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Seminar information archive
Seminar information archive ～07/28｜Today's seminar 07/29 | Future seminars 07/30～
2017/07/03
Tokyo Probability Seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Lu Xu (Faculty of Mathematics, Kyushu University)
Equilibrium fluctuation for a chain of anharmonic oscillators (JAPANESE)
Lu Xu (Faculty of Mathematics, Kyushu University)
Equilibrium fluctuation for a chain of anharmonic oscillators (JAPANESE)
[ Abstract ]
A chain of oscillators is a particle system whose microscopic time evolution is given by Hamilton equations with various kinds of conservative noises. Mathematicians and physicians are interested in its macroscopic behaviors (ε → 0) under different space-time scales: ballistic (hyperbolic) (εx, εt), diffusive (εx, ε^2t) and superdiffusive (εx, ε^αt) for 1 < α < 2. In this talk, we consider a 1-dimensional chain of anharmonic oscillators perturbed by noises preserving the total momentum as well as the total energy. We present a result about the hyperbolic scaling limit of its equilibrium fluctuation as well as some further discussions. (A joint work with S. Olla, Université Paris-Dauphine)
A chain of oscillators is a particle system whose microscopic time evolution is given by Hamilton equations with various kinds of conservative noises. Mathematicians and physicians are interested in its macroscopic behaviors (ε → 0) under different space-time scales: ballistic (hyperbolic) (εx, εt), diffusive (εx, ε^2t) and superdiffusive (εx, ε^αt) for 1 < α < 2. In this talk, we consider a 1-dimensional chain of anharmonic oscillators perturbed by noises preserving the total momentum as well as the total energy. We present a result about the hyperbolic scaling limit of its equilibrium fluctuation as well as some further discussions. (A joint work with S. Olla, Université Paris-Dauphine)
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yasuyuki Nagatomo (Meiji University)
Holomorphic isometric embeddings into Grassmannians of rank $2$
Yasuyuki Nagatomo (Meiji University)
Holomorphic isometric embeddings into Grassmannians of rank $2$
[ Abstract ]
We suppose that Grassmannians are equipped with the standard Kähler metrics of Fubini-Study type. This means that the ${\it universal \ quotient}$ bundles over Grassmannians are provided with not only fibre metrics but also connections. Such connections are called the ${\it canonical}$ connection.
First of all, we classify $\text{SU}(2)$ equivariant holomorphic embeddings of the complex projective line into complex Grassmannians of $2$-planes. To do so, we focus our attention on the pull-back connection of the canonical connection, which is an $\text{SU}(2)$ invariant connection by our hypothesis. We use ${\it extensions}$ of vector bundles to classify $\text{SU}(2)$ invariant connections on vector bundles of rank $2$ over the complex projective line. Since the extensions are in one-to-one correspondence with $H^1(\mathbf CP^1;\mathcal O(-2))$, the moduli space of non-trivial invariant connections modulo gauge transformations is identified with the quotient space of $H^1(\mathbf CP^1;\mathcal O(-2))$ by $S^1$-action. The positivity of the mean curvature of the pull-back connection implies that the moduli spaces of $\text{SU}(2)$ equivariant holomorphic embeddings are the open intervals $(0,l)$, where $l$ depends only on the ${\it degree}$ of the map.
Next, we describe moduli spaces of holomorphic isometric embeddings of the complex projective line into complex quadric hypersurfaces of the projective spaces. A harmonic map from a Riemannian manifold into a Grassmannian is characterized by the universal quotient bundle, a space of sections of the bundle and the Laplace operator. This characterization can be considered as a generalization of Theorem of Takahashi on minimal immersions into a sphere (J.Math.Soc.Japan 18 (1966)). Due to this, we can generalize do Carmo-Wallach theory. We apply a generalized do Carmo-Wallach theory to obtain the moduli spaces. This method also gives a description of the moduli space of Einstein-Hermitian harmonic maps with constant Kähler angles of the complex projective line into complex quadrics. It turns out that the moduli space is diffeomorphic to the moduli of holomorphic isometric embeddings of the same degree.
We suppose that Grassmannians are equipped with the standard Kähler metrics of Fubini-Study type. This means that the ${\it universal \ quotient}$ bundles over Grassmannians are provided with not only fibre metrics but also connections. Such connections are called the ${\it canonical}$ connection.
