joint work with G. Occhetta and L. E. Sola Conde (arXiv:1604.06867).
2016/05/30
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Takeo Ohsawa (Nagoya University)
(JAPANESE)
Takeo Ohsawa (Nagoya University)
(JAPANESE)
Tokyo Probability Seminar
16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)
Takafumi Otsuka (Graduate school of science and engineering, Tokyo metropolitan university)
Takafumi Otsuka (Graduate school of science and engineering, Tokyo metropolitan university)
Operator Algebra Seminars
16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)
Yosuke Kubota (Univ. Tokyo)
TBA
Yosuke Kubota (Univ. Tokyo)
TBA
Seminar on Probability and Statistics
13:00-14:10 Room #052 (Graduate School of Math. Sci. Bldg.)
OKADA, Yukinori (Osaka University)
Statistical genetics contributes to elucidation of disease biology and genomic drug discovery
OKADA, Yukinori (Osaka University)
Statistical genetics contributes to elucidation of disease biology and genomic drug discovery
2016/05/27
Colloquium
15:30-16:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Takahiro Kitayama (Graduate School of Mathematical Sciences, University of Tokyo)
Moduli spaces of linear representations and splittings of 3-manifolds
Takahiro Kitayama (Graduate School of Mathematical Sciences, University of Tokyo)
Moduli spaces of linear representations and splittings of 3-manifolds
Geometry Colloquium
10:00-11:30 Room #118 (Graduate School of Math. Sci. Bldg.)
Yohsuke Imagi (Kavli IPMU)
Compact Special Lagrangian T^2-conifolds (Japanese)
Yohsuke Imagi (Kavli IPMU)
Compact Special Lagrangian T^2-conifolds (Japanese)
[ Abstract ]
Special Lagrangian submanifolds may be defined as volume-minimizing Lagrangian submanifolds of Calabi--Yau manifolds. Some interesting but difficult topics are (1) the SYZ conjecture, (2) counting compact special Lagrangian homology spheres, and (3) relation to Fukaya categories---all concerned with singularity of special Lagrangian submanifolds. I first recall some basic facts about these things and then talk about a simple class of singularity modelled on a certain T^2-cone.
Special Lagrangian submanifolds may be defined as volume-minimizing Lagrangian submanifolds of Calabi--Yau manifolds. Some interesting but difficult topics are (1) the SYZ conjecture, (2) counting compact special Lagrangian homology spheres, and (3) relation to Fukaya categories---all concerned with singularity of special Lagrangian submanifolds. I first recall some basic facts about these things and then talk about a simple class of singularity modelled on a certain T^2-cone.
Geometry Colloquium
13:00-14:30 Room #118 (Graduate School of Math. Sci. Bldg.)
Yoshihiko Matsumoto (Osaka University)
Deformation of Einstein metrics and $L^2$ cohomology on strictly pseudoconvex domains (Japanese)
Yoshihiko Matsumoto (Osaka University)
Deformation of Einstein metrics and $L^2$ cohomology on strictly pseudoconvex domains (Japanese)
[ Abstract ]
Any bounded strictly pseudoconvex domain of a Stein manifold carries a complete Kähler-Einstein metric of negative scalar curvature, which is unique up to homothety, as shown by S. Y. Cheng and S. T. Yau. I will discuss the fact that this Cheng-Yau metric deforms into a family of Einstein metrics parametrized by partially integrable CR structures on the boundary under the assumption that the dimension is at least three. The necessary analysis on the linearized Einstein operator can be reduced to a vanishing result of the $L^2$ Dolbeault cohomology with values in the holomorphic tangent bundle.
Any bounded strictly pseudoconvex domain of a Stein manifold carries a complete Kähler-Einstein metric of negative scalar curvature, which is unique up to homothety, as shown by S. Y. Cheng and S. T. Yau. I will discuss the fact that this Cheng-Yau metric deforms into a family of Einstein metrics parametrized by partially integrable CR structures on the boundary under the assumption that the dimension is at least three. The necessary analysis on the linearized Einstein operator can be reduced to a vanishing result of the $L^2$ Dolbeault cohomology with values in the holomorphic tangent bundle.
