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Seminar information archive
Seminar information archive ～07/26｜Today's seminar 07/27 | Future seminars 07/28～
Number Theory Seminar
16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Takahiro Tsushima (University of Tokyo)
On the stable reduction of $X_0(p^4)$ (JAPANESE)
Takahiro Tsushima (University of Tokyo)
On the stable reduction of $X_0(p^4)$ (JAPANESE)
2010/07/06
Tuesday Seminar on Topology
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Akira Kono (Kyoto University)
On the cohomology of free and twisted loop spaces (JAPANESE)
Akira Kono (Kyoto University)
On the cohomology of free and twisted loop spaces (JAPANESE)
[ Abstract ]
A natural extension of cohomology suspension to a free loop space is
constructed from the evaluation map and is shown to have a good
properties in cohomology calculation. This map is generalized to a
twisted loop space.
As an application, the cohomology of free and twisted loop space of
classifying spaces of compact Lie groups, including certain finite
Chevalley groups is calculated.
A natural extension of cohomology suspension to a free loop space is
constructed from the evaluation map and is shown to have a good
properties in cohomology calculation. This map is generalized to a
twisted loop space.
As an application, the cohomology of free and twisted loop space of
classifying spaces of compact Lie groups, including certain finite
Chevalley groups is calculated.
Operator Algebra Seminars
16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)
Robert Sims (Univ. Arizona)
On the Existence of the Dynamics for Anharmonic Quantum Oscillator Systems (ENGLISH)
Robert Sims (Univ. Arizona)
On the Existence of the Dynamics for Anharmonic Quantum Oscillator Systems (ENGLISH)
2010/07/05
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Shin-ichi MATSUMURA (Univ. of Tokyo)
Expression of restricted volumes with current integration (JAPANESE)
Shin-ichi MATSUMURA (Univ. of Tokyo)
Expression of restricted volumes with current integration (JAPANESE)
Algebraic Geometry Seminar
16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)
Katsuhisa Furukawa (Waseda University)
Rational curves on hypersurfaces (JAPANESE)
Katsuhisa Furukawa (Waseda University)
Rational curves on hypersurfaces (JAPANESE)
[ Abstract ]
Our purpose is to study the family of smooth rational curves of degree $e$ lying on a hypersurface of degree $d$ in $\\mathbb{P}^n$, and to investigate properties of this family (e.g., dimension, smoothness, connectedness).
Our starting point is the research about the family of lines (i.e., $e = 1$), which was studied by W. Barth and A. Van de Ven over $\\mathbb{C}$, and by J. Koll\\'{a}r over an algebraically closed field of arbitrary characteristic.
For the degree $e > 1$, the family of rational curves was studied by J. Harris, M. Roth, and J. Starr over $\\mathbb{C}$ in the case of $d < (n+1)/2$.
In this talk, we study the family of rational curves in arbitrary characteristic under the assumption $e = 2,3$ and $d > 1$, or $e > 3$ and $d > 2e-4$.
Our purpose is to study the family of smooth rational curves of degree $e$ lying on a hypersurface of degree $d$ in $\\mathbb{P}^n$, and to investigate properties of this family (e.g., dimension, smoothness, connectedness).
Our starting point is the research about the family of lines (i.e., $e = 1$), which was studied by W. Barth and A. Van de Ven over $\\mathbb{C}$, and by J. Koll\\'{a}r over an algebraically closed field of arbitrary characteristic.
For the degree $e > 1$, the family of rational curves was studied by J. Harris, M. Roth, and J. Starr over $\\mathbb{C}$ in the case of $d < (n+1)/2$.
In this talk, we study the family of rational curves in arbitrary characteristic under the assumption $e = 2,3$ and $d > 1$, or $e > 3$ and $d > 2e-4$.