First of all, we classify $\text{SU}(2)$ equivariant holomorphic embeddings of the complex projective line into complex Grassmannians of $2$-planes. To do so, we focus our attention on the pull-back connection of the canonical connection, which is an $\text{SU}(2)$ invariant connection by our hypothesis. We use ${\it extensions}$ of vector bundles to classify $\text{SU}(2)$ invariant connections on vector bundles of rank $2$ over the complex projective line. Since the extensions are in one-to-one correspondence with $H^1(\mathbf CP^1;\mathcal O(-2))$, the moduli space of non-trivial invariant connections modulo gauge transformations is identified with the quotient space of $H^1(\mathbf CP^1;\mathcal O(-2))$ by $S^1$-action. The positivity of the mean curvature of the pull-back connection implies that the moduli spaces of $\text{SU}(2)$ equivariant holomorphic embeddings are the open intervals $(0,l)$, where $l$ depends only on the ${\it degree}$ of the map.
Next, we describe moduli spaces of holomorphic isometric embeddings of the complex projective line into complex quadric hypersurfaces of the projective spaces. A harmonic map from a Riemannian manifold into a Grassmannian is characterized by the universal quotient bundle, a space of sections of the bundle and the Laplace operator. This characterization can be considered as a generalization of Theorem of Takahashi on minimal immersions into a sphere (J.Math.Soc.Japan 18 (1966)). Due to this, we can generalize do Carmo-Wallach theory. We apply a generalized do Carmo-Wallach theory to obtain the moduli spaces. This method also gives a description of the moduli space of Einstein-Hermitian harmonic maps with constant Kähler angles of the complex projective line into complex quadrics. It turns out that the moduli space is diffeomorphic to the moduli of holomorphic isometric embeddings of the same degree.
Operator Algebra Seminars
16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)
Yuichiro Kitajima (Nihon University)
A State-Dependent Noncontextuality Inequality in Algebraic Quantum Theory
Yuichiro Kitajima (Nihon University)
A State-Dependent Noncontextuality Inequality in Algebraic Quantum Theory
2017/06/28
Mathematical Biology Seminar
14:55-15:45 Room #122 (Graduate School of Math. Sci. Bldg.)
Malay Banerjee (Department of Mathematics & Statistics，IIT Kanpur)
Stabilizing role of maturation delay on prey-predator dynamics (ENGLISH)
Malay Banerjee (Department of Mathematics & Statistics，IIT Kanpur)
Stabilizing role of maturation delay on prey-predator dynamics (ENGLISH)
[ Abstract ]
Discrete and continuous time delays are often introduced into mathematical models of interacting populations to take into account stage-structuring of one or more species. There are other aspects for the incorporation of time delays. In prey-predator models, maturation time delay is introduced to the growth equation of predators to implicitly model the stage-structure of predators. Most of the prey-predator models with maturation delay are known to exhibit regular and rregular, even chaotic, oscillations due to destabilization of coexistence steady-state when maturation time period is significantly large. However, such kind of instability can results in due to the introduction of maturation delay into predator’s growth equation with lack of ecological justification and inappropriate choice of the length of time delay. Recently we have worked on a class of delayed prey-predator models, where discrete time delay represents the maturation time for specialist predator implicitly, with ratio-dependent functional response [1] and Michaelis-Menten type
functional response [2]. We have established (i) the stabilizing role of maturation delay, (ii)extinction of predator for significantly long maturation period and (iii) suppression of Hopf bifurcation for large time delay, when the delayed model is constructed with appropriate biological rationale. Main objective of this talk is to discuss analytical results for the stable coexistence of both the species for a class of delayed prey-predator models with maturation delay for specialist predator. Analytical results will be illustrated with the help of numerical simulation results and appropriate bifurcation diagrams with time delay as bifurcation parameter. Main content of this talk is based upon the recent work with Prof. Y. Takeuchi [2].
References:
[1] M. Sen, M. Banerjee, A. Morozov. (2014). Stage-structured ratio-dependent predatorprey models revisited: When should the maturation lag result in systems destabilization?, Ecological Complexity, 19(2), 23–34.
[2] M. Banerjee, Y. Takeuchi. (2017). Maturation delay for the predators can enhance stable coexistence for a class of prey-predator models, Journal of Theoretical Biology, 412, 154–171.
