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Seminar information archive
Seminar information archive ～07/26｜Today's seminar 07/27 | Future seminars 07/28～
2010/12/13
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Katsutoshi Yamanoi (Tokyo Institute of Technology)
An equality estimate for the second main theorem (JAPANESE)
Katsutoshi Yamanoi (Tokyo Institute of Technology)
An equality estimate for the second main theorem (JAPANESE)
Algebraic Geometry Seminar
16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)
Sergey Fomin (University of Michigan)
Enumeration of plane curves and labeled floor diagrams (ENGLISH)
Sergey Fomin (University of Michigan)
Enumeration of plane curves and labeled floor diagrams (ENGLISH)
[ Abstract ]
Floor diagrams are a class of weighted oriented graphs introduced by E. Brugalle and G. Mikhalkin. Tropical geometry arguments yield combinatorial descriptions of (ordinary and relative) Gromov-Witten invariants of projective spaces in terms of floor diagrams and their generalizations. In the case of the projective plane, these descriptions can be used to obtain new formulas for the corresponding enumerative invariants. In particular, we give a proof of Goettsche's polynomiality conjecture for plane curves, and enumerate plane rational curves of given degree passing through given points and having maximal tangency to a given line. On the combinatorial side, we show that labeled floor diagrams of genus 0 are equinumerous to labeled trees, and therefore counted by the celebrated Cayley's formula. The corresponding bijections lead to interpretations of the Kontsevich numbers (the genus-0 Gromov-Witten invariants of the projective plane) in terms of certain statistics on trees.
This is joint work with Grisha Mikhalkin.
Floor diagrams are a class of weighted oriented graphs introduced by E. Brugalle and G. Mikhalkin. Tropical geometry arguments yield combinatorial descriptions of (ordinary and relative) Gromov-Witten invariants of projective spaces in terms of floor diagrams and their generalizations. In the case of the projective plane, these descriptions can be used to obtain new formulas for the corresponding enumerative invariants. In particular, we give a proof of Goettsche's polynomiality conjecture for plane curves, and enumerate plane rational curves of given degree passing through given points and having maximal tangency to a given line. On the combinatorial side, we show that labeled floor diagrams of genus 0 are equinumerous to labeled trees, and therefore counted by the celebrated Cayley's formula. The corresponding bijections lead to interpretations of the Kontsevich numbers (the genus-0 Gromov-Witten invariants of the projective plane) in terms of certain statistics on trees.
This is joint work with Grisha Mikhalkin.
2010/12/10
Colloquium
16:30-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)
Yoshikazu Giga (The University of Tokyo, Graduate School of Mathematical Sciences)
Hamilton-Jacobi equations and crystal growth (JAPANESE)
Yoshikazu Giga (The University of Tokyo, Graduate School of Mathematical Sciences)
Hamilton-Jacobi equations and crystal growth (JAPANESE)
2010/12/09
Operator Algebra Seminars
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Ryszard Nest (Univ. Copenhagen)
Spectral flow associated to KMS states with periodic KMS group action (ENGLISH)
Ryszard Nest (Univ. Copenhagen)
Spectral flow associated to KMS states with periodic KMS group action (ENGLISH)
2010/12/07
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Raphael Ponge (The University of Tokyo)
Diffeomorphism-invariant geometries and noncommutative geometry (ENGLISH)
Raphael Ponge (The University of Tokyo)
Diffeomorphism-invariant geometries and noncommutative geometry (ENGLISH)
[ Abstract ]
In many geometric situations we may encounter the action of
a group $G$ on a manifold $M$, e.g., in the context of foliations. If
the action is free and proper, then the quotient $M/G$ is a smooth
manifold. However, in general the quotient $M/G$ need not even be
Hausdorff. Furthermore, it is well-known that a manifold has structure
invariant under the full group of diffeomorphisms except the
differentiable structure itself. Under these conditions how can one do
diffeomorphism-invariant geometry?
Noncommutative geometry provides us with the solution of trading the
ill-behaved space $M/G$ for a non-commutative algebra which
essentially plays the role of the algebra of smooth functions on that
space. The local index formula of Atiyah-Singer ultimately holds in
the setting of noncommutative geometry. Using this framework Connes
and Moscovici then obtained in the 90s a striking reformulation of the
local index formula in diffeomorphism-invariant geometry.
An important part the talk will be devoted to reviewing noncommutative
geometry and Connes-Moscovici's index formula. We will then hint to on-
going projects about reformulating the local index formula in two new
geometric settings: biholomorphism-invariant geometry of strictly
pseudo-convex domains and contactomorphism-invariant geometry.
In many geometric situations we may encounter the action of
a group $G$ on a manifold $M$, e.g., in the context of foliations. If
the action is free and proper, then the quotient $M/G$ is a smooth
manifold. However, in general the quotient $M/G$ need not even be
Hausdorff. Furthermore, it is well-known that a manifold has structure
invariant under the full group of diffeomorphisms except the
differentiable structure itself. Under these conditions how can one do
diffeomorphism-invariant geometry?
