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Seminar information archive
Seminar information archive ～12/08｜Today's seminar 12/09 | Future seminars 12/10～
2017/05/08
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Taro Fujisawa (Tokyo Denki University)
Semipositivity theorems for a variation of Hodge structure
Taro Fujisawa (Tokyo Denki University)
Semipositivity theorems for a variation of Hodge structure
[ Abstract ]
I will talk about my recent joint work with Osamu Fujino. The main purpose of our joint work is to generalize the Fujita-Zukcer-Kawamata semipositivity theorem from the analytic viewpoint. In this talk, I would like to illustrate the relation between the two objects, the asymptotic behavior of a variation of Hodge structure and good properties of the induced singular hermitian metric on an invertible subbundle of the Hodge bundle.
I will talk about my recent joint work with Osamu Fujino. The main purpose of our joint work is to generalize the Fujita-Zukcer-Kawamata semipositivity theorem from the analytic viewpoint. In this talk, I would like to illustrate the relation between the two objects, the asymptotic behavior of a variation of Hodge structure and good properties of the induced singular hermitian metric on an invertible subbundle of the Hodge bundle.
Geometry Colloquium
16:00-17:00 Room #056 (Graduate School of Math. Sci. Bldg.)
2017/04/28
Colloquium
15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Chihiro Matsui (Graduate School of Mathematical Sciences, the University of Tokyo)
可積分量子スピン鎖における隠れた超対称性 (JAPANESE)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~matsui/index.html
Chihiro Matsui (Graduate School of Mathematical Sciences, the University of Tokyo)
可積分量子スピン鎖における隠れた超対称性 (JAPANESE)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~matsui/index.html
2017/04/26
Discrete mathematical modelling seminar
15:30-17:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Yohei Tutiya (Kanagawa Institute of Technology)
[Recent topics in nonlocal classical integrable systems] (JAPANESE)
Yohei Tutiya (Kanagawa Institute of Technology)
[Recent topics in nonlocal classical integrable systems] (JAPANESE)
2017/04/25
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Yusuke Kuno (Tsuda University)
Formality of the Goldman-Turaev Lie bialgebra and the Kashiwara-Vergne problem in positive genus (JAPANESE)
Yusuke Kuno (Tsuda University)
Formality of the Goldman-Turaev Lie bialgebra and the Kashiwara-Vergne problem in positive genus (JAPANESE)
[ Abstract ]
This talk is based on a joint work with A. Alekseev, N. Kawazumi and F. Naef. Given a compact oriented surface with non-empty boundary and a framing of the surface, one can define the Lie bracket (Goldman bracket) and the Lie cobracket (Turaev bracket) on the vector space spanned by free homotopy classes of loops on the surface. These maps are of degree minus two with respect to a certain filtration. Then one can ask the formality of this Lie bialgebra: is the Goldman-Turaev Lie bialgebra isomorphic to its associated graded?
For surfaces of genus zero, we showed that this question is closely related to the Kashiwara-Vergne (KV) problem in Lie theory (arXiv:1703.05813). A similar result was obtained by G. Massuyeau by using the Kontsevich integral.
Our new topological interpretation of the classical KV problem leads us to introduce a generalization of the KV problem in connection with the formality of the Goldman-Turaev Lie bialgebra for surfaces of positive genus. We will discuss the existence and uniqueness of solutions to the generalized KV problem.
This talk is based on a joint work with A. Alekseev, N. Kawazumi and F. Naef. Given a compact oriented surface with non-empty boundary and a framing of the surface, one can define the Lie bracket (Goldman bracket) and the Lie cobracket (Turaev bracket) on the vector space spanned by free homotopy classes of loops on the surface. These maps are of degree minus two with respect to a certain filtration. Then one can ask the formality of this Lie bialgebra: is the Goldman-Turaev Lie bialgebra isomorphic to its associated graded?
For surfaces of genus zero, we showed that this question is closely related to the Kashiwara-Vergne (KV) problem in Lie theory (arXiv:1703.05813). A similar result was obtained by G. Massuyeau by using the Kontsevich integral.
Our new topological interpretation of the classical KV problem leads us to introduce a generalization of the KV problem in connection with the formality of the Goldman-Turaev Lie bialgebra for surfaces of positive genus. We will discuss the existence and uniqueness of solutions to the generalized KV problem.
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Taku Suzuki (Waseda University)
On the Picard number of Fano 6-folds with a non-small contraction (English)
Taku Suzuki (Waseda University)
On the Picard number of Fano 6-folds with a non-small contraction (English)
[ Abstract ]
A generalization of S. Mukai's conjecture says that $\rho(i-1) \leq n$ holds for any Fano $n$-fold with Picard number $\rho$ and pseudo-index $i$, with equality if and only if it is isomorphic to $(\mathbb{P}^{i-1})^{\rho}$. In this talk, we consider this conjecture for $n=6$, which is an open problem, and give a proof of some special cases.