Discrete and continuous time delays are often introduced into mathematical models of interacting populations to take into account stage-structuring of one or more species. There are other aspects for the incorporation of time delays. In prey-predator models, maturation time delay is introduced to the growth equation of predators to implicitly model the stage-structure of predators. Most of the prey-predator models with maturation delay are known to exhibit regular and rregular, even chaotic, oscillations due to destabilization of coexistence steady-state when maturation time period is significantly large. However, such kind of instability can results in due to the introduction of maturation delay into predator’s growth equation with lack of ecological justification and inappropriate choice of the length of time delay. Recently we have worked on a class of delayed prey-predator models, where discrete time delay represents the maturation time for specialist predator implicitly, with ratio-dependent functional response [1] and Michaelis-Menten type
functional response [2]. We have established (i) the stabilizing role of maturation delay, (ii)extinction of predator for significantly long maturation period and (iii) suppression of Hopf bifurcation for large time delay, when the delayed model is constructed with appropriate biological rationale. Main objective of this talk is to discuss analytical results for the stable coexistence of both the species for a class of delayed prey-predator models with maturation delay for specialist predator. Analytical results will be illustrated with the help of numerical simulation results and appropriate bifurcation diagrams with time delay as bifurcation parameter. Main content of this talk is based upon the recent work with Prof. Y. Takeuchi [2].
References:
[1] M. Sen, M. Banerjee, A. Morozov. (2014). Stage-structured ratio-dependent predatorprey models revisited: When should the maturation lag result in systems destabilization?, Ecological Complexity, 19(2), 23–34.
[2] M. Banerjee, Y. Takeuchi. (2017). Maturation delay for the predators can enhance stable coexistence for a class of prey-predator models, Journal of Theoretical Biology, 412, 154–171.
Mathematical Biology Seminar
15:50-16:40 Room #122 (Graduate School of Math. Sci. Bldg.)
Moitri Sen (Department. of Mathematics, National Institute of Technology Patna)
Allee effect induced rich dynamics of a two prey one predator model where the predator is
generalist (ENGLISH)
Moitri Sen (Department. of Mathematics, National Institute of Technology Patna)
Allee effect induced rich dynamics of a two prey one predator model where the predator is
generalist (ENGLISH)
[ Abstract ]
One of the important ecological challenges is to capture the chaotic dynamics and understand the underlying regulating factors. Allee effect is one of the important factors in ecology and taking it into account can cause signi cant changes to the system dynamics. In this work we propose a two prey-one predator model where the growth of both the prey population is governed by Allee effect, and the predator is generalist and hence survived on both the prey populations. We analyze the role of Allee e ect on the chaotic dynamics of the system. Interestingly we have observed through a comprehensive bifurcation study that incorporation of Allee e ect enriches the dynamics of the system. Specially after a certain threshold of the Allee e ect, it has a very signi cant e ect on the chaotic dynamics of the system. In course of the bifurcation analysis we have explored all possible bifurca-tions such as namely the existence of transcritical bifurcation, saddle-node bifurcation, Hopf-bifurcation, Bogdanov-Takens bifurcation and Bautin bifurcation and period-doubling route to chaos respectively.
One of the important ecological challenges is to capture the chaotic dynamics and understand the underlying regulating factors. Allee effect is one of the important factors in ecology and taking it into account can cause signi cant changes to the system dynamics. In this work we propose a two prey-one predator model where the growth of both the prey population is governed by Allee effect, and the predator is generalist and hence survived on both the prey populations. We analyze the role of Allee e ect on the chaotic dynamics of the system. Interestingly we have observed through a comprehensive bifurcation study that incorporation of Allee e ect enriches the dynamics of the system. Specially after a certain threshold of the Allee e ect, it has a very signi cant e ect on the chaotic dynamics of the system. In course of the bifurcation analysis we have explored all possible bifurca-tions such as namely the existence of transcritical bifurcation, saddle-node bifurcation, Hopf-bifurcation, Bogdanov-Takens bifurcation and Bautin bifurcation and period-doubling route to chaos respectively.
2017/06/27
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Takashi Kishimoto (Saitama University)
Cylinders in del Pezzo fibrations (English )
Takashi Kishimoto (Saitama University)
Cylinders in del Pezzo fibrations (English )
[ Abstract ]
The cylinder is, by definition, an algebraic variety of the form Z × A1 . Certainly it is geometrically a very simple object, but it plays often an important role to connect unipotent group actions on special kinds of affine algebraic varieties to projective geometry. From the point of view of birational geometry, it is essential to look into cylinders found on Mori fiber spaces. In this talk, we shall focus mainly on Mori fiber spaces of relative dimension two or three. One of main results asserts that a del Pezzo fibration π : V → W contains a cylinder respecting the structure of π (so-called a vertical cylinder) if and only if the degree deg π of π is greater than or equal to 5 and π admits a rational section. Especially, in case of dim V = 3, the existence of a vertical cylinder is equivalent to saying deg π ≧ 5 in consideration of Tsen’s theorem, nevertheless, it is worthwhile to note that the affine 3-space A3C is embedded into certains del Pezzo fibrations π : V → P1C of deg π ≦ 4 in a twisted way. This is a joint work with Adrien Dubouloz (Universit ́e de Bourgogne).
