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Colloquium
Seminar information archive ～01/17｜Next seminar｜Future seminars 01/18～
| Organizer(s) | ASUKE Taro, TERADA Itaru, HASEGAWA Ryu, MIYAMOTO Yasuhito (chair) |
|---|---|
| URL | https://www.ms.u-tokyo.ac.jp/seminar/colloquium_e/index_e.html |
Seminar information archive
2013/06/28
16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Hiroki Kodama (Graduate School of Mathematical Sciences, The University of Tokyo)
The Geometry of protain modelling (JAPANESE)
Hiroki Kodama (Graduate School of Mathematical Sciences, The University of Tokyo)
The Geometry of protain modelling (JAPANESE)
2013/05/31
16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Yasuhito MIYAMOTO (Graduate School of Mathematical Sciences, The University of Tokyo)
Stable patterns and the nonlinear ``hot spots'' conjecture (JAPANESE)
Yasuhito MIYAMOTO (Graduate School of Mathematical Sciences, The University of Tokyo)
Stable patterns and the nonlinear ``hot spots'' conjecture (JAPANESE)
2013/03/18
15:00-17:30 Room #050 (Graduate School of Math. Sci. Bldg.)
NOGUCHI, Junjiro (University of Tokyo) 15:00-16:00
Value distribution theory and analytic function theory in several variables (JAPANESE)
OSHIMA, Toshio (University of Tokyo) 16:30-17:30
My fifty years of differential equations (JAPANESE)
NOGUCHI, Junjiro (University of Tokyo) 15:00-16:00
Value distribution theory and analytic function theory in several variables (JAPANESE)
OSHIMA, Toshio (University of Tokyo) 16:30-17:30
My fifty years of differential equations (JAPANESE)
2013/01/25
16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Mitsuhiro T. Nakao (Sasebo National College of Technology)
State of the art in numerical verification methods of solutions for partial differential equations (JAPANESE)
Mitsuhiro T. Nakao (Sasebo National College of Technology)
State of the art in numerical verification methods of solutions for partial differential equations (JAPANESE)
2012/11/30
16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Siegfried BOECHERER (University of Tokyo)
What do Siegel Eisenstein series know about all modular forms? (ENGLISH)
Siegfried BOECHERER (University of Tokyo)
What do Siegel Eisenstein series know about all modular forms? (ENGLISH)
[ Abstract ]
Eisenstein series came up in C.L.Siegel's famous work on quadratic forms. The main properties of such Eisensetin series such as analytic continuation and explict form of Fourier expansion are well understood. Nowadays, we use Eisenstein series of higher rank symplectic groups and their restrictions to study properties of all modular forms. I will try to survey the use of “pullbacks of Eisenstein series”: Basis problem, L-functions, p-adic properties, rationality and integrality questions.
Eisenstein series came up in C.L.Siegel's famous work on quadratic forms. The main properties of such Eisensetin series such as analytic continuation and explict form of Fourier expansion are well understood. Nowadays, we use Eisenstein series of higher rank symplectic groups and their restrictions to study properties of all modular forms. I will try to survey the use of “pullbacks of Eisenstein series”: Basis problem, L-functions, p-adic properties, rationality and integrality questions.
2012/11/16
16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Akito FUTAKI (University of Tokyo)
Integral invariants in complex differential geometry (JAPANESE)
Akito FUTAKI (University of Tokyo)
Integral invariants in complex differential geometry (JAPANESE)
2012/10/12
16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Antonio Siconolfi (La Sapienza - University of Rome)
Homogenization on arbitrary manifolds (ENGLISH)
Antonio Siconolfi (La Sapienza - University of Rome)
Homogenization on arbitrary manifolds (ENGLISH)
[ Abstract ]
We show that results on periodic homogenization for Hamilton-Jacobi equations can be generalized replacing the torus by an arbitrary compact manifold. This allows to reach a deeper understanding of the matter and unveils phenomena somehow hidden in the periodic case, for instance the fact that the ambient spaces of oscillating equations and that of the limit problem are different, and possess even different dimensions. Repetition structure for the base manifold, changes of scale in it and asymptotic analysis, which are the basic ingredients of homogenization, need substantial modification to work in the new frame, and this task is partially accomplished using tools from algebraic topology. An adapted notion of convergence allowing approximating entities and limit to lie in different spaces is also provided.
