Text only print
Full screen print
Seminar information archive
Seminar information archive ～05/05｜Today's seminar 05/06 | Future seminars 05/07～
2010/12/01
Number Theory Seminar
16:30-18:45 Room #056 (Graduate School of Math. Sci. Bldg.)
Yuichiro Hoshi (RIMS, Kyoto University) 16:30-17:30
On a problem of Matsumoto and Tamagawa concerning monodromic fullness of hyperbolic curves (JAPANESE)
Galois theory for schemes (ENGLISH)
Yuichiro Hoshi (RIMS, Kyoto University) 16:30-17:30
On a problem of Matsumoto and Tamagawa concerning monodromic fullness of hyperbolic curves (JAPANESE)
[ Abstract ]
In this talk, we will discuss the following problem posed by Makoto Matsumoto and Akio Tamagawa concerning monodromic fullness of hyperbolic curves.
For a hyperbolic curve X over a number field, are the following three conditions equivalent?
(A) For any prime number l, X is quasi-l-monodromically full.
(B) There exists a prime number l such that X is l-monodromically full.
(C) X is l-monodromically full for all but finitely many prime numbers l.
The property of being (quasi-)monodromically full may be regarded as an analogue for hyperbolic curves of the property of not admitting complex multiplication for elliptic curves, and the above equivalence may be regarded as an analogue for hyperbolic curves of the following result concerning the Galois representation on the Tate module of an elliptic curve over a number field proven by Jean-Pierre Serre.
For an elliptic curve E over a number field, the following four conditions are equivalent:
(0) E does not admit complex multiplication.
(1) For any prime number l, the image of the l-adic Galois representation associated to E is open.
(2) There exists a prime number l such that the l-adic Galois representation associated to E is surjective.
(3) The l-adic Galois representation associated to E is surjective for all but finitely many prime numbers l.
In this talk, I will present some results concerning the above problem in the case where the given hyperbolic curve is of genus zero. In particular, I will give an example of a hyperbolic curve of type (0,4) over a number field which satisfies condition (C) but does not satisfy condition (A).
Marco Garuti (University of Padova) 17:45-18:45In this talk, we will discuss the following problem posed by Makoto Matsumoto and Akio Tamagawa concerning monodromic fullness of hyperbolic curves.
For a hyperbolic curve X over a number field, are the following three conditions equivalent?
(A) For any prime number l, X is quasi-l-monodromically full.
(B) There exists a prime number l such that X is l-monodromically full.
(C) X is l-monodromically full for all but finitely many prime numbers l.
The property of being (quasi-)monodromically full may be regarded as an analogue for hyperbolic curves of the property of not admitting complex multiplication for elliptic curves, and the above equivalence may be regarded as an analogue for hyperbolic curves of the following result concerning the Galois representation on the Tate module of an elliptic curve over a number field proven by Jean-Pierre Serre.
For an elliptic curve E over a number field, the following four conditions are equivalent:
(0) E does not admit complex multiplication.
(1) For any prime number l, the image of the l-adic Galois representation associated to E is open.
(2) There exists a prime number l such that the l-adic Galois representation associated to E is surjective.
(3) The l-adic Galois representation associated to E is surjective for all but finitely many prime numbers l.
In this talk, I will present some results concerning the above problem in the case where the given hyperbolic curve is of genus zero. In particular, I will give an example of a hyperbolic curve of type (0,4) over a number field which satisfies condition (C) but does not satisfy condition (A).
Galois theory for schemes (ENGLISH)
[ Abstract ]
We discuss some aspects of finite group scheme actions: the Galois correspondence and the notion of Galois closure.
We discuss some aspects of finite group scheme actions: the Galois correspondence and the notion of Galois closure.
2010/11/30
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Yasunori Aoki (University of Waterloo/NII)
Finite volume element method for singular solutions of elliptic PDEs
(JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Yasunori Aoki (University of Waterloo/NII)
Finite volume element method for singular solutions of elliptic PDEs
(JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Nobuhiro Nakamura (The University of Tokyo)
Pin^-(2)-monopole equations and intersection forms with local coefficients of 4-manifolds (JAPANESE)
Nobuhiro Nakamura (The University of Tokyo)
Pin^-(2)-monopole equations and intersection forms with local coefficients of 4-manifolds (JAPANESE)
[ Abstract ]
We introduce a variant of the Seiberg-Witten equations, Pin^-(2)-monopole equations, and explain its applications to intersection forms with local coefficients of 4-manifolds.