The cylinder is, by definition, an algebraic variety of the form Z × A1 . Certainly it is geometrically a very simple object, but it plays often an important role to connect unipotent group actions on special kinds of affine algebraic varieties to projective geometry. From the point of view of birational geometry, it is essential to look into cylinders found on Mori fiber spaces. In this talk, we shall focus mainly on Mori fiber spaces of relative dimension two or three. One of main results asserts that a del Pezzo fibration π : V → W contains a cylinder respecting the structure of π (so-called a vertical cylinder) if and only if the degree deg π of π is greater than or equal to 5 and π admits a rational section. Especially, in case of dim V = 3, the existence of a vertical cylinder is equivalent to saying deg π ≧ 5 in consideration of Tsen’s theorem, nevertheless, it is worthwhile to note that the affine 3-space A3C is embedded into certains del Pezzo fibrations π : V → P1C of deg π ≦ 4 in a twisted way. This is a joint work with Adrien Dubouloz (Universit ́e de Bourgogne).
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Eiko Kin (Osaka University)
Braids and hyperbolic 3-manifolds from simple mixing devices (JAPANESE)
Eiko Kin (Osaka University)
Braids and hyperbolic 3-manifolds from simple mixing devices (JAPANESE)
[ Abstract ]
Taffy pullers are devices for pulling candy. One can build braids from the motion of rods for taffy pullers. According to a beautiful article ``A mathematical history of taffy pullers" by Jean-Luc Thiffeault, all taffy pullers (except the first one) give rise to pseudo-Anosov braids. This means that the devices mix candies effectively. Following a study of Thiffeault, I will discuss which pseudo-Anosov braid is realized by taffy pullers. I will explain an interesting connection between braids coming from taffy pullers. I also discuss the hyperbolic mapping tori obtained from taffy pullers. Intriguingly, the two most common taffy pullers give rise to the complements of the the minimally twisted 4-chain link and 5-chain link which are important examples for the study of cusped hyperbolic 3-manifolds with small volumes.
Reference: A mathematical history of taffy pullers, Jean-Luc Thiffeault, https://arxiv.org/pdf/1608.00152.pdf
Taffy pullers are devices for pulling candy. One can build braids from the motion of rods for taffy pullers. According to a beautiful article ``A mathematical history of taffy pullers" by Jean-Luc Thiffeault, all taffy pullers (except the first one) give rise to pseudo-Anosov braids. This means that the devices mix candies effectively. Following a study of Thiffeault, I will discuss which pseudo-Anosov braid is realized by taffy pullers. I will explain an interesting connection between braids coming from taffy pullers. I also discuss the hyperbolic mapping tori obtained from taffy pullers. Intriguingly, the two most common taffy pullers give rise to the complements of the the minimally twisted 4-chain link and 5-chain link which are important examples for the study of cusped hyperbolic 3-manifolds with small volumes.
Reference: A mathematical history of taffy pullers, Jean-Luc Thiffeault, https://arxiv.org/pdf/1608.00152.pdf
2017/06/26
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Akito Futaki (The University of Tokyo)
Volume minimization and obstructions to geometric problems
Akito Futaki (The University of Tokyo)
Volume minimization and obstructions to geometric problems
[ Abstract ]
We discuss on the volume minimization principle for conformally Kaehler Einstein-Maxwell metrics in the similar spirit as the Kaehler-Ricci solitons and Sasaki-Einstein metrics. This talk is base on a joint work with Hajime Ono.
We discuss on the volume minimization principle for conformally Kaehler Einstein-Maxwell metrics in the similar spirit as the Kaehler-Ricci solitons and Sasaki-Einstein metrics. This talk is base on a joint work with Hajime Ono.
Operator Algebra Seminars
16:45-18:15 Room #118 (Graduate School of Math. Sci. Bldg.)
David Kerr (Texas A & M Univ.)
Dimension, comparison, and almost finiteness (English)
David Kerr (Texas A & M Univ.)
Dimension, comparison, and almost finiteness (English)
2017/06/20
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Anh Tran (The University of Texas at Dallas)
Introduction to the AJ conjecture (ENGLISH)
Anh Tran (The University of Texas at Dallas)
Introduction to the AJ conjecture (ENGLISH)
[ Abstract ]
The AJ conjecture was proposed by Garoufalidis about 15 years ago. It predicts a strong connection between two important knot invariants derived from very different background, namely the colored Jones function (a quantum invariant) and the A-polynomial (a geometric invariant). The colored Jones function is a sequence of Laurent polynomials which is known to satisfy a linear q-difference equation. The AJ conjecture states that by writing the linear q-difference equation into an operator form and setting q=1, one gets the A-polynomial. In this talk, I will give an introduction to this conjecture.