We show that results on periodic homogenization for Hamilton-Jacobi equations can be generalized replacing the torus by an arbitrary compact manifold. This allows to reach a deeper understanding of the matter and unveils phenomena somehow hidden in the periodic case, for instance the fact that the ambient spaces of oscillating equations and that of the limit problem are different, and possess even different dimensions. Repetition structure for the base manifold, changes of scale in it and asymptotic analysis, which are the basic ingredients of homogenization, need substantial modification to work in the new frame, and this task is partially accomplished using tools from algebraic topology. An adapted notion of convergence allowing approximating entities and limit to lie in different spaces is also provided.
2012/07/06
16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
S.R.Srinivasa Varadhan (Courant Institute of Mathematical Sciences, New York University)
Large Deviations of Random Graphs and Random Matrices (ENGLISH)
S.R.Srinivasa Varadhan (Courant Institute of Mathematical Sciences, New York University)
Large Deviations of Random Graphs and Random Matrices (ENGLISH)
[ Abstract ]
A random graph with $n$ vertices is a random symmetric matrix of $0$'s and $1$'s and they share some common aspects in their large deviation behavior. For random matrices it is the question of having large eigenvalues. For random graphs it is having too many or too few subgraph counts, like the number of triangles etc. The question that we will try to answer is what would a random matrix or a random graph conditioned to exhibit such a large deviation look like. Since the randomness is of size $n^2$ large deviation rates of order $n^2$ are possible.
A random graph with $n$ vertices is a random symmetric matrix of $0$'s and $1$'s and they share some common aspects in their large deviation behavior. For random matrices it is the question of having large eigenvalues. For random graphs it is having too many or too few subgraph counts, like the number of triangles etc. The question that we will try to answer is what would a random matrix or a random graph conditioned to exhibit such a large deviation look like. Since the randomness is of size $n^2$ large deviation rates of order $n^2$ are possible.
2012/05/25
16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Harald Niederreiter (RICAM, Austrian Academy of Sciences)
Quasi-Monte Carlo methods: deterministic is often better than random (ENGLISH)
https://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html
Harald Niederreiter (RICAM, Austrian Academy of Sciences)
Quasi-Monte Carlo methods: deterministic is often better than random (ENGLISH)
[ Abstract ]
Quasi-Monte Carlo (QMC) methods are deterministic analogs of statistical Monte Carlo methods in computational mathematics. QMC methods employ evenly distributed low-discrepancy sequences instead of the random samples used in Monte Carlo methods. For many types of computational problems, QMC methods are more efficient than Monte Carlo methods. After a general introduction to QMC methods, the talk focuses on the problem of constructing low-discrepancy sequences which has fascinating links with subjects such as finite fields, error-correcting codes, and algebraic curves.
This talk also serves as the first talk of the four lecture series. The other three are on 5/28, 5/29, 5/30, 14:50-16:20 at room 123.
[ Reference URL ]Quasi-Monte Carlo (QMC) methods are deterministic analogs of statistical Monte Carlo methods in computational mathematics. QMC methods employ evenly distributed low-discrepancy sequences instead of the random samples used in Monte Carlo methods. For many types of computational problems, QMC methods are more efficient than Monte Carlo methods. After a general introduction to QMC methods, the talk focuses on the problem of constructing low-discrepancy sequences which has fascinating links with subjects such as finite fields, error-correcting codes, and algebraic curves.
This talk also serves as the first talk of the four lecture series. The other three are on 5/28, 5/29, 5/30, 14:50-16:20 at room 123.
https://www.ms.u-tokyo.ac.jp/~matumoto/WORKSHOP/workshop2012.html
2012/05/11
16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
SAKASAI Takuya (University of Tokyo)
Moduli spaces and symplectic derivation Lie algebras (JAPANESE)
SAKASAI Takuya (University of Tokyo)
Moduli spaces and symplectic derivation Lie algebras (JAPANESE)
[ Abstract ]
First we overview Kontsevich's theorem describing a deep connection between homology of certain infinite dimensional Lie algebras (symplectic derivation Lie algebras) and cohomology of various moduli spaces. Then we discuss some computational results on the Lie algebras together with their applications (joint work with Shigeyuki Morita and Masaaki Suzuki).
First we overview Kontsevich's theorem describing a deep connection between homology of certain infinite dimensional Lie algebras (symplectic derivation Lie algebras) and cohomology of various moduli spaces. Then we discuss some computational results on the Lie algebras together with their applications (joint work with Shigeyuki Morita and Masaaki Suzuki).