2010/07/02
Colloquium
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)
2010/06/29
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Takahiro Kitayama (The University of Tokyo)
Non-commutative Reidemeister torsion and Morse-Novikov theory (JAPANESE)
Takahiro Kitayama (The University of Tokyo)
Non-commutative Reidemeister torsion and Morse-Novikov theory (JAPANESE)
[ Abstract ]
For a circle-valued Morse function of a closed oriented manifold, we
show that Reidemeister torsion over a non-commutative formal Laurent
polynomial ring equals the product of a certain non-commutative
Lefschetz-type zeta function and the algebraic torsion of the Novikov
complex over the ring. This gives a generalization of the results of
Hutchings-Lee and Pazhitnov on abelian coefficients. As a consequence we
obtain Morse theoretical and dynamical descriptions of the higher-order
Alexander polynomials.
For a circle-valued Morse function of a closed oriented manifold, we
show that Reidemeister torsion over a non-commutative formal Laurent
polynomial ring equals the product of a certain non-commutative
Lefschetz-type zeta function and the algebraic torsion of the Novikov
complex over the ring. This gives a generalization of the results of
Hutchings-Lee and Pazhitnov on abelian coefficients. As a consequence we
obtain Morse theoretical and dynamical descriptions of the higher-order
Alexander polynomials.
2010/06/28
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Kengo HIRACHI (Univ. of Tokyo)
Total Q-curvature vanishes on integrable CR manifolds (ENGLISH)
Kengo HIRACHI (Univ. of Tokyo)
Total Q-curvature vanishes on integrable CR manifolds (ENGLISH)
2010/06/26
GCOE lecture series
13:50-14:50 Room #056 (Graduate School of Math. Sci. Bldg.)
Feng Xu (UC Riverside)
On a subfactor generalization of Wall's conjecture (ENGLISH)
Feng Xu (UC Riverside)
On a subfactor generalization of Wall's conjecture (ENGLISH)
Lectures
10:00-16:10 Room #056 (Graduate School of Math. Sci. Bldg.)
Yoshimichi Ueda (Kyushu Univ.) 10:00-11:00
On the predual of non-commutative $H^\\infty$ (ENGLISH)
Hiroki Matui (Chiba Univ.) 11:20-12:20
${\\mathbf Z}^N$-actions on UHF algebras of infinite type (ENGLISH)
Feng Xu (UC Riverside) 13:50-14:50
On a subfactor generalization of Wall's conjecture (ENGLISH)
Masaki Izumi (Kyoto Univ.) 15:10-16:10
Group actions on Kirchberg algebras (ENGLISH)
Yoshimichi Ueda (Kyushu Univ.) 10:00-11:00
On the predual of non-commutative $H^\\infty$ (ENGLISH)
Hiroki Matui (Chiba Univ.) 11:20-12:20
${\\mathbf Z}^N$-actions on UHF algebras of infinite type (ENGLISH)
Feng Xu (UC Riverside) 13:50-14:50
On a subfactor generalization of Wall's conjecture (ENGLISH)
Masaki Izumi (Kyoto Univ.) 15:10-16:10
Group actions on Kirchberg algebras (ENGLISH)
2010/06/25
Classical Analysis
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Kazuki Hiroe (University of Tokyo)
Euler transform and Weyl groups of symmetric Kac-Moody Lie algebras (JAPANESE)
Kazuki Hiroe (University of Tokyo)
Euler transform and Weyl groups of symmetric Kac-Moody Lie algebras (JAPANESE)
Lectures
15:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Narutaka Ozawa (Univ. Tokyo) 15:00-16:00
Quasi-homomorphism rigidity with noncommutative targets (ENGLISH)
Yoshiko Ogata (Univ. Tokyo) 16:30-17:30
Ruelle-Lanford functions for quantum spin systems (ENGLISH)
Narutaka Ozawa (Univ. Tokyo) 15:00-16:00
Quasi-homomorphism rigidity with noncommutative targets (ENGLISH)
Yoshiko Ogata (Univ. Tokyo) 16:30-17:30
Ruelle-Lanford functions for quantum spin systems (ENGLISH)
2010/06/24
Operator Algebra Seminars
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Thomas Sinclair (Vanderbilt Univ.)