The AJ conjecture was proposed by Garoufalidis about 15 years ago. It predicts a strong connection between two important knot invariants derived from very different background, namely the colored Jones function (a quantum invariant) and the A-polynomial (a geometric invariant). The colored Jones function is a sequence of Laurent polynomials which is known to satisfy a linear q-difference equation. The AJ conjecture states that by writing the linear q-difference equation into an operator form and setting q=1, one gets the A-polynomial. In this talk, I will give an introduction to this conjecture.
Colloquium
15:30-16:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Nicolas Bacaër (Institute de Resherrche pour le Developpement, the University of Tokyo)
Some stochastic population models in a random environment (English)
http://www.ummisco.ird.fr/perso/bacaer/
Nicolas Bacaër (Institute de Resherrche pour le Developpement, the University of Tokyo)
Some stochastic population models in a random environment (English)
[ Abstract ]
Two population models will be considered: an epidemic model [1] and a linear birth-and-death process [2]. The goal is to study the first non-zero eigenvalue, which is related to the speed of convergence towards extinction, using either WKB approximations or probabilistic arguments.
[1] "Le modèle stochastique SIS pour une épidémie dans un environnement aléatoire". Journal of Mathematical Biology (2016)
[2] "Sur les processus linéaires de naissance et de mort sous-critiques dans un environnement aléatoire". Journal of Mathematical Biology (2017)
[ Reference URL ]Two population models will be considered: an epidemic model [1] and a linear birth-and-death process [2]. The goal is to study the first non-zero eigenvalue, which is related to the speed of convergence towards extinction, using either WKB approximations or probabilistic arguments.
[1] "Le modèle stochastique SIS pour une épidémie dans un environnement aléatoire". Journal of Mathematical Biology (2016)
[2] "Sur les processus linéaires de naissance et de mort sous-critiques dans un environnement aléatoire". Journal of Mathematical Biology (2017)
http://www.ummisco.ird.fr/perso/bacaer/
2017/06/19
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yuya Takeuchi (The University of Tokyo)
$Q$-prime curvature and Sasakian $\eta$-Einstein manifolds
Yuya Takeuchi (The University of Tokyo)
$Q$-prime curvature and Sasakian $\eta$-Einstein manifolds
[ Abstract ]
The $Q$-prime curvature is defined for a pseudo-Einstein contact form on a strictly pseudoconvex CR manifold, and its integral, the total $Q$-prime curvature, defines a global CR invariant under some assumptions. In this talk, we will compute the $Q$-prime curvature for Sasakian $\eta$-Einstein manifolds. We will also study the first and the second variation of the total $Q$-prime curvature under deformations of real hypersurfaces at Sasakian $\eta$-Einstein manifolds.
The $Q$-prime curvature is defined for a pseudo-Einstein contact form on a strictly pseudoconvex CR manifold, and its integral, the total $Q$-prime curvature, defines a global CR invariant under some assumptions. In this talk, we will compute the $Q$-prime curvature for Sasakian $\eta$-Einstein manifolds. We will also study the first and the second variation of the total $Q$-prime curvature under deformations of real hypersurfaces at Sasakian $\eta$-Einstein manifolds.
Tokyo Probability Seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Kensuke Ishitani (Graduate School of Science and Engineering, Tokyo Metropolitan University)
Computation of first-order Greeks for barrier options using chain rules for Wiener path integrals (JAPANESE)
Kensuke Ishitani (Graduate School of Science and Engineering, Tokyo Metropolitan University)
Computation of first-order Greeks for barrier options using chain rules for Wiener path integrals (JAPANESE)
[ Abstract ]
In this presentation, we present a new methodology to compute first-order Greeks for barrier options under the framework of path-dependent payoff functions with European, Lookback, or Asian type and with time-dependent trigger levels. In particular, we develop chain rules for Wiener path integrals between two curves that arise in the computation of first-order Greeks for barrier options. We also illustrate the effectiveness of our method through numerical examples.
In this presentation, we present a new methodology to compute first-order Greeks for barrier options under the framework of path-dependent payoff functions with European, Lookback, or Asian type and with time-dependent trigger levels. In particular, we develop chain rules for Wiener path integrals between two curves that arise in the computation of first-order Greeks for barrier options. We also illustrate the effectiveness of our method through numerical examples.