2012/03/16
16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Chun LIU (University of Tokyo / Penn State University)
On Complex Fluids (ENGLISH)
Chun LIU (University of Tokyo / Penn State University)
On Complex Fluids (ENGLISH)
[ Abstract ]
The talk is on the mathematical theories, in particular the energetic variational approaches, of anisotropic complex fluids, such as viscoelastic materials, liquid crystals and ionic fluids in proteins and bio-solutions.
Complex fluids, including mixtures and solutions, are abundant in our daily life. The complicated phenomena and properties exhibited by these materials reflects the coupling and competition between the microscopic interactions and the macroscopic dynamics. We study the underlying energetic variational structures that is common among all these multiscale-multiphysics systems.
In this talk, I will demonstrate the modeling as well as analysis and numerical issues arising from various complex fluids.
The talk is on the mathematical theories, in particular the energetic variational approaches, of anisotropic complex fluids, such as viscoelastic materials, liquid crystals and ionic fluids in proteins and bio-solutions.
Complex fluids, including mixtures and solutions, are abundant in our daily life. The complicated phenomena and properties exhibited by these materials reflects the coupling and competition between the microscopic interactions and the macroscopic dynamics. We study the underlying energetic variational structures that is common among all these multiscale-multiphysics systems.
In this talk, I will demonstrate the modeling as well as analysis and numerical issues arising from various complex fluids.
2012/03/13
15:00-16:00 Room #050 (Graduate School of Math. Sci. Bldg.)
Aleksandar Ivic (University of Belgrade, the Serbian Academy of Science and Arts)
Problems and results on Hardy's Z-function (JAPANESE)
Aleksandar Ivic (University of Belgrade, the Serbian Academy of Science and Arts)
Problems and results on Hardy's Z-function (JAPANESE)
[ Abstract ]
The title is self-explanatory: G.H. Hardy first used the function
$Z(t)$ to show that there are infinitely many zeta-zeros on the
critical line $\\Re s = 1/2$. In recent years there is a revived
interest in this function, with many results and open problems.
The title is self-explanatory: G.H. Hardy first used the function
$Z(t)$ to show that there are infinitely many zeta-zeros on the
critical line $\\Re s = 1/2$. In recent years there is a revived
interest in this function, with many results and open problems.
2012/01/27
16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Taro YOSHINO (Graduate School of Mathematical Sciences, University of Tokyo)
On Topological Blow-up (JAPANESE)
Taro YOSHINO (Graduate School of Mathematical Sciences, University of Tokyo)
On Topological Blow-up (JAPANESE)
[ Abstract ]
Topological blow-up is a method to understand non-Hausdorff spaces. We define an obstruction to Hausdorffness, and call it crack. By `blowing up' the points in crack, we can obtain better space.
Topological blow-up is a method to understand non-Hausdorff spaces. We define an obstruction to Hausdorffness, and call it crack. By `blowing up' the points in crack, we can obtain better space.
2011/12/16
16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
TAKAGI, Shunsuke (Graduate School of Mathematical Sciences, University of Tokyo)
Application of positive characteristic methods to singularity theory (JAPANESE)
TAKAGI, Shunsuke (Graduate School of Mathematical Sciences, University of Tokyo)
Application of positive characteristic methods to singularity theory (JAPANESE)
[ Abstract ]
As an application of positive characteristic methods to singularity theory, I will talk about a characterization of singularities in characteristic zero using Frobenius maps. Log canonical singularities form a class of singularities associated to the minimal model program. It is conjectured that they correspond to $F$-pure singularities, which form a class of singularities defined via splitting of Frobenius maps. In this talk, I will explain a recent progress on this conjecture, especially its connection to another conjecture on ordinary reductions of Calabi-Yau varieties defined over number fields.
As an application of positive characteristic methods to singularity theory, I will talk about a characterization of singularities in characteristic zero using Frobenius maps. Log canonical singularities form a class of singularities associated to the minimal model program. It is conjectured that they correspond to $F$-pure singularities, which form a class of singularities defined via splitting of Frobenius maps. In this talk, I will explain a recent progress on this conjecture, especially its connection to another conjecture on ordinary reductions of Calabi-Yau varieties defined over number fields.