2016/05/24
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Katsutoshi Yamanoi (Osaka University)
ON PSEUDO KOBAYASHI HYPERBOLICITY OF SUBVARIETIES OF ABELIAN VARIETIES
(tba)
Katsutoshi Yamanoi (Osaka University)
ON PSEUDO KOBAYASHI HYPERBOLICITY OF SUBVARIETIES OF ABELIAN VARIETIES
(tba)
[ Abstract ]
We prove that the Kobayashi pseudo distance of a closed subvariety X of an abelian variety A is a true distance outside the special set Sp(X) of X, where Sp(X) is the union of all positive dimensional translated abelian subvarieties of A which are contained in X. More strongly, we prove that a closed subvariety X of an abelian variety is taut modulo Sp(X); Every sequence fn : D → X of holomorphic mappings from the unit disc D admits a subsequence which converges locally uniformly, unless the image fn(K) of a fixed compact set K of D eventually gets arbitrarily close to Sp(X) as n gets larger. These generalize a classical theorem on algebraic degeneracy of entire holomorphic curves in irregular varieties.
We prove that the Kobayashi pseudo distance of a closed subvariety X of an abelian variety A is a true distance outside the special set Sp(X) of X, where Sp(X) is the union of all positive dimensional translated abelian subvarieties of A which are contained in X. More strongly, we prove that a closed subvariety X of an abelian variety is taut modulo Sp(X); Every sequence fn : D → X of holomorphic mappings from the unit disc D admits a subsequence which converges locally uniformly, unless the image fn(K) of a fixed compact set K of D eventually gets arbitrarily close to Sp(X) as n gets larger. These generalize a classical theorem on algebraic degeneracy of entire holomorphic curves in irregular varieties.
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Kokoro Tanaka (Tokyo Gakugei University)
Independence of Roseman moves for surface-knot diagrams (JAPANESE)
Kokoro Tanaka (Tokyo Gakugei University)
Independence of Roseman moves for surface-knot diagrams (JAPANESE)
[ Abstract ]
Roseman moves are seven types of local modifications for surface-knot diagrams in 3-space which generate ambient isotopies of surface-knots in 4-space. In this talk, I will discuss independence among the seven Roseman moves. In particular, I will focus on Roseman moves involving triple points and on those involving branch points. The former is joint work with Kanako Oshiro (Sophia University) and Kengo Kawamura (Osaka City University), and the latter is joint work with Masamichi Takase (Seikei University).
Roseman moves are seven types of local modifications for surface-knot diagrams in 3-space which generate ambient isotopies of surface-knots in 4-space. In this talk, I will discuss independence among the seven Roseman moves. In particular, I will focus on Roseman moves involving triple points and on those involving branch points. The former is joint work with Kanako Oshiro (Sophia University) and Kengo Kawamura (Osaka City University), and the latter is joint work with Masamichi Takase (Seikei University).
2016/05/23
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Katsusuke Nabeshima (The University of Tokushima)
A computation method for algebraic local cohomology and its applications (JAPANESE)
Katsusuke Nabeshima (The University of Tokushima)
A computation method for algebraic local cohomology and its applications (JAPANESE)
[ Abstract ]
Local cohomology was introduced by A. Grothendieck. Subsequent development to a great extent has been motivated by Grothendieck's ideas. Nowadays, local cohomology is a key ingredient in algebraic geometry, commutative algebra, topology and D-modules, and is a fundamental tool for applications in several fields.
In this talk, an algorithmic method to compute algebraic local cohomology classes (with parameters), supported at a point, associated with a given zero-dimensional ideal, is considered in the context of symbolic computation. There are several applications of the method. For example, the method can be used to analyze properties of singularities and deformations of Artin algebra. As the applications, methods for computing standard bases of zero-dimensional ideals and solving ideal membership problems, are also introduced.
Local cohomology was introduced by A. Grothendieck. Subsequent development to a great extent has been motivated by Grothendieck's ideas. Nowadays, local cohomology is a key ingredient in algebraic geometry, commutative algebra, topology and D-modules, and is a fundamental tool for applications in several fields.
In this talk, an algorithmic method to compute algebraic local cohomology classes (with parameters), supported at a point, associated with a given zero-dimensional ideal, is considered in the context of symbolic computation. There are several applications of the method. For example, the method can be used to analyze properties of singularities and deformations of Artin algebra. As the applications, methods for computing standard bases of zero-dimensional ideals and solving ideal membership problems, are also introduced.