2017/06/14
Number Theory Seminar
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Yongquan Hu (Chinese Academy of Sciences, Morningside Center of Mathematics)
Multiplicity one for the mod p cohomology of Shimura curves (ENGLISH)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~t-saito/title_Hu.pdf
Yongquan Hu (Chinese Academy of Sciences, Morningside Center of Mathematics)
Multiplicity one for the mod p cohomology of Shimura curves (ENGLISH)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~t-saito/title_Hu.pdf
2017/06/13
Numerical Analysis Seminar
16:50-18:20 Room #002 (Graduate School of Math. Sci. Bldg.)
Hirofumi Notsu (Kanazawa University)
Numerical analysis of viscoelastic fluid models (Japanese)
Hirofumi Notsu (Kanazawa University)
Numerical analysis of viscoelastic fluid models (Japanese)
[ Abstract ]
Numerical methods for viscoelastic fluid models are studied. In viscoelastic fluid models the stress tensor is often written as a sum of the viscous stress tensor depending linearly on the strain rate tensor and the extra stress tensor for the viscoelastic contribution. In order to describe the viscoelastic contribution another equation for the extra stress tensor is required. In the talk we mainly deal with the Oldroyd-B and the Peterlin models among several proposed viscoelastic fluid models, and present error estimates of finite element schemes based on the method of characteristics. The key issue in the estimates is the treatment of the divergence of the extra stress tensor appearing in the equation for the velocity and the pressure.
Numerical methods for viscoelastic fluid models are studied. In viscoelastic fluid models the stress tensor is often written as a sum of the viscous stress tensor depending linearly on the strain rate tensor and the extra stress tensor for the viscoelastic contribution. In order to describe the viscoelastic contribution another equation for the extra stress tensor is required. In the talk we mainly deal with the Oldroyd-B and the Peterlin models among several proposed viscoelastic fluid models, and present error estimates of finite element schemes based on the method of characteristics. The key issue in the estimates is the treatment of the divergence of the extra stress tensor appearing in the equation for the velocity and the pressure.
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Noboru Ogawa (Tokai University)
Local criteria for non-embeddability of Levi-flat manifolds (JAPANESE)
Noboru Ogawa (Tokai University)
Local criteria for non-embeddability of Levi-flat manifolds (JAPANESE)
[ Abstract ]
In this talk, we consider the Levi-flat embedding problem. Barrett showed that a smooth Reeb foliation on S^3 cannot be realized as a Levi-flat hypersurface in any complex surfaces. To do this, he focused the relationship between the holonomy along the compact leaf and a system of its defining functions. We will show a new criterion for non-embeddability of Levi-flat manifolds. Our result is a higher dimensional analogue of Barrett's theorem. In particular, this enables us to weaken the compactness assumption. For this purpose, we pose a partial generalization of Ueda theory on the analytic neighborhood structure of complex hypersurfaces. This talk is based on a joint work with Takayuki Koike (Kyoto University).
In this talk, we consider the Levi-flat embedding problem. Barrett showed that a smooth Reeb foliation on S^3 cannot be realized as a Levi-flat hypersurface in any complex surfaces. To do this, he focused the relationship between the holonomy along the compact leaf and a system of its defining functions. We will show a new criterion for non-embeddability of Levi-flat manifolds. Our result is a higher dimensional analogue of Barrett's theorem. In particular, this enables us to weaken the compactness assumption. For this purpose, we pose a partial generalization of Ueda theory on the analytic neighborhood structure of complex hypersurfaces. This talk is based on a joint work with Takayuki Koike (Kyoto University).
2017/06/12
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yoshihiko Matsumoto (Osaka University)
On Sp(2)-invariant asymptotically complex hyperbolic Einstein metrics on the 8-ball
Yoshihiko Matsumoto (Osaka University)
On Sp(2)-invariant asymptotically complex hyperbolic Einstein metrics on the 8-ball
[ Abstract ]
Following a pioneering work of Pedersen, Hitchin studied SU(2)-invariant asymptotically real/complex hyperbolic (often abbreviated as AH/ACH) solution to the Einstein equation on the 4-dimensional unit open ball. We discuss a similar problem on the 8-ball, on which the quaternionic unitary group Sp(2) acts naturally, focusing on ACH solutions rather than AH ones. The Einstein equation is treated as an asymptotic Dirichlet problem, and the Dirichlet data are Sp(2)-invariant “partially integrable” CR structures on the 7-sphere. A remarkable point is that most of such structures are actually non-integrable. I will present how we can practically compute the formal series expansion of the Einstein ACH metric corresponding to a given Dirichlet data, that is, an invariant partially integrable CR structure on the sphere.