The first application is an analogue of Froyshov's results on 4-manifolds which have definite forms with local coefficients.
The second one is a local coefficient version of Furuta's 10/8-inequality.
As a corollary, we construct nonsmoothable spin 4-manifolds satisfying Rohlin's theorem and the 10/8-inequality.
We introduce a variant of the Seiberg-Witten equations, Pin^-(2)-monopole equations, and explain its applications to intersection forms with local coefficients of 4-manifolds.
The first application is an analogue of Froyshov's results on 4-manifolds which have definite forms with local coefficients.
The second one is a local coefficient version of Furuta's 10/8-inequality.
As a corollary, we construct nonsmoothable spin 4-manifolds satisfying Rohlin's theorem and the 10/8-inequality.
Operator Algebra Seminars
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Yi-Jun Yao (Fudan Univ.)
Noncommutative geometry and Rankin-Cohen brackets (ENGLISH)
Yi-Jun Yao (Fudan Univ.)
Noncommutative geometry and Rankin-Cohen brackets (ENGLISH)
2010/11/29
Kavli IPMU Komaba Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Scott Carnahan (IPMU)
Borcherds products in monstrous moonshine. (ENGLISH)
Scott Carnahan (IPMU)
Borcherds products in monstrous moonshine. (ENGLISH)
[ Abstract ]
During the 1980s, Koike, Norton, and Zagier independently found an
infinite product expansion for the difference of two modular j-functions
on a product of half planes. Borcherds showed that this product identity
is the Weyl denominator formula for an infinite dimensional Lie algebra
that has an action of the monster simple group by automorphisms, and used
this action to prove the monstrous moonshine conjectures.
I will describe a more general construction that yields an infinite
product identity and an infinite dimensional Lie algebra for each element
of the monster group. The above objects then arise as the special cases
assigned to the identity element. Time permitting, I will attempt to
describe a connection to conformal field theory.
During the 1980s, Koike, Norton, and Zagier independently found an
infinite product expansion for the difference of two modular j-functions
on a product of half planes. Borcherds showed that this product identity
is the Weyl denominator formula for an infinite dimensional Lie algebra
that has an action of the monster simple group by automorphisms, and used
this action to prove the monstrous moonshine conjectures.
I will describe a more general construction that yields an infinite
product identity and an infinite dimensional Lie algebra for each element
of the monster group. The above objects then arise as the special cases
assigned to the identity element. Time permitting, I will attempt to
describe a connection to conformal field theory.
Algebraic Geometry Seminar
16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)
Hisanori Ohashi (Nagoya Univ. )
K3 surfaces and log del Pezzo surfaces of index three (JAPANESE)
Hisanori Ohashi (Nagoya Univ. )
K3 surfaces and log del Pezzo surfaces of index three (JAPANESE)
[ Abstract ]
Alexeev and Nikulin have classified log del Pezzo surfaces of index 1 and 2 by using the classification of non-symplectic involutions on K3 surfaces. We want to discuss the generalization of this result to the index 3 cases. In this case we are also able to construct log del Pezzos $Z$ from K3 surfaces $X$, but the converse is not necessarily true. The condition on $Z$ is exactly the "multiple smooth divisor property", which we will define. Our theorem is the classification of log del Pezzo surfaces of index 3 with this property.
The idea of the proof is similar to that of Alexeev and Nikulin, but the methods are different because of the existence of singularities: although the singularity is mild, the description of nef cone by reflection groups cannot be used. Instead
we construct and analyze good elliptic fibrations on K3 surfaces $X$ and use it to obtain the classification. It includes a partial but geometric generalization of the classification of non-symplectic automorphisms of order three, recently done by Artebani, Sarti and Taki.
Alexeev and Nikulin have classified log del Pezzo surfaces of index 1 and 2 by using the classification of non-symplectic involutions on K3 surfaces. We want to discuss the generalization of this result to the index 3 cases. In this case we are also able to construct log del Pezzos $Z$ from K3 surfaces $X$, but the converse is not necessarily true. The condition on $Z$ is exactly the "multiple smooth divisor property", which we will define. Our theorem is the classification of log del Pezzo surfaces of index 3 with this property.