A generalization of S. Mukai's conjecture says that $\rho(i-1) \leq n$ holds for any Fano $n$-fold with Picard number $\rho$ and pseudo-index $i$, with equality if and only if it is isomorphic to $(\mathbb{P}^{i-1})^{\rho}$. In this talk, we consider this conjecture for $n=6$, which is an open problem, and give a proof of some special cases.
Numerical Analysis Seminar
16:50-18:20 Room #002 (Graduate School of Math. Sci. Bldg.)
Koya Sakakibara (University of Tokyo)
Theory and application of the method of fundamental solutions (日本語)
Koya Sakakibara (University of Tokyo)
Theory and application of the method of fundamental solutions (日本語)
2017/04/24
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Hiroshi Konno (Meiji University)
Lagrangian Mean Curvature Flows and Moment maps
Hiroshi Konno (Meiji University)
Lagrangian Mean Curvature Flows and Moment maps
[ Abstract ]
In this talk, we construct various examples of Lagrangian mean curvature flows in Calabi-Yau manifolds, using moment maps for actions of abelian Lie groups on them. The examples include Lagrangian self-shrinkers and translating solitons in the Euclid spaces. We also construct Lagrangian mean curvature flows in non-flat Calabi-Yau manifolds. In particular, we describe Lagrangian mean curvature flows in 4-dimensional Ricci-flat ALE spaces in detail and investigate their singularities.
In this talk, we construct various examples of Lagrangian mean curvature flows in Calabi-Yau manifolds, using moment maps for actions of abelian Lie groups on them. The examples include Lagrangian self-shrinkers and translating solitons in the Euclid spaces. We also construct Lagrangian mean curvature flows in non-flat Calabi-Yau manifolds. In particular, we describe Lagrangian mean curvature flows in 4-dimensional Ricci-flat ALE spaces in detail and investigate their singularities.
Operator Algebra Seminars
16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)
Kei Hasegawa (Kyushu Univ.)
Bass-Serre trees of amalgamated free product $C^*$-algebras (English)
Kei Hasegawa (Kyushu Univ.)
Bass-Serre trees of amalgamated free product $C^*$-algebras (English)
Tokyo Probability Seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Shigeki Aida (Graduate School of Mathematical Science, the University of Tokyo)
Rough differential equations containing path-dependent bounded variation terms (JAPANESE)
Shigeki Aida (Graduate School of Mathematical Science, the University of Tokyo)
Rough differential equations containing path-dependent bounded variation terms (JAPANESE)
2017/04/20
Seminar on Probability and Statistics
15:00- Room #117 (Graduate School of Math. Sci. Bldg.)
David Nualart (Kansas University) -
Central limit theorem for symmetric integrals
David Nualart (Kansas University) -
Stochastic heat equation with rough multiplicative noise
David Nualart (Kansas University) -
Central limit theorem for symmetric integrals
David Nualart (Kansas University) -
Stochastic heat equation with rough multiplicative noise
[ Abstract ]
The aim of this talk is to present some results on the existence and uniqueness of a solution for the one-dimensional heat equation driven by a Gaussian noise which is white in time and it has the covariance of a fractional Brownian motion with Hurst parameter less than 1/2 in the space variable. In the linear case we establish a Feynman-Kac formula for the moments of the solution and discuss intermittency properties.
The aim of this talk is to present some results on the existence and uniqueness of a solution for the one-dimensional heat equation driven by a Gaussian noise which is white in time and it has the covariance of a fractional Brownian motion with Hurst parameter less than 1/2 in the space variable. In the linear case we establish a Feynman-Kac formula for the moments of the solution and discuss intermittency properties.
2017/04/18
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Takeru Fukuoka (The University of Tokyo)
On the existence of almost Fano threefolds with del Pezzo fibrations (English)
Takeru Fukuoka (The University of Tokyo)
On the existence of almost Fano threefolds with del Pezzo fibrations (English)
[ Abstract ]
We say that a smooth projective 3-fold is almost Fano if its anti-canonical divisor is nef and big but not ample. By Jahnke-Peternell-Radloff and Takeuchi, the numerical classification of such 3-folds was given. Among the classification results, there exists precisely 10 cases such that it was yet to be known whether these have an example or not. The main result of this talk shows the existence of examples of each of 10 cases. In 9 cases of the 10 cases, the degree of del Pezzo fibrations are 6. We will discuss one of the reason of difficulty constructing del Pezzo fibrations of degree 6. After that, we will show that every almost Fano del Pezzo fibration of degree 6 with specific anti-canonical volume can be embedded into some higher dimensional del Pezzo fibration as a relative linear section.
