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Seminar information archive
Seminar information archive ～10/15｜Today's seminar 10/16 | Future seminars 10/17～
2012/10/05
Seminar on Probability and Statistics
14:50-16:00 Room #006 (Graduate School of Math. Sci. Bldg.)
OGIHARA, Teppei (Center for the Study of Finance and Insurance, Osaka University)
Quasi-likelihood analysis for stochastic regression models from nonsynchronous observations (JAPANESE)
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/07.html
OGIHARA, Teppei (Center for the Study of Finance and Insurance, Osaka University)
Quasi-likelihood analysis for stochastic regression models from nonsynchronous observations (JAPANESE)
[ Abstract ]
高頻度金融時系列データの解析時に, 二資産価格データの共変動を解析する上での問題として
"観測の非同期性"がある. データの線形補完や直前データを用いた補完などによるシンプルな
"同期化"を行ったデータに対する共分散推定量は深刻なバイアスが存在することが知られている.
Hayashi and Yoshida (2005)では, 非同期観測下での共分散のノンパラメトリックな不偏推定量を提案し,
推定量の一致性, 漸近(混合)正規性などを示している.
本発表ではパラメータ付2次元拡散過程の非同期観測の問題に対する, 尤度解析を用いたアプローチを紹介し,
最尤型推定量, ベイズ型推定量の構築とその一致性, 漸近混合正規性に関する結果を紹介する.
[ Reference URL ]高頻度金融時系列データの解析時に, 二資産価格データの共変動を解析する上での問題として
"観測の非同期性"がある. データの線形補完や直前データを用いた補完などによるシンプルな
"同期化"を行ったデータに対する共分散推定量は深刻なバイアスが存在することが知られている.
Hayashi and Yoshida (2005)では, 非同期観測下での共分散のノンパラメトリックな不偏推定量を提案し,
推定量の一致性, 漸近(混合)正規性などを示している.
本発表ではパラメータ付2次元拡散過程の非同期観測の問題に対する, 尤度解析を用いたアプローチを紹介し,
最尤型推定量, ベイズ型推定量の構築とその一致性, 漸近混合正規性に関する結果を紹介する.
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/07.html
2012/10/02
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Akito Futaki (The University of Tokyo)
Geometric flows and their self-similar solutions
(JAPANESE)
Akito Futaki (The University of Tokyo)
Geometric flows and their self-similar solutions
(JAPANESE)
[ Abstract ]
In the first half of this expository talk we consider the Ricci flow and its self-similar solutions,
namely the Ricci solitons. We then specialize in the K\\"ahler case and discuss on the K\\"ahler-Einstein
problem. In the second half of this talk we consider the mean curvature flow and its self-similar
solutions, and see common aspects of the two geometric flows.
In the first half of this expository talk we consider the Ricci flow and its self-similar solutions,
namely the Ricci solitons. We then specialize in the K\\"ahler case and discuss on the K\\"ahler-Einstein
problem. In the second half of this talk we consider the mean curvature flow and its self-similar
solutions, and see common aspects of the two geometric flows.
2012/10/01
Algebraic Geometry Seminar
13:30-15:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Robert Laterveer (CNRS, IRMA, Université de Strasbourg)
Weak Lefschetz for divisors (ENGLISH)
Robert Laterveer (CNRS, IRMA, Université de Strasbourg)
Weak Lefschetz for divisors (ENGLISH)
[ Abstract ]
Let $X$ be a complex projective variety (possibly singular), and $Y\\subset X$ a generic hyperplane section. We prove several weak Lefschetz results concerning the restriction $A^1(X)_{\\qq}\\to A^1(Y)_{\\qq}$, where $A^1$ denotes Fulton--MacPherson's operational Chow cohomology group. In addition, we reprove (and slightly extend) a weak Lefschetz result concerning the Chow group of Weil divisors first proven by Ravindra and Srinivas. As an application of these weak Lefschetz results, we can say something about when the natural map from the Picard group to $A^1$ is an isomorphism.
Let $X$ be a complex projective variety (possibly singular), and $Y\\subset X$ a generic hyperplane section. We prove several weak Lefschetz results concerning the restriction $A^1(X)_{\\qq}\\to A^1(Y)_{\\qq}$, where $A^1$ denotes Fulton--MacPherson's operational Chow cohomology group. In addition, we reprove (and slightly extend) a weak Lefschetz result concerning the Chow group of Weil divisors first proven by Ravindra and Srinivas. As an application of these weak Lefschetz results, we can say something about when the natural map from the Picard group to $A^1$ is an isomorphism.
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Ryo Ohkawa (RIMS, Kyoto University)
Frobenius morphisms and derived categories on two dimensional toric Deligne--Mumford stacks (JAPANESE)
Ryo Ohkawa (RIMS, Kyoto University)
Frobenius morphisms and derived categories on two dimensional toric Deligne--Mumford stacks (JAPANESE)
[ Abstract ]
For a toric Deligne-Mumford (DM) stack over the complex number field, we can consider a certain generalization of the Frobenius endomorphism. For such an endomorphism of a two-dimensional toric DM stack, we show that the push-forward of the structure sheaf generates the bounded derived category of coherent sheaves on the stack. This is joint work with Hokuto Uehara.