The idea of the proof is similar to that of Alexeev and Nikulin, but the methods are different because of the existence of singularities: although the singularity is mild, the description of nef cone by reflection groups cannot be used. Instead
we construct and analyze good elliptic fibrations on K3 surfaces $X$ and use it to obtain the classification. It includes a partial but geometric generalization of the classification of non-symplectic automorphisms of order three, recently done by Artebani, Sarti and Taki.
2010/11/26
Kavli IPMU Komaba Seminar
14:40-16:10 Room #002 (Graduate School of Math. Sci. Bldg.)
Tomoo Matsumura (Cornell University)
Hamiltonian torus actions on orbifolds and orbifold-GKM theorem (joint
work with T. Holm) (JAPANESE)
Tomoo Matsumura (Cornell University)
Hamiltonian torus actions on orbifolds and orbifold-GKM theorem (joint
work with T. Holm) (JAPANESE)
[ Abstract ]
When a symplectic manifold M carries a Hamiltonian torus R action, the
injectivity theorem states that the R-equivariant cohomology of M is a
subring of the one of the fixed points and the GKM theorem allows us
to compute this subring by only using the data of 1-dimensional
orbits. The results in the first part of this talk are a
generalization of this technique to Hamiltonian R actions on orbifolds
and an application to the computation of the equivariant cohomology of
toric orbifolds. In the second part, we will introduce the equivariant
Chen-Ruan cohomology ring which is a symplectic invariant of the
action on the orbifold and explain the injectivity/GKM theorem for this ring.
When a symplectic manifold M carries a Hamiltonian torus R action, the
injectivity theorem states that the R-equivariant cohomology of M is a
subring of the one of the fixed points and the GKM theorem allows us
to compute this subring by only using the data of 1-dimensional
orbits. The results in the first part of this talk are a
generalization of this technique to Hamiltonian R actions on orbifolds
and an application to the computation of the equivariant cohomology of
toric orbifolds. In the second part, we will introduce the equivariant
Chen-Ruan cohomology ring which is a symplectic invariant of the
action on the orbifold and explain the injectivity/GKM theorem for this ring.
2010/11/25
Operator Algebra Seminars
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Reiji Tomatsu (Tokyo Univ. Science)
Classification of actions of Kac algebras (JAPANESE)
Reiji Tomatsu (Tokyo Univ. Science)
Classification of actions of Kac algebras (JAPANESE)
2010/11/18
Operator Algebra Seminars
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Jean Roydor (Univ. Tokyo)
Perturbation of dual operator algebras and similarity (ENGLISH)
Jean Roydor (Univ. Tokyo)
Perturbation of dual operator algebras and similarity (ENGLISH)
2010/11/17
Number Theory Seminar
16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Shin Harase (University of Tokyo)
Fast lattice reduction for F_2-linear pseudorandom number generators (JAPANESE)
Shin Harase (University of Tokyo)
Fast lattice reduction for F_2-linear pseudorandom number generators (JAPANESE)
2010/11/16
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Xuefeng Liu (Waseda University/CREST, JST)
On verified evaluation of eigenvalues for elliptic operator over arbitrary polygonal domain (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Xuefeng Liu (Waseda University/CREST, JST)
On verified evaluation of eigenvalues for elliptic operator over arbitrary polygonal domain (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Noboru Ito (Waseda University)
On a colored Khovanov bicomplex (JAPANESE)
Noboru Ito (Waseda University)
On a colored Khovanov bicomplex (JAPANESE)
[ Abstract ]
We discuss the existence of a bicomplex which is a Khovanov-type
complex associated with categorification of a colored Jones polynomial.
This is an answer to the question proposed by A. Beliakova and S. Wehrli.
Then the second term of the spectral sequence of the bicomplex corresponds
to the Khovanov-type homology group. In this talk, we explain how to define
the bicomplex. If time permits, we also define a colored Rasmussen invariant
by using another spectral sequence of the colored Jones polynomial.
We discuss the existence of a bicomplex which is a Khovanov-type
complex associated with categorification of a colored Jones polynomial.
This is an answer to the question proposed by A. Beliakova and S. Wehrli.
Then the second term of the spectral sequence of the bicomplex corresponds
to the Khovanov-type homology group. In this talk, we explain how to define
the bicomplex. If time permits, we also define a colored Rasmussen invariant
by using another spectral sequence of the colored Jones polynomial.