Following a pioneering work of Pedersen, Hitchin studied SU(2)-invariant asymptotically real/complex hyperbolic (often abbreviated as AH/ACH) solution to the Einstein equation on the 4-dimensional unit open ball. We discuss a similar problem on the 8-ball, on which the quaternionic unitary group Sp(2) acts naturally, focusing on ACH solutions rather than AH ones. The Einstein equation is treated as an asymptotic Dirichlet problem, and the Dirichlet data are Sp(2)-invariant “partially integrable” CR structures on the 7-sphere. A remarkable point is that most of such structures are actually non-integrable. I will present how we can practically compute the formal series expansion of the Einstein ACH metric corresponding to a given Dirichlet data, that is, an invariant partially integrable CR structure on the sphere.
Algebraic Geometry Seminar
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Ivan Cheltsov (The University of Edinburgh)
Rational and irrational singular quartic threefolds (English)
Ivan Cheltsov (The University of Edinburgh)
Rational and irrational singular quartic threefolds (English)
[ Abstract ]
Burkhardt and Igusa quartics admit a faithful action of the symmetric group of degree 6.
There are other quartic threefolds with this property. All of them are singular.
Beauville proved that all but four of them are irrational. Burkhardt and Igusa quartics are known to be rational.
Two constructions of Todd imply the rationality of the remaining two quartic threefolds.
In this talk, I will give an alternative proof of both these (irrationality and rationality) results.
This proof is based on explicit small resolutions of the so-called Coble fourfold.
This fourfold is the double cover of the four-dimensional projective space branched over Igusa quartic.
This is a joint work with Sasha Kuznetsov and Costya Shramov.
Burkhardt and Igusa quartics admit a faithful action of the symmetric group of degree 6.
There are other quartic threefolds with this property. All of them are singular.
Beauville proved that all but four of them are irrational. Burkhardt and Igusa quartics are known to be rational.
Two constructions of Todd imply the rationality of the remaining two quartic threefolds.
In this talk, I will give an alternative proof of both these (irrationality and rationality) results.
This proof is based on explicit small resolutions of the so-called Coble fourfold.
This fourfold is the double cover of the four-dimensional projective space branched over Igusa quartic.
This is a joint work with Sasha Kuznetsov and Costya Shramov.
2017/06/06
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Chen Jiang (IPMU)
Fano varieties: K-stability and boundedness (English)
https://sites.google.com/site/chenjiangmath/
Chen Jiang (IPMU)
Fano varieties: K-stability and boundedness (English)
[ Abstract ]
There are two interesting problems for Fano varieties, K-stability and boundedness.
Significant progress has been made for both problems recently.
In this talk, I will show the boundedness of K-semistable Fano varieties with anti-canonical degree bounded from below, by using methods from birational geometry.
[ Reference URL ]There are two interesting problems for Fano varieties, K-stability and boundedness.
Significant progress has been made for both problems recently.
In this talk, I will show the boundedness of K-semistable Fano varieties with anti-canonical degree bounded from below, by using methods from birational geometry.
https://sites.google.com/site/chenjiangmath/
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Shunsuke Tsuji (The University of Tokyo)
A formula for the action of Dehn twists on the HOMFLY-PT type skein algebra and its application (JAPANESE)
Shunsuke Tsuji (The University of Tokyo)
A formula for the action of Dehn twists on the HOMFLY-PT type skein algebra and its application (JAPANESE)
[ Abstract ]
We give an explicit formula for the action of the Dehn twist along a simple closed curve of a surface on the completed HOMFLY-PT type skein modules of the surface in terms of the action of the completed HOMFLY-PT type skein algebra of the surface. As an application, using this formula, we construct an invariant for an integral homology 3-sphere which is an element of Q[ρ] [[h]].
We give an explicit formula for the action of the Dehn twist along a simple closed curve of a surface on the completed HOMFLY-PT type skein modules of the surface in terms of the action of the completed HOMFLY-PT type skein algebra of the surface. As an application, using this formula, we construct an invariant for an integral homology 3-sphere which is an element of Q[ρ] [[h]].