Tokyo Probability Seminar
16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)
Fabrice Baudoin (Department of mathematics, Purdue university)
Sub-Riemannian diffusions on foliated manifolds
Fabrice Baudoin (Department of mathematics, Purdue university)
Sub-Riemannian diffusions on foliated manifolds
[ Abstract ]
We study the horizontal diffusion of a totally geodesic Riemannian foliation. We particularly focus on integration by parts formulas on the path space of the diffusion and present several heat semigroup gradient bounds as a consequence. Connections with a generalized sub-Riemannian curvature dimension inequality are made.
We study the horizontal diffusion of a totally geodesic Riemannian foliation. We particularly focus on integration by parts formulas on the path space of the diffusion and present several heat semigroup gradient bounds as a consequence. Connections with a generalized sub-Riemannian curvature dimension inequality are made.
Numerical Analysis Seminar
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Keiichi Morikuni (University of Tsukuba)
Inner-iteration preconditioning for least squares problems and its applications (日本語)
Keiichi Morikuni (University of Tsukuba)
Inner-iteration preconditioning for least squares problems and its applications (日本語)
[ Abstract ]
We discuss inner-iteration preconditioning for Krylov subspace methods for solving large-scale linear least squares problems. The preconditioning uses several steps of stationary iterative methods, and is efficient when the successive overrelaxation (SOR) method for the normal equations is employed. The SOR inner-iteration left/right-preconditioned generalized minimal residual (BA/AB-GMRES) methods determine a least squares solution/the minimum-norm solution of linear systems of equations without breakdown even in the rank-deficient case. The inner-iteration preconditioning requires less memory than incomplete matrix factorization-type one, and is effective for ill-conditioned and/or rank-deficient least squares problems.
We present applications of inner-iteration preconditioning to solutions of (1) general least squares problems, which is to find a least squares solution whose Euclidean norm is minimum; (2) linear systems of equations which arise in an interior-point method for solving linear programming problems. In (1), we focus on a two-step procedure for the solution of general least squares problems; the first step is to determine a least squares solution and the second step is to determine the minimum-norm solution to a linear system of equation. The solution of each step can be done by using the inner-iteration preconditioned GMRES methods. Numerical experiments show that the SOR inner-iteration preconditioned GMRES methods are more efficient than previous methods for some problems. In (2), the linear systems of equations at each interior-point step become ill-conditioned in the late phase of the interior-point iterations. To solve the linear systems of equation robustly, the inner-iteration preconditioning applies. We present efficient techniques to apply the inner-iteration preconditioning to the linear systems of equations. Numerical experiments on benchmark problems show that the inner-iteration preconditioning is robust compared to previous methods. (2) is joint work with Yiran Cui (University College London), Takashi Tsuchiya (National Graduate Institute for Policy Studies) , and Ken Hayami (National Institute of Informatics and SOKENDAI).
We discuss inner-iteration preconditioning for Krylov subspace methods for solving large-scale linear least squares problems. The preconditioning uses several steps of stationary iterative methods, and is efficient when the successive overrelaxation (SOR) method for the normal equations is employed. The SOR inner-iteration left/right-preconditioned generalized minimal residual (BA/AB-GMRES) methods determine a least squares solution/the minimum-norm solution of linear systems of equations without breakdown even in the rank-deficient case. The inner-iteration preconditioning requires less memory than incomplete matrix factorization-type one, and is effective for ill-conditioned and/or rank-deficient least squares problems.
We present applications of inner-iteration preconditioning to solutions of (1) general least squares problems, which is to find a least squares solution whose Euclidean norm is minimum; (2) linear systems of equations which arise in an interior-point method for solving linear programming problems. In (1), we focus on a two-step procedure for the solution of general least squares problems; the first step is to determine a least squares solution and the second step is to determine the minimum-norm solution to a linear system of equation. The solution of each step can be done by using the inner-iteration preconditioned GMRES methods. Numerical experiments show that the SOR inner-iteration preconditioned GMRES methods are more efficient than previous methods for some problems. In (2), the linear systems of equations at each interior-point step become ill-conditioned in the late phase of the interior-point iterations. To solve the linear systems of equation robustly, the inner-iteration preconditioning applies. We present efficient techniques to apply the inner-iteration preconditioning to the linear systems of equations. Numerical experiments on benchmark problems show that the inner-iteration preconditioning is robust compared to previous methods. (2) is joint work with Yiran Cui (University College London), Takashi Tsuchiya (National Graduate Institute for Policy Studies) , and Ken Hayami (National Institute of Informatics and SOKENDAI).