Algebraic Geometry Seminar
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Viacheslav Nikulin (Univ Liverpool and Steklov Moscow)
Self-corresponences of K3 surfaces via moduli of sheaves (ENGLISH)
Viacheslav Nikulin (Univ Liverpool and Steklov Moscow)
Self-corresponences of K3 surfaces via moduli of sheaves (ENGLISH)
[ Abstract ]
In series of our papers with Carlo Madonna (2002--2008) we described self-correspondences via moduli of sheaves with primitive isotropic Mukai vectors for K3 surfaces with Picard number one or two. Here, we give a natural and functorial answer to the same problem for arbitrary Picard number of K3 surfaces. As an application, we characterize in terms of self-correspondences via moduli of sheaves K3 surfaces with reflective Picard lattices, that is when the automorphism group of the lattice is generated by reflections up to finite index. See some details in arXiv:0810.2945.
In series of our papers with Carlo Madonna (2002--2008) we described self-correspondences via moduli of sheaves with primitive isotropic Mukai vectors for K3 surfaces with Picard number one or two. Here, we give a natural and functorial answer to the same problem for arbitrary Picard number of K3 surfaces. As an application, we characterize in terms of self-correspondences via moduli of sheaves K3 surfaces with reflective Picard lattices, that is when the automorphism group of the lattice is generated by reflections up to finite index. See some details in arXiv:0810.2945.
Algebraic Geometry Seminar
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Viacheslav Nikulin (Univ Liverpool and Steklov Moscow)
Self-corresponences of K3 surfaces via moduli of sheaves (ENGLISH)
Viacheslav Nikulin (Univ Liverpool and Steklov Moscow)
Self-corresponences of K3 surfaces via moduli of sheaves (ENGLISH)
[ Abstract ]
In series of our papers with Carlo Madonna (2002--2008) we described self-correspondences via moduli of sheaves with primitive isotropic Mukai vectors for K3 surfaces with Picard number one or two. Here, we give a natural and functorial answer to the same problem for arbitrary Picard number of K3 surfaces. As an application, we characterize in terms of self-correspondences via moduli of sheaves K3 surfaces with reflective Picard lattices, that is when the automorphism group of the lattice is generated by reflections up to finite index. See some details in arXiv:0810.2945.
In series of our papers with Carlo Madonna (2002--2008) we described self-correspondences via moduli of sheaves with primitive isotropic Mukai vectors for K3 surfaces with Picard number one or two. Here, we give a natural and functorial answer to the same problem for arbitrary Picard number of K3 surfaces. As an application, we characterize in terms of self-correspondences via moduli of sheaves K3 surfaces with reflective Picard lattices, that is when the automorphism group of the lattice is generated by reflections up to finite index. See some details in arXiv:0810.2945.
Tuesday Seminar of Analysis
16:00-18:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Keisuke Uchikoshi (National Defense Academy of Japan) 16:00-16:45
Hyperfunctions and vortex sheets (ENGLISH)
L. Boutet de Monvel (University of Paris 6) 17:00-18:30
Residual trace and equivariant asymptotic trace of Toeplitz operators (ENGLISH)
Keisuke Uchikoshi (National Defense Academy of Japan) 16:00-16:45
Hyperfunctions and vortex sheets (ENGLISH)
L. Boutet de Monvel (University of Paris 6) 17:00-18:30
Residual trace and equivariant asymptotic trace of Toeplitz operators (ENGLISH)
2010/11/15
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Tatsuo Suwa (Hokkaido Univ*)
Excess intersections and residues in improper dimension (JAPANESE)
Tatsuo Suwa (Hokkaido Univ*)
Excess intersections and residues in improper dimension (JAPANESE)
[ Abstract ]
This talk concerns localization of characteristic classes and associated residues, in the context of intersection theory and residue theory of singular holomorphic foliations. The localization comes from the vanishing of certain characteristic forms, usually caused by the existence of some geometric object, away from the "singular set" of the object. This gives rise to residues in the homology of the singular set and residue theorems relating local and global invariants. In the generic situation, i.e., if the dimension of the singular set is "proper", we have a reasonable understanding of the residues. We indicate how to cope with the problem when the dimension is "excessive" (partly a joint work with F. Bracci).