2011/11/25
16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
SHIMOMURA Akihiro (Graduate School of mathematical Sciences, University of Tokyo)
Nonlinear dispersive evolution equations (JAPANESE)
SHIMOMURA Akihiro (Graduate School of mathematical Sciences, University of Tokyo)
Nonlinear dispersive evolution equations (JAPANESE)
[ Abstract ]
I will talk about the time evolution of solutions to nonlinear dispersive equations.
I will talk about the time evolution of solutions to nonlinear dispersive equations.
2011/11/04
16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
KANAI Masahiko (Graduate School of Mathematical Sciences, University of Tokyo)
Cross ratio, and all that
(JAPANESE)
KANAI Masahiko (Graduate School of Mathematical Sciences, University of Tokyo)
Cross ratio, and all that
(JAPANESE)
[ Abstract ]
Although the origin of cross ratio goes back to ancient Greek mathematics, new discoveries about it has been made even in the past few decades. It seems that our understanding as to cross ratio is still limited. I am going to show you the present status and my own concerns, as well.
Although the origin of cross ratio goes back to ancient Greek mathematics, new discoveries about it has been made even in the past few decades. It seems that our understanding as to cross ratio is still limited. I am going to show you the present status and my own concerns, as well.
2011/07/29
16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Shihoko Ishii (Graduate School of Mathematical Sciences, University of Tokyo)
Arc spaces and algebraic geometry (JAPANESE)
Shihoko Ishii (Graduate School of Mathematical Sciences, University of Tokyo)
Arc spaces and algebraic geometry (JAPANESE)
2011/06/24
16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Jun SHIHO (Graduate School of Mathematical Sciences, University of Tokyo)
On logarithmic extension of p-adic differential equations (JAPANESE)
Jun SHIHO (Graduate School of Mathematical Sciences, University of Tokyo)
On logarithmic extension of p-adic differential equations (JAPANESE)
2011/01/28
16:30-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)
Shirai Tomoyuki (Kyushu University)
Conformal invariance in probability theory (JAPANESE)
Shirai Tomoyuki (Kyushu University)
Conformal invariance in probability theory (JAPANESE)
2010/12/10
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)
2010/10/29
16:30-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Robin Graham (University of Washington)
Ambient metrics and exceptional holonomy (ENGLISH)
Robin Graham (University of Washington)
Ambient metrics and exceptional holonomy (ENGLISH)
[ Abstract ]
The holonomy of a pseudo-Riemannian metric is a subgroup of the orthogonal group which measures the structure preserved by parallel translation. Construction of pseudo-Riemannian metrics whose holonomy is an exceptional Lie group has been of great interest in recent years. This talk will outline a construction of metrics in dimension 7 whose holonomy is contained in the split real form of the exceptional group $G_2$. The datum for the construction is a generic real-analytic 2-plane field on a manifold of dimension 5; the metric in dimension 7 arises as the ambient metric of a conformal structure on the 5-manifold defined by Nurowski in terms of the 2-plane field.
The holonomy of a pseudo-Riemannian metric is a subgroup of the orthogonal group which measures the structure preserved by parallel translation. Construction of pseudo-Riemannian metrics whose holonomy is an exceptional Lie group has been of great interest in recent years. This talk will outline a construction of metrics in dimension 7 whose holonomy is contained in the split real form of the exceptional group $G_2$. The datum for the construction is a generic real-analytic 2-plane field on a manifold of dimension 5; the metric in dimension 7 arises as the ambient metric of a conformal structure on the 5-manifold defined by Nurowski in terms of the 2-plane field.
2010/10/08
16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Ryu Sasaki (Yukawa Institute for Theoretical Physics, Kyoto University)
Exceptional Jacobi polynomials as solutions of a Schroedinger
(Sturm-Liouville) equation with $3 +¥ell$ ($¥ell=1,2,¥ldots) regular
singularities (JAPANESE)
Ryu Sasaki (Yukawa Institute for Theoretical Physics, Kyoto University)
Exceptional Jacobi polynomials as solutions of a Schroedinger
(Sturm-Liouville) equation with $3 +¥ell$ ($¥ell=1,2,¥ldots) regular
singularities (JAPANESE)
[ Abstract ]
Global solutions of Fuchsian differential equations with more than 3 (hypergeometric) or four (Heun) regular singularities had been virtually unkown. Here I present a complete set of eigenfunctions of a Schroedinger (Sturm-Liouville) equation with $3 + ¥ell$ ($¥ell=1,2,¥ldots$) regular singularities. They are deformations of the Darboux-P¥" oschl-Teller potential with the Hamiltonian (Schroedinger operator) ¥[ ¥mathcal{H}=-¥frac{d^2}{dx^2}+¥frac{g(g-1)}{¥sin^2x}+¥frac{h(h-1)} {¥cos^2x}¥] The eigenfunctions consist of the {¥em exceptional Jacobi polynomials} $¥{P_{¥ell,n}(¥eta)¥}$, $n=0,1,2,¥ldots$, with deg($P_{¥ell,n}$)$=n+¥ell$. Thus the restriction due to Bochner's theorem does not apply. The confluent limit produces two sets of the exceptional Laguerre polynomials for $¥ell=1,2,¥ldots$. Similar deformation method provides the exceptional Wilson and Askey-Wilson polynomials for $¥ell=1,2,¥ldots$.