We say that a smooth projective 3-fold is almost Fano if its anti-canonical divisor is nef and big but not ample. By Jahnke-Peternell-Radloff and Takeuchi, the numerical classification of such 3-folds was given. Among the classification results, there exists precisely 10 cases such that it was yet to be known whether these have an example or not. The main result of this talk shows the existence of examples of each of 10 cases. In 9 cases of the 10 cases, the degree of del Pezzo fibrations are 6. We will discuss one of the reason of difficulty constructing del Pezzo fibrations of degree 6. After that, we will show that every almost Fano del Pezzo fibration of degree 6 with specific anti-canonical volume can be embedded into some higher dimensional del Pezzo fibration as a relative linear section.
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Takefumi Nosaka (Tokyo institute of Technology)
Milnor invariants via unipotent Magnus embeddings (JAPANESE)
Takefumi Nosaka (Tokyo institute of Technology)
Milnor invariants via unipotent Magnus embeddings (JAPANESE)
[ Abstract ]
We reconfigured the Milnor invariant, in terms of central group extensions and unipotent Magnus embeddings, and develop a diagrammatic computation of the invariant. In this talk, we explain the reconfiguration and the computation with mentioning some examples. I also introduce some properties of the unipotent embeddings. This is a joint work with Hisatoshi Kodani.
We reconfigured the Milnor invariant, in terms of central group extensions and unipotent Magnus embeddings, and develop a diagrammatic computation of the invariant. In this talk, we explain the reconfiguration and the computation with mentioning some examples. I also introduce some properties of the unipotent embeddings. This is a joint work with Hisatoshi Kodani.
2017/04/17
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yuta Kusakabe (Osaka University)
Dense holomorphic curves in spaces of holomorphic maps
Yuta Kusakabe (Osaka University)
Dense holomorphic curves in spaces of holomorphic maps
[ Abstract ]
We study when there exists a dense holomorphic curve in a space of holomorphic maps from a Stein space. Our results state that for any bounded convex domain $\Omega \Subset \mathbb{C}^n$ and any connected complex manifold $Y$, the space $\mathcal{O}(\Omega,Y)$ contains a dense holomorphic disc, and that $Y$ is an Oka manifold if and only if for any Stein space $X$ there exists a dense entire curve in every path component of $\mathcal{O}(X,Y)$. The latter gives a new characterization of Oka manifolds. As an application of the former, we construct universal maps from bounded convex domains to any connected complex manifold.
We study when there exists a dense holomorphic curve in a space of holomorphic maps from a Stein space. Our results state that for any bounded convex domain $\Omega \Subset \mathbb{C}^n$ and any connected complex manifold $Y$, the space $\mathcal{O}(\Omega,Y)$ contains a dense holomorphic disc, and that $Y$ is an Oka manifold if and only if for any Stein space $X$ there exists a dense entire curve in every path component of $\mathcal{O}(X,Y)$. The latter gives a new characterization of Oka manifolds. As an application of the former, we construct universal maps from bounded convex domains to any connected complex manifold.
Operator Algebra Seminars
16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)
Yoshikata Kida (Univ. Tokyo)
On diagonal actions whose full group is closed (English)
Yoshikata Kida (Univ. Tokyo)
On diagonal actions whose full group is closed (English)
Tokyo Probability Seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
David Croydon (University of Warwick)
Scaling limits of random walks via resistance forms (ENGLISH)
David Croydon (University of Warwick)
Scaling limits of random walks via resistance forms (ENGLISH)
[ Abstract ]
In this talk, I will describe some recent work (partly joint with T. Kumagai, Kyoto University, and B. M. Hambly, University of Oxford) regarding scaling limits for random walks on spaces where the scaling limit of the associated resistance metric can be understood. This work is particularly applicable to "low-dimensional" graphs, whose scaling limits are trees and fractals, for example. It also gives a framework for understanding various time-changed processes on the spaces in question, such as those arising from Liouville Brownian motion, the Bouchaud trap model and the random conductance model.
In this talk, I will describe some recent work (partly joint with T. Kumagai, Kyoto University, and B. M. Hambly, University of Oxford) regarding scaling limits for random walks on spaces where the scaling limit of the associated resistance metric can be understood. This work is particularly applicable to "low-dimensional" graphs, whose scaling limits are trees and fractals, for example. It also gives a framework for understanding various time-changed processes on the spaces in question, such as those arising from Liouville Brownian motion, the Bouchaud trap model and the random conductance model.