Strong solidity of factors from lattices in SO(n,1) and SU(n,1) (ENGLISH)
Thomas Sinclair (Vanderbilt Univ.)
Strong solidity of factors from lattices in SO(n,1) and SU(n,1) (ENGLISH)
[ Abstract ]
Generalizing techniques found in Ozawa and Popa,
``On a class of II$_1$ factors with at most one Cartan subalgebra, II''
(Amer. J. Math., to appear), we show that the group factors of ICC
lattices in SO(n,1) and SU(n,1), $n\\ge2$, are strongly solid. If
time permits, we will also discuss applications to $L^2$-rigidity.
Generalizing techniques found in Ozawa and Popa,
``On a class of II$_1$ factors with at most one Cartan subalgebra, II''
(Amer. J. Math., to appear), we show that the group factors of ICC
lattices in SO(n,1) and SU(n,1), $n\\ge2$, are strongly solid. If
time permits, we will also discuss applications to $L^2$-rigidity.
Applied Analysis
16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
Hideki Murakawa (University of Toyama)
Reaction-diffusion approximation to nonlinear diffusion problems (JAPANESE)
Hideki Murakawa (University of Toyama)
Reaction-diffusion approximation to nonlinear diffusion problems (JAPANESE)
GCOE Seminars
16:00-17:30 Room #002 (Graduate School of Math. Sci. Bldg.)
村川 秀樹 (富山大学大学院理工学研究部)
非線形拡散問題の反応拡散系近似 (JAPANESE)
村川 秀樹 (富山大学大学院理工学研究部)
非線形拡散問題の反応拡散系近似 (JAPANESE)
[ Abstract ]
氷の融解・水の凝固の過程を記述するステファン問題、地下水の流れを表す多孔質媒体流方程式、2種生物種の競合問題における互いの動的な干渉作用を記述する重定-川崎-寺本交差拡散系など、様々な問題を含む非線形拡散問題を取り扱う。本講演では、非線形拡散問題の解が、拡散が線形である半線形反応拡散系の解により近似されることを示す。この結果は、非線形拡散問題の解構造が、ある種の半線形反応拡散系の中に再現されることを示唆するものである。一般に、非線形問題を扱うよりも半線形問題を取り扱う方が容易であるため、本研究は非線形問題の解析や数値解析に応用できることが期待される。
氷の融解・水の凝固の過程を記述するステファン問題、地下水の流れを表す多孔質媒体流方程式、2種生物種の競合問題における互いの動的な干渉作用を記述する重定-川崎-寺本交差拡散系など、様々な問題を含む非線形拡散問題を取り扱う。本講演では、非線形拡散問題の解が、拡散が線形である半線形反応拡散系の解により近似されることを示す。この結果は、非線形拡散問題の解構造が、ある種の半線形反応拡散系の中に再現されることを示唆するものである。一般に、非線形問題を扱うよりも半線形問題を取り扱う方が容易であるため、本研究は非線形問題の解析や数値解析に応用できることが期待される。
2010/06/23
GCOE Seminars
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
村川 秀樹 (富山大学大学院理工学研究部(理学))
非線形交差拡散系の数値解法―反応拡散系近似理論の応用― (JAPANESE)
http://www.infsup.jp/utnas/
村川 秀樹 (富山大学大学院理工学研究部(理学))
非線形交差拡散系の数値解法―反応拡散系近似理論の応用― (JAPANESE)
[ Abstract ]
多成分反応拡散系において、他の成分同士、拡散が相互に依存しあっているときに、拡散が交差していると言い、そのような系は交差拡散系と呼ばれる。2種生物種の競合問題におけるお互いの動的な干渉作用を記述する重定-川崎-寺本モデルは非線形交差拡散を含む問題の代表例である。非線形交差拡散系に対する効果的な数値解法は個別の問題に対して構成され、解析されるのが現状である。現象のモデリングを行う場合など、パラメータの変更のみでなく、非線形項そのものを変えて多くの数値実験を行いたい場合がある。この様な状況に対応するために、汎用的で簡便な数値解法が望まれる。講演では、非線形交差拡散系を近似するある半線形反応拡散系を媒介することにより、そのような数値解法を導出、解析し、数値計算を通してその有用性を示す。時間が許せば、半線形反応拡散系を用いた退化放物型方程式の数値解法についても触れたい。
[ Reference URL ]多成分反応拡散系において、他の成分同士、拡散が相互に依存しあっているときに、拡散が交差していると言い、そのような系は交差拡散系と呼ばれる。2種生物種の競合問題におけるお互いの動的な干渉作用を記述する重定-川崎-寺本モデルは非線形交差拡散を含む問題の代表例である。非線形交差拡散系に対する効果的な数値解法は個別の問題に対して構成され、解析されるのが現状である。現象のモデリングを行う場合など、パラメータの変更のみでなく、非線形項そのものを変えて多くの数値実験を行いたい場合がある。この様な状況に対応するために、汎用的で簡便な数値解法が望まれる。講演では、非線形交差拡散系を近似するある半線形反応拡散系を媒介することにより、そのような数値解法を導出、解析し、数値計算を通してその有用性を示す。時間が許せば、半線形反応拡散系を用いた退化放物型方程式の数値解法についても触れたい。