2016/05/18
Number Theory Seminar
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Takenori Kataoka (University of Tokyo)
A consequence of Greenberg's generalized conjecture on Iwasawa invariants of Z_p-extensions (Japanese)
Takenori Kataoka (University of Tokyo)
A consequence of Greenberg's generalized conjecture on Iwasawa invariants of Z_p-extensions (Japanese)
2016/05/17
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Atsushi Ito (Dep. of Math. Kyoto Univ. )
On dual defects of toric varieties (TBA)
https://sites.google.com/site/atsushiito221/
Atsushi Ito (Dep. of Math. Kyoto Univ. )
On dual defects of toric varieties (TBA)
[ Abstract ]
For a projective variety embedded in a projective space,
we can define the dual variety in the dual projective space.
By dimension count, the codimension of the dual variety is expected to be one,
but it can be greater than one for some varieties.
For a smooth toric variety, it is known that the codimension of the dual variety is greater than one
if and only if the toric variety is a suitable projective bundle over some toric variety.
In this talk, I will explain a generalization of this result to toric varieties without the assumption of singularities.
This is a joint work with Katsuhisa Furukawa.
[ Reference URL ]For a projective variety embedded in a projective space,
we can define the dual variety in the dual projective space.
By dimension count, the codimension of the dual variety is expected to be one,
but it can be greater than one for some varieties.
For a smooth toric variety, it is known that the codimension of the dual variety is greater than one
if and only if the toric variety is a suitable projective bundle over some toric variety.
In this talk, I will explain a generalization of this result to toric varieties without the assumption of singularities.
This is a joint work with Katsuhisa Furukawa.
https://sites.google.com/site/atsushiito221/
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Hidetoshi Masai (The University of Tokyo)
Some dynamics of random walks on the mapping class groups (JAPANESE)
Hidetoshi Masai (The University of Tokyo)
Some dynamics of random walks on the mapping class groups (JAPANESE)
[ Abstract ]
The dynamics of random walks on the mapping class groups on closed surfaces of genus >1 will be discussed. We define the topological entropy of random walks. Then we prove that the drift with respect to Thurston or Teichmüller metrics and the Lyapunov exponent all coincide with the topological entropy. This is a "random version" of pseudo-Anosov dynamics observed by Thurston and I will begin this talk by recalling the work of Thurston.
The dynamics of random walks on the mapping class groups on closed surfaces of genus >1 will be discussed. We define the topological entropy of random walks. Then we prove that the drift with respect to Thurston or Teichmüller metrics and the Lyapunov exponent all coincide with the topological entropy. This is a "random version" of pseudo-Anosov dynamics observed by Thurston and I will begin this talk by recalling the work of Thurston.
2016/05/16
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Masataka Tomari (Nihon University)
(JAPANESE)
Masataka Tomari (Nihon University)
(JAPANESE)
Tokyo Probability Seminar
16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)
Hiroshi Matano (Graduate School of Mathematical Sciences, the university of Tokyocho)
Generation and propagation of fine transition layers for the Allen-Cahn equation with mild noise
Hiroshi Matano (Graduate School of Mathematical Sciences, the university of Tokyocho)
Generation and propagation of fine transition layers for the Allen-Cahn equation with mild noise
2016/05/11
Number Theory Seminar
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Wiesława Nizioł (CNRS & ENS de Lyon)
Syntomic complexes and p-adic nearby cycles (English)
Wiesława Nizioł (CNRS & ENS de Lyon)
Syntomic complexes and p-adic nearby cycles (English)
[ Abstract ]
I will present a proof of a comparison isomorphism, up to some universal constants, between truncated sheaves of p-adic nearby cycles and syntomic cohomology sheaves on semistable schemes over a mixed characteristic local rings. This generalizes the comparison results of Kato, Kurihara, and Tsuji for small Tate twists (where no constants are necessary) as well as the comparison result of Tsuji that holds over the algebraic closure of the field. This is a joint work with Pierre Colmez.