This talk concerns localization of characteristic classes and associated residues, in the context of intersection theory and residue theory of singular holomorphic foliations. The localization comes from the vanishing of certain characteristic forms, usually caused by the existence of some geometric object, away from the "singular set" of the object. This gives rise to residues in the homology of the singular set and residue theorems relating local and global invariants. In the generic situation, i.e., if the dimension of the singular set is "proper", we have a reasonable understanding of the residues. We indicate how to cope with the problem when the dimension is "excessive" (partly a joint work with F. Bracci).
Algebraic Geometry Seminar
16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)
Shuhei Yoshitomi (Univ. of Tokyo)
Generators of tropical modules (JAPANESE)
Shuhei Yoshitomi (Univ. of Tokyo)
Generators of tropical modules (JAPANESE)
2010/11/09
Tuesday Seminar on Topology
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Ken'ichi Ohshika (Osaka University)
Characterising bumping points on deformation spaces of Kleinian groups (JAPANESE)
Ken'ichi Ohshika (Osaka University)
Characterising bumping points on deformation spaces of Kleinian groups (JAPANESE)
[ Abstract ]
It is known that components of the interior of a deformation space of a Kleinian group can bump, and a component of the interior can bump itself, on the boundary of the deformation space.
Anderson-Canary-McCullogh gave a necessary and sufficient condition for two components to bump.
In this talk, I shall give a criterion for points on the boundary to be bumping points.
It is known that components of the interior of a deformation space of a Kleinian group can bump, and a component of the interior can bump itself, on the boundary of the deformation space.
Anderson-Canary-McCullogh gave a necessary and sufficient condition for two components to bump.
In this talk, I shall give a criterion for points on the boundary to be bumping points.
2010/11/08
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Hajime Tsuji (Sophia Univ)
Variation of canonical measures under Kaehler deformations (JAPANESE)
Hajime Tsuji (Sophia Univ)
Variation of canonical measures under Kaehler deformations (JAPANESE)
GCOE lecture series
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Michael Eastwood (Australian National University)
Invariant differential operators on the sphere (ENGLISH)
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20101102eastwood
Michael Eastwood (Australian National University)
Invariant differential operators on the sphere (ENGLISH)
[ Abstract ]
The circle is acted upon by the rotation group SO(2) and there are plenty of differential operators invariant under this action. But the circle is also acted upon by SL(2,R) and this larger symmetry group cuts down the list of invariant differential operators to something smaller but more interesting! I shall explain what happens and how this phenomenon generalises to spheres. These constructions are part of a general theory but have numerous unexpected applications, for example in suggesting a new stable finite-element scheme in linearised elasticity (due to Arnold, Falk, and Winther).
[ Reference URL ]The circle is acted upon by the rotation group SO(2) and there are plenty of differential operators invariant under this action. But the circle is also acted upon by SL(2,R) and this larger symmetry group cuts down the list of invariant differential operators to something smaller but more interesting! I shall explain what happens and how this phenomenon generalises to spheres. These constructions are part of a general theory but have numerous unexpected applications, for example in suggesting a new stable finite-element scheme in linearised elasticity (due to Arnold, Falk, and Winther).
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20101102eastwood
2010/11/05
GCOE lecture series
16:30-18:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Michael Eastwood (Australian National University)
How to recognise the geodesics of a metric connection (ENGLISH)
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20101102eastwood
Michael Eastwood (Australian National University)
How to recognise the geodesics of a metric connection (ENGLISH)
[ Abstract ]
The geodesics on a Riemannian manifold form a distinguished family of curves, one in every direction through every point. Sometimes two metrics can provide the same family of curves: the Euclidean metric and the round metric on the hemisphere have this property. It is also possible that a family of curves does not arise from a metric at all. Following a classical procedure due to Roger Liouville, I shall explain how to tell these cases apart on a surface. This is joint work with Robert Bryant and Maciej Dunajski.
[ Reference URL ]The geodesics on a Riemannian manifold form a distinguished family of curves, one in every direction through every point. Sometimes two metrics can provide the same family of curves: the Euclidean metric and the round metric on the hemisphere have this property. It is also possible that a family of curves does not arise from a metric at all. Following a classical procedure due to Roger Liouville, I shall explain how to tell these cases apart on a surface. This is joint work with Robert Bryant and Maciej Dunajski.
https://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar2010.html#20101102eastwood
2010/11/04
Operator Algebra Seminars
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Yoshiko Ogata (Univ.Tokyo)
Nonequilibrium Statistical Mechanics (JAPANESE)
Yoshiko Ogata (Univ.Tokyo)
Nonequilibrium Statistical Mechanics (JAPANESE)
Lectures
10:40-12:10 Room #123 (Graduate School of Math. Sci. Bldg.)