http://www.infsup.jp/utnas/
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Hideki Murakawa (University of Toyama)
Numerical methods for nonlinear cross diffusion system: application of reaction-diffusion approximation theory (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Hideki Murakawa (University of Toyama)
Numerical methods for nonlinear cross diffusion system: application of reaction-diffusion approximation theory (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
2010/06/22
Tuesday Seminar of Analysis
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Ivana Alexandrova (East Carolina University)
Resonances for Magnetic Scattering by Two Solenoidal Fields at Large Separation (ENGLISH)
Ivana Alexandrova (East Carolina University)
Resonances for Magnetic Scattering by Two Solenoidal Fields at Large Separation (ENGLISH)
[ Abstract ]
We consider the problem of quantum resonances in magnetic scattering by two
solenoidal fields at large separation in two dimensions, and we study how a trajectory
oscillating between the two fields gives rise to resonances near the real axis when
the distance between two centers of fields goes to infinity. We give a sharp lower
bound on resonance widths in terms of backward amplitudes calculated explicitly for
scattering by each solenoidal field. The study is based on a new type of complex
scaling method. As an application, we also discuss the relation to semiclassical
resonances in scattering by two solenoidal fields. This is joint work with Hideo Tamura.
We consider the problem of quantum resonances in magnetic scattering by two
solenoidal fields at large separation in two dimensions, and we study how a trajectory
oscillating between the two fields gives rise to resonances near the real axis when
the distance between two centers of fields goes to infinity. We give a sharp lower
bound on resonance widths in terms of backward amplitudes calculated explicitly for
scattering by each solenoidal field. The study is based on a new type of complex
scaling method. As an application, we also discuss the relation to semiclassical
resonances in scattering by two solenoidal fields. This is joint work with Hideo Tamura.
2010/06/21
Algebraic Geometry Seminar
16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)
Toru Tsukioka (Osaka Prefecture University)
Pseudo-index and minimal length of extremal rays for Fano manifolds (JAPANESE)
Toru Tsukioka (Osaka Prefecture University)
Pseudo-index and minimal length of extremal rays for Fano manifolds (JAPANESE)
[ Abstract ]
The minimum of intersection numbers of the anticanonical
divisor with rational curves on a Fano manifold is called pseudo-index.