2017/06/01
Classical Analysis
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Akishi Ikeda (IPMU, University of Tokyo)
Homological and monodromy representations of framed braid groups
(JAPANESE)
Akishi Ikeda (IPMU, University of Tokyo)
Homological and monodromy representations of framed braid groups
(JAPANESE)
2017/05/31
Number Theory Seminar
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Ryotaro Sakamoto (University of Tokyo)
Stark Systems over Gorenstein Rings (JAPANESE)
Ryotaro Sakamoto (University of Tokyo)
Stark Systems over Gorenstein Rings (JAPANESE)
2017/05/30
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Takayuki Morifuji (Keio University)
On a conjecture of Dunfield, Friedl and Jackson for hyperbolic knots (JAPANESE)
Takayuki Morifuji (Keio University)
On a conjecture of Dunfield, Friedl and Jackson for hyperbolic knots (JAPANESE)
[ Abstract ]
The hyperbolic torsion polynomial is defined to be the twisted Alexander polynomial associated to the holonomy representation of a hyperbolic knot. Dunfield, Friedl and Jackson conjecture that the hyperbolic torsion polynomial determines the genus and fiberedness of a hyperbolic knot. In this talk we will survey recent results on the conjecture and explain its generalization to hyperbolic links.
The hyperbolic torsion polynomial is defined to be the twisted Alexander polynomial associated to the holonomy representation of a hyperbolic knot. Dunfield, Friedl and Jackson conjecture that the hyperbolic torsion polynomial determines the genus and fiberedness of a hyperbolic knot. In this talk we will survey recent results on the conjecture and explain its generalization to hyperbolic links.
Infinite Analysis Seminar Tokyo
17:30-18:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Soichi Okada (Graduate School of Mathematics, Nagoya University)
$Q$-functions associated to the root system of type $C$ (JAPANESE)
Soichi Okada (Graduate School of Mathematics, Nagoya University)
$Q$-functions associated to the root system of type $C$ (JAPANESE)
[ Abstract ]
Schur $Q$-functions are a family of symmetric functions introduced
by Schur in his study of projective representations of symmetric
groups. They are obtained by putting $t=-1$ in the Hall-Littlewood
functions associated to the root system of type $A$. (Schur
functions are the $t=0$ specialization.) This talk concerns
symplectic $Q$-functions, which are obtained by putting $t=-1$
in the Hall-Littlewood functions associated to the root system
of type $C$. We discuss several Pfaffian identities as well
as a combinatorial description for them. Also we present some
positivity conjectures.
Schur $Q$-functions are a family of symmetric functions introduced
by Schur in his study of projective representations of symmetric
groups. They are obtained by putting $t=-1$ in the Hall-Littlewood
functions associated to the root system of type $A$. (Schur
functions are the $t=0$ specialization.) This talk concerns
symplectic $Q$-functions, which are obtained by putting $t=-1$
in the Hall-Littlewood functions associated to the root system
of type $C$. We discuss several Pfaffian identities as well
as a combinatorial description for them. Also we present some
positivity conjectures.
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Masaru Nagaoka (The University of Tokyo)
Contractible affine threefolds in smooth Fano threefolds (English or Japanese)
Masaru Nagaoka (The University of Tokyo)
Contractible affine threefolds in smooth Fano threefolds (English or Japanese)
[ Abstract ]
By the contribution of M. Furushima, N. Nakayama, Th. Peternell and M.
Schneider, it is completed to classify all projective compactifications
of the affine $3$-space $\mathbb{A}^3$ with Picard number one.
As a similar question, T. Kishimoto raised the problem to classify all
triplets $(V, U, D_1 \cup D_2)$ which consist of smooth Fano threefolds
$V$ of Picard number two, contractible affine threefolds $U$ as open
subsets of $V$, and the complements $D_1 \cup D_2 =V \setminus U$.
He also solved this problem when the log canonical divisors $K_V+D_1+D_2
$ are not nef.
In this talk, I will discuss the triplets $(V, U, D_1 \cup D_2)$ whose
log canonical divisors are linearly equivalent to zero.
I will also explain how to determine all Fano threefolds $V$ which
appear in such triplets.
By the contribution of M. Furushima, N. Nakayama, Th. Peternell and M.
Schneider, it is completed to classify all projective compactifications
of the affine $3$-space $\mathbb{A}^3$ with Picard number one.
As a similar question, T. Kishimoto raised the problem to classify all
triplets $(V, U, D_1 \cup D_2)$ which consist of smooth Fano threefolds
$V$ of Picard number two, contractible affine threefolds $U$ as open
subsets of $V$, and the complements $D_1 \cup D_2 =V \setminus U$.
He also solved this problem when the log canonical divisors $K_V+D_1+D_2
$ are not nef.
In this talk, I will discuss the triplets $(V, U, D_1 \cup D_2)$ whose
log canonical divisors are linearly equivalent to zero.
I will also explain how to determine all Fano threefolds $V$ which
appear in such triplets.
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