Jean Meyer, Yasuko HISAMATSU (Risk Capital Market Tokyo, BNP Paribas)
Market, Liquidity and Counterparty Risk (ENGLISH)
Jean Meyer, Yasuko HISAMATSU (Risk Capital Market Tokyo, BNP Paribas)
Market, Liquidity and Counterparty Risk (ENGLISH)
[ Abstract ]
1. Introduction to the market risk
- Introduction to the Risk Management
in the Financial institutions
- Overview of the main market risks
2. Market & Liquidity Risks –Basics
-Presentation of the main Greeks
-Focus on volatility risk
-Focus on correlation risk
-Conclusion (common features of the market risks)
3. Risk measure
- Stress test
- Value at risk
- Risks measure for counterparty risk
1. Introduction to the market risk
- Introduction to the Risk Management
in the Financial institutions
- Overview of the main market risks
2. Market & Liquidity Risks –Basics
-Presentation of the main Greeks
-Focus on volatility risk
-Focus on correlation risk
-Conclusion (common features of the market risks)
3. Risk measure
- Stress test
- Value at risk
- Risks measure for counterparty risk
2010/11/02
Lectures
13:00-16:10 Room #122 (Graduate School of Math. Sci. Bldg.)
Vladimir Bogachev (Moscow)
The Malliavin calculus on configuration spaces and applications (ENGLISH)
Vladimir Bogachev (Moscow)
The Malliavin calculus on configuration spaces and applications (ENGLISH)
[ Abstract ]
It is planned to discuss first a general scheme of the Malliavin
calculus on an abstract measurable
manifold with minimal assumptions about the manifold.
Then a practical realization of this scheme will be discussed in
several concrete examples with emphasis
on configuration spaces, i.e., spaces of locally finite configurations
in a given manifold (for example, just
a finite-dimensional Euclidean space), which can be alternatively
described as the spaces of integer-valued
discrete measures equipped with suitable differential structures.
No acquaintance with the Malliavin calculus and differential geometry
is assumed.
It is planned to discuss first a general scheme of the Malliavin
calculus on an abstract measurable
manifold with minimal assumptions about the manifold.
Then a practical realization of this scheme will be discussed in
several concrete examples with emphasis
on configuration spaces, i.e., spaces of locally finite configurations
in a given manifold (for example, just
a finite-dimensional Euclidean space), which can be alternatively
described as the spaces of integer-valued
discrete measures equipped with suitable differential structures.
No acquaintance with the Malliavin calculus and differential geometry
is assumed.
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Daniel Ruberman (Brandeis University)
Periodic-end manifolds and SW theory (ENGLISH)
Daniel Ruberman (Brandeis University)
Periodic-end manifolds and SW theory (ENGLISH)
[ Abstract ]
We study an extension of Seiberg-Witten invariants to
4-manifolds with the homology of S^1 \\times S^3. This extension has
many potential applications in low-dimensional topology, including the
study of the homology cobordism group. Because b_2^+ =0, the usual
strategy for defining invariants does not work--one cannot disregard
reducible solutions. In fact, the count of solutions can jump in a
family of metrics or perturbations. To remedy this, we define an
index-theoretic counter-term that jumps by the same amount. The
counterterm is the index of the Dirac operator on a manifold with a
periodic end modeled at infinity by the infinite cyclic cover of the
manifold. This is joint work with Tomasz Mrowka and Nikolai Saveliev.
We study an extension of Seiberg-Witten invariants to
4-manifolds with the homology of S^1 \\times S^3. This extension has
many potential applications in low-dimensional topology, including the
study of the homology cobordism group. Because b_2^+ =0, the usual
strategy for defining invariants does not work--one cannot disregard
reducible solutions. In fact, the count of solutions can jump in a
family of metrics or perturbations. To remedy this, we define an
index-theoretic counter-term that jumps by the same amount. The
counterterm is the index of the Dirac operator on a manifold with a
periodic end modeled at infinity by the infinite cyclic cover of the
manifold. This is joint work with Tomasz Mrowka and Nikolai Saveliev.
< Previous 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186 Next >