In view of the fact that the geometry of Fano manifolds is governed by
its extremal rays, it is important to consider the extremal rational
curves. In this talk, we show that for Fano 4-folds having birational
contractions, the minimal length of extremal rays coincides with the
pseudo-index.
The minimum of intersection numbers of the anticanonical
divisor with rational curves on a Fano manifold is called pseudo-index.
In view of the fact that the geometry of Fano manifolds is governed by
its extremal rays, it is important to consider the extremal rational
curves. In this talk, we show that for Fano 4-folds having birational
contractions, the minimal length of extremal rays coincides with the
pseudo-index.
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Sachiko HAMANO (Fukushima Univ)
A remark on C^1 subharmonicity of the harmonic spans for discontinuously moving Riemann surfaces (JAPANESE)
Sachiko HAMANO (Fukushima Univ)
A remark on C^1 subharmonicity of the harmonic spans for discontinuously moving Riemann surfaces (JAPANESE)
2010/06/17
GCOE lecture series
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Feng Xu (UC Riverside)
On a relative version of Wall's conjecture (ENGLISH)
Feng Xu (UC Riverside)
On a relative version of Wall's conjecture (ENGLISH)
Operator Algebra Seminars
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Feng Xu (UC Riverside)
On a relative version of Wall's conjecture (ENGLISH)
Feng Xu (UC Riverside)
On a relative version of Wall's conjecture (ENGLISH)
Classical Analysis
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Teruhisa Tsuda (University of Kyushu)
On a class of the Schlesinger systems (JAPANESE)
Teruhisa Tsuda (University of Kyushu)
On a class of the Schlesinger systems (JAPANESE)
2010/06/16
Number Theory Seminar
16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Luc Illusie (Universite de Paris-Sud)
Vanishing theorems revisited, after K.-W. Lan and J. Suh (ENGLISH)
Luc Illusie (Universite de Paris-Sud)
Vanishing theorems revisited, after K.-W. Lan and J. Suh (ENGLISH)
[ Abstract ]
Let k be an algebraically closed field of characteristic p and X,
Y proper, smooth k-schemes. J. Suh has proved a vanishing theorem of Kollar
type for certain nef and big line bundles L on Y and morphisms f : X -> Y
having semistable reduction along a divisor with simple normal crossings. It
holds both if p = 0 and if p > 0 modulo some additional liftability mod p^2
and dimension assumptions, and generalizes vanishing theorems of Esnault-
Viehweg and of mine. I'll give an outline of the proof and sketch some
applications, due to K.-W. Lan and J. Suh, to the cohomology of certain
automorphic bundles arising from PEL type Shimura varieties.
Let k be an algebraically closed field of characteristic p and X,
Y proper, smooth k-schemes. J. Suh has proved a vanishing theorem of Kollar
type for certain nef and big line bundles L on Y and morphisms f : X -> Y
having semistable reduction along a divisor with simple normal crossings. It
holds both if p = 0 and if p > 0 modulo some additional liftability mod p^2
and dimension assumptions, and generalizes vanishing theorems of Esnault-
Viehweg and of mine. I'll give an outline of the proof and sketch some
applications, due to K.-W. Lan and J. Suh, to the cohomology of certain
automorphic bundles arising from PEL type Shimura varieties.
2010/06/15
Tuesday Seminar of Analysis
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Takashi Takiguchi (Department of Mathematics, National Defense Academy)
Sato's counterexample and the structure of generalized functions (JAPANESE)
Takashi Takiguchi (Department of Mathematics, National Defense Academy)
Sato's counterexample and the structure of generalized functions (JAPANESE)
[ Abstract ]
In this talk, we discuss the relation between the structure and the microlocal unique continuation property of generalized functions. We also mention some applications of the microlocal unique continuation property.
In this talk, we discuss the relation between the structure and the microlocal unique continuation property of generalized functions. We also mention some applications of the microlocal unique continuation property.
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