2017/04/12
Number Theory Seminar
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Hiraku Atobe (University of Tokyo)
A conjecture of Gross-Prasad and Rallis for metaplectic groups (JAPANESE)
Hiraku Atobe (University of Tokyo)
A conjecture of Gross-Prasad and Rallis for metaplectic groups (JAPANESE)
2017/04/11
Number Theory Seminar
17:30-18:30 Room #117 (Graduate School of Math. Sci. Bldg.)
Peter Scholze (University of Bonn)
The geometric Satake equivalence in mixed characteristic (ENGLISH)
Peter Scholze (University of Bonn)
The geometric Satake equivalence in mixed characteristic (ENGLISH)
[ Abstract ]
In order to apply V. Lafforgue's ideas to the study of representations of p-adic groups, one needs a version of the geometric Satake equivalence in that setting. For the affine Grassmannian defined using the Witt vectors, this has been proven by Zhu. However, one actually needs a version for the affine Grassmannian defined using Fontaine's ring B_dR, and related results on the Beilinson-Drinfeld Grassmannian over a self-product of Spa Q_p. These objects exist as diamonds, and in particular one can make sense of the fusion product in this situation; this is a priori surprising, as it entails colliding two distinct points of Spec Z. The focus of the talk will be on the geometry of the fusion product, and an analogue of the technically crucial ULA (Universally Locally Acyclic) condition that works in this non-algebraic setting.
In order to apply V. Lafforgue's ideas to the study of representations of p-adic groups, one needs a version of the geometric Satake equivalence in that setting. For the affine Grassmannian defined using the Witt vectors, this has been proven by Zhu. However, one actually needs a version for the affine Grassmannian defined using Fontaine's ring B_dR, and related results on the Beilinson-Drinfeld Grassmannian over a self-product of Spa Q_p. These objects exist as diamonds, and in particular one can make sense of the fusion product in this situation; this is a priori surprising, as it entails colliding two distinct points of Spec Z. The focus of the talk will be on the geometry of the fusion product, and an analogue of the technically crucial ULA (Universally Locally Acyclic) condition that works in this non-algebraic setting.
Numerical Analysis Seminar
16:50-18:20 Room #002 (Graduate School of Math. Sci. Bldg.)
Shinya Uchiumi (Waseda University)
Some issues in the Lagrange-Galerkin method and solutions: computability, dependence on the viscosity and inflow boundary conditions (日本語)
Shinya Uchiumi (Waseda University)
Some issues in the Lagrange-Galerkin method and solutions: computability, dependence on the viscosity and inflow boundary conditions (日本語)
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Alexander Voronov (University of Minnesota)
Homotopy Lie algebroids (ENGLISH)
Alexander Voronov (University of Minnesota)
Homotopy Lie algebroids (ENGLISH)
[ Abstract ]
A well-known result of A. Vaintrob [Vai97] characterizes Lie algebroids and their morphisms in terms of homological vector fields on supermanifolds. We give an interpretation of Lie bialgebroids and their morphisms in terms of odd symplectic dg-manifolds, building on the approach of D. Roytenberg [Roy99]. This extends naturally to the homotopy Lie case and leads to the notion of L∞-bialgebroids and L∞-morphisms between them.
A well-known result of A. Vaintrob [Vai97] characterizes Lie algebroids and their morphisms in terms of homological vector fields on supermanifolds. We give an interpretation of Lie bialgebroids and their morphisms in terms of odd symplectic dg-manifolds, building on the approach of D. Roytenberg [Roy99]. This extends naturally to the homotopy Lie case and leads to the notion of L∞-bialgebroids and L∞-morphisms between them.
2017/04/10
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Kengo Hirachi (The University of Tokyo)
Slice theorem for CR structures near the sphere and its applications
Kengo Hirachi (The University of Tokyo)
Slice theorem for CR structures near the sphere and its applications
[ Abstract ]
We formulate a slice theorem for CR structures by following Bland-Duchamp and give some applications to the rigidity theorems.
We formulate a slice theorem for CR structures by following Bland-Duchamp and give some applications to the rigidity theorems.
Operator Algebra Seminars
16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)
Yosuke Kubota (Riken)
Reconstruction of the Bost-Connes groupoid from K-theoretic data (English)
Yosuke Kubota (Riken)
Reconstruction of the Bost-Connes groupoid from K-theoretic data (English)
2017/04/06
Mathematical Biology Seminar
16:00-17:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Shinji Nakaoka
(JAPANESE)
Shinji Nakaoka
(JAPANESE)
Mathematical Biology Seminar
17:00-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Colloquium of mathematical sciences and society
15:00-16:00 Room #002 (Graduate School of Math. Sci. Bldg.)
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