I will present a proof of a comparison isomorphism, up to some universal constants, between truncated sheaves of p-adic nearby cycles and syntomic cohomology sheaves on semistable schemes over a mixed characteristic local rings. This generalizes the comparison results of Kato, Kurihara, and Tsuji for small Tate twists (where no constants are necessary) as well as the comparison result of Tsuji that holds over the algebraic closure of the field. This is a joint work with Pierre Colmez.
2016/05/10
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Yuka Kotorii (The University of Tokyo)
On Milnor's link-homotopy invariants for handlebody-links (JAPANESE)
Yuka Kotorii (The University of Tokyo)
On Milnor's link-homotopy invariants for handlebody-links (JAPANESE)
[ Abstract ]
A handlebody-link is a disjoint union of handlebodies embedded in $S^3$ and HL-homotopy is an equivalence relation on handlebody-links generated by self-crossing changes. A. Mizusawa and R. Nikkuni classified the set of HL-homotopy classes of 2-component handlebody-links completely using the linking numbers for handlebody-links. In this talk, by using Milnor's link-homotopy invariants, we construct an invariant for handlebody-links and give a bijection between the set of HL-homotopy classes of n-component handlebody-links with some assumption and a quotient of the action of the general linear group on a tensor product of modules. This is joint work with Atsuhiko Mizusawa at Waseda University.
A handlebody-link is a disjoint union of handlebodies embedded in $S^3$ and HL-homotopy is an equivalence relation on handlebody-links generated by self-crossing changes. A. Mizusawa and R. Nikkuni classified the set of HL-homotopy classes of 2-component handlebody-links completely using the linking numbers for handlebody-links. In this talk, by using Milnor's link-homotopy invariants, we construct an invariant for handlebody-links and give a bijection between the set of HL-homotopy classes of n-component handlebody-links with some assumption and a quotient of the action of the general linear group on a tensor product of modules. This is joint work with Atsuhiko Mizusawa at Waseda University.
2016/05/09
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Atsushi Atsuji (Keio University)
Nevanlinna type theorems for meromorphic functions on negatively curved Kähler manifolds (JAPANESE)
Atsushi Atsuji (Keio University)
Nevanlinna type theorems for meromorphic functions on negatively curved Kähler manifolds (JAPANESE)
[ Abstract ]
We discuss a generalization of classical Nevanlinna theory to meromorphic functions on complete Kähler manifolds. Several generalization of domains of functions are known in Nevanlinna theory, especially the results due to W.Stoll are well-known. In general Kähler case the remainder term of the second main theorem of Nevanlinna theory usually takes a complicated form. It seems that we have to modify classical
methods in order to simplify the second main theorem. We will use heat diffusion to do that and show some defect relations. We would also like to give some Liouville type theorems for holomorphic maps by using similar heat diffusion methods.
We discuss a generalization of classical Nevanlinna theory to meromorphic functions on complete Kähler manifolds. Several generalization of domains of functions are known in Nevanlinna theory, especially the results due to W.Stoll are well-known. In general Kähler case the remainder term of the second main theorem of Nevanlinna theory usually takes a complicated form. It seems that we have to modify classical
methods in order to simplify the second main theorem. We will use heat diffusion to do that and show some defect relations. We would also like to give some Liouville type theorems for holomorphic maps by using similar heat diffusion methods.
Tokyo Probability Seminar
16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)
Yosuke Kawamoto (Graduate school of Mathematics, Kyushu university)
Yosuke Kawamoto (Graduate school of Mathematics, Kyushu university)
Numerical Analysis Seminar
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Ken'ichiro Tanaka (Musashino University)
Potential theoretic approach to design of formulas for function approximation and numerical integration in weighted Hardy spaces
(日本語)
Ken'ichiro Tanaka (Musashino University)
Potential theoretic approach to design of formulas for function approximation and numerical integration in weighted Hardy spaces
(日本語)
Operator Algebra Seminars
16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)
Mikael Pichot (McGill Univ./Univ．Tokyo)
Surgery theory and discrete groups (English)
Mikael Pichot (McGill Univ./Univ．Tokyo)
Surgery theory and discrete groups (English)
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