Noncommutative geometry provides us with the solution of trading the
ill-behaved space $M/G$ for a non-commutative algebra which
essentially plays the role of the algebra of smooth functions on that
space. The local index formula of Atiyah-Singer ultimately holds in
the setting of noncommutative geometry. Using this framework Connes
and Moscovici then obtained in the 90s a striking reformulation of the
local index formula in diffeomorphism-invariant geometry.
An important part the talk will be devoted to reviewing noncommutative
geometry and Connes-Moscovici's index formula. We will then hint to on-
going projects about reformulating the local index formula in two new
geometric settings: biholomorphism-invariant geometry of strictly
pseudo-convex domains and contactomorphism-invariant geometry.
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Akitoshi Takayasu (Waseda University)
Numerical verification of existence for solutions to Dirichlet
boundary value problems of semilinear elliptic equations
(JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Akitoshi Takayasu (Waseda University)
Numerical verification of existence for solutions to Dirichlet
boundary value problems of semilinear elliptic equations
(JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
2010/12/06
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Hajime Ono (Tokyo Univ of Science)
Chow semistability of polarized toric manifolds (JAPANESE)
Hajime Ono (Tokyo Univ of Science)
Chow semistability of polarized toric manifolds (JAPANESE)
2010/12/04
Classical Analysis
09:30-10:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Toshihiko Matsuki (Kyoto University)
Orbit decomposition of multiple flag varieties and representations of of quiver (JAPANESE)
Toshihiko Matsuki (Kyoto University)
Orbit decomposition of multiple flag varieties and representations of of quiver (JAPANESE)
Classical Analysis
10:40-11:40 Room #056 (Graduate School of Math. Sci. Bldg.)
Kouichi Takemura (Chuo University)
Integral transformations on the Heun equation and its applications (JAPANESE)
Kouichi Takemura (Chuo University)
Integral transformations on the Heun equation and its applications (JAPANESE)
Classical Analysis
13:00-14:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Kazuki Hiroe (University of Tokyo)
Weyl group symmetries of double confluent Heun equations (JAPANESE)
Kazuki Hiroe (University of Tokyo)
Weyl group symmetries of double confluent Heun equations (JAPANESE)
Classical Analysis
14:10-15:10 Room #056 (Graduate School of Math. Sci. Bldg.)
Takao Suzuki (Kobe University)
Affine root systems, monodromy preserving deformation, and hypergeometric functions (JAPANESE)
Takao Suzuki (Kobe University)
Affine root systems, monodromy preserving deformation, and hypergeometric functions (JAPANESE)
Classical Analysis
15:30-16:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Jiro Sekiguchi (Tokyo University of Agriculture and Technology)
On the uniformization equations which have singularities along discriminant of complex reflection groups of rank three (JAPANESE)
Jiro Sekiguchi (Tokyo University of Agriculture and Technology)
On the uniformization equations which have singularities along discriminant of complex reflection groups of rank three (JAPANESE)
2010/12/03
GCOE Seminars
11:00-12:00 Room #270 (Graduate School of Math. Sci. Bldg.)
Jarmo Hietarinta (University of Turku)
Discrete Integrability and Consistency-Around-the-Cube (CAC) (ENGLISH)
Jarmo Hietarinta (University of Turku)
Discrete Integrability and Consistency-Around-the-Cube (CAC) (ENGLISH)
[ Abstract ]
For integrable lattice equations we can still apply many integrability criteria that are regularly used for continuous systems, but there are also some that are specific for discrete systems. One particularly successful discrete integrability criterion is the multidimensional consistency, or CAC. We review the classic results of Nijhoff and of Adler-Bobenko-Suris and then present some extensions.
For integrable lattice equations we can still apply many integrability criteria that are regularly used for continuous systems, but there are also some that are specific for discrete systems. One particularly successful discrete integrability criterion is the multidimensional consistency, or CAC. We review the classic results of Nijhoff and of Adler-Bobenko-Suris and then present some extensions.
GCOE Seminars
13:30-14:30 Room #370 (Graduate School of Math. Sci. Bldg.)
Nalini Joshi (University of Sydney)
Geometric asymptotics of the first Painleve equation (ENGLISH)
Nalini Joshi (University of Sydney)
Geometric asymptotics of the first Painleve equation (ENGLISH)
[ Abstract ]
I will report on my recent collaboration with Hans Duistermaat on the geometry of the space of initial values of the first Painleve equation, which was first constructed by Okamoto. We show that highly accurate information about solutions can be found by utilizing the regularized and compactified space of initial values in Boutroux's coordinates. I will also describe numerical explorations based on this work obtained in collaboration with Holger Dullin.
I will report on my recent collaboration with Hans Duistermaat on the geometry of the space of initial values of the first Painleve equation, which was first constructed by Okamoto. We show that highly accurate information about solutions can be found by utilizing the regularized and compactified space of initial values in Boutroux's coordinates. I will also describe numerical explorations based on this work obtained in collaboration with Holger Dullin.
Classical Analysis
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Daisuke Yamakawa (Kobe University)
The third Painlev¥'e equation and quiver varieties (JAPANESE)
Daisuke Yamakawa (Kobe University)
The third Painlev¥'e equation and quiver varieties (JAPANESE)
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)
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