Global solutions of Fuchsian differential equations with more than 3 (hypergeometric) or four (Heun) regular singularities had been virtually unkown. Here I present a complete set of eigenfunctions of a Schroedinger (Sturm-Liouville) equation with $3 + ¥ell$ ($¥ell=1,2,¥ldots$) regular singularities. They are deformations of the Darboux-P¥" oschl-Teller potential with the Hamiltonian (Schroedinger operator) ¥[ ¥mathcal{H}=-¥frac{d^2}{dx^2}+¥frac{g(g-1)}{¥sin^2x}+¥frac{h(h-1)} {¥cos^2x}¥] The eigenfunctions consist of the {¥em exceptional Jacobi polynomials} $¥{P_{¥ell,n}(¥eta)¥}$, $n=0,1,2,¥ldots$, with deg($P_{¥ell,n}$)$=n+¥ell$. Thus the restriction due to Bochner's theorem does not apply. The confluent limit produces two sets of the exceptional Laguerre polynomials for $¥ell=1,2,¥ldots$. Similar deformation method provides the exceptional Wilson and Askey-Wilson polynomials for $¥ell=1,2,¥ldots$.
2010/07/02
16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Mitsuhiro Shishikura (Kyoto University)
Hausdorff dimension and measure of conformal fractals (JAPANESE)
Mitsuhiro Shishikura (Kyoto University)
Hausdorff dimension and measure of conformal fractals (JAPANESE)
2010/06/11
17:00-18:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Masaaki Umehara (Osaka University)
The Gauss-Bonnet Theorem and singular points on surfaces (JAPANESE)
Masaaki Umehara (Osaka University)
The Gauss-Bonnet Theorem and singular points on surfaces (JAPANESE)
[ Abstract ]
We generalize the classical Gauss-Bonnet formula for closed surfaces as wave fronts. Using it, we can find a new view point of inflection points and the topology of immersed surfaces in Euclidean 3-space via the singularities of their Gauss maps.
We generalize the classical Gauss-Bonnet formula for closed surfaces as wave fronts. Using it, we can find a new view point of inflection points and the topology of immersed surfaces in Euclidean 3-space via the singularities of their Gauss maps.
2010/05/07
16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Jean-Pierre Puel (The University of Tokyo, Universite de Versailles Saint-Quentin)
Why to study controllability problems and the mathematical tools involved (ENGLISH)
Jean-Pierre Puel (The University of Tokyo, Universite de Versailles Saint-Quentin)
Why to study controllability problems and the mathematical tools involved (ENGLISH)
[ Abstract ]
We will give some examples of controllability problems and the underlying applications to practical situations. This includes vibrations of membranes or plates, motion of incompressible fluids or quantum systems occuring in quantum chemistry or in quantum logic information theory. These examples correspond to different types of partial differential equations for which specific analysis has to be done. Of course, at the moment, very few results are known and the domain is widely open. We will describe very briefly the mathematical tools used for each type of PDE, in particular microlocal analysis, global Carleman estimates or some specific real analysis estimates.These methods appear to be also useful to study some inverse problems and, if time permits, we will give a few elements on some examples.
We will give some examples of controllability problems and the underlying applications to practical situations. This includes vibrations of membranes or plates, motion of incompressible fluids or quantum systems occuring in quantum chemistry or in quantum logic information theory. These examples correspond to different types of partial differential equations for which specific analysis has to be done. Of course, at the moment, very few results are known and the domain is widely open. We will describe very briefly the mathematical tools used for each type of PDE, in particular microlocal analysis, global Carleman estimates or some specific real analysis estimates.These methods appear to be also useful to study some inverse problems and, if time permits, we will give a few elements on some examples.