For a toric Deligne-Mumford (DM) stack over the complex number field, we can consider a certain generalization of the Frobenius endomorphism. For such an endomorphism of a two-dimensional toric DM stack, we show that the push-forward of the structure sheaf generates the bounded derived category of coherent sheaves on the stack. This is joint work with Hokuto Uehara.
2012/09/20
Applied Analysis
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Bernold Fiedler (Free University of Berlin)
Fusco-Rocha meanders: from Temperley-Lieb algebras to black holes
(ENGLISH)
Bernold Fiedler (Free University of Berlin)
Fusco-Rocha meanders: from Temperley-Lieb algebras to black holes
(ENGLISH)
[ Abstract ]
Fusco and Rocha studied Neumann boundary value problems for ODEs of second order via a shooting approach. They introduced the notion of what we now call Sturm permutation. These permutation relate, on the one hand, to a special class of meandering curves as introduced by Arnol'd in a singularity context. On the other hand, their special class became central in the study of global attractors of parabolic PDEs of Sturm type.
We discuss relations of Fusco-Rocha meanders with further areas: the multiplicative and trace structure in Temperley-Lieb algebras, discrete versions of Cartesian billiards, and the problem of constructing initial conditions for black hole dynamics which satisfy the Einstein constraints. We also risk a brief glimpse at the long and meandric history of meander patterns themselves.
This is joint work with Juliette Hell, Brian Smith, Carlos Rocha, Pablo Castaneda, and Matthias Wolfrum.
Fusco and Rocha studied Neumann boundary value problems for ODEs of second order via a shooting approach. They introduced the notion of what we now call Sturm permutation. These permutation relate, on the one hand, to a special class of meandering curves as introduced by Arnol'd in a singularity context. On the other hand, their special class became central in the study of global attractors of parabolic PDEs of Sturm type.
We discuss relations of Fusco-Rocha meanders with further areas: the multiplicative and trace structure in Temperley-Lieb algebras, discrete versions of Cartesian billiards, and the problem of constructing initial conditions for black hole dynamics which satisfy the Einstein constraints. We also risk a brief glimpse at the long and meandric history of meander patterns themselves.
This is joint work with Juliette Hell, Brian Smith, Carlos Rocha, Pablo Castaneda, and Matthias Wolfrum.
2012/09/15
Monthly Seminar on Arithmetic of Automorphic Forms
13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Tadashi Miyazaki (Kitazato University) 13:30-14:30
Matrix coefficients of the large discrete series of SU(2,1) and SU(3,1) (JAPANESE)
Hiro-aki Narita (Kumamoto University) 15:00-16:00
Strict positivity of the central values of some Rankin L-functions of GSp(1,1) and special values of hypergeometric functions (JAPANESE)
Tadashi Miyazaki (Kitazato University) 13:30-14:30
Matrix coefficients of the large discrete series of SU(2,1) and SU(3,1) (JAPANESE)
Hiro-aki Narita (Kumamoto University) 15:00-16:00
Strict positivity of the central values of some Rankin L-functions of GSp(1,1) and special values of hypergeometric functions (JAPANESE)
[ Abstract ]
We discuss the strict positivity of the central values of certain convolution type L-functions for several theta lifts to GSp(1,1). Such strict positivity is closely related to special values of some hypergeometric functions.
We discuss the strict positivity of the central values of certain convolution type L-functions for several theta lifts to GSp(1,1). Such strict positivity is closely related to special values of some hypergeometric functions.
2012/09/04
Tuesday Seminar on Topology
17:00-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Piotr Nowak (the Institute of Mathematics, Polish Academy of Sciences)
Poincare inequalities, rigid groups and applications (ENGLISH)
Piotr Nowak (the Institute of Mathematics, Polish Academy of Sciences)
Poincare inequalities, rigid groups and applications (ENGLISH)
[ Abstract ]
Kazhdan’s property (T) for a group G can be expressed as a
fixed point property for affine isometric actions of G on a Hilbert
space. This definition generalizes naturally to other normed spaces. In
this talk we will focus on the spectral (aka geometric) method for
proving property (T), based on the work of Garland and studied earlier
by Pansu, Zuk, Ballmann-Swiatkowski, Dymara-Januszkiewicz
(“lambda_1>1/2” conditions) and we generalize it to to the setting of
all reflexive Banach spaces.
As applications we will show estimates of the conformal dimension of the
boundary of random hyperbolic groups in the Gromov density model and
present progress on Shalom’s conjecture on vanishing of 1-cohomology
with coefficients in uniformly bounded representations on Hilbert spaces.
Kazhdan’s property (T) for a group G can be expressed as a
fixed point property for affine isometric actions of G on a Hilbert
space. This definition generalizes naturally to other normed spaces. In
this talk we will focus on the spectral (aka geometric) method for
proving property (T), based on the work of Garland and studied earlier
by Pansu, Zuk, Ballmann-Swiatkowski, Dymara-Januszkiewicz
(“lambda_1>1/2” conditions) and we generalize it to to the setting of
all reflexive Banach spaces.
As applications we will show estimates of the conformal dimension of the
boundary of random hyperbolic groups in the Gromov density model and
present progress on Shalom’s conjecture on vanishing of 1-cohomology
with coefficients in uniformly bounded representations on Hilbert spaces.
2012/08/29
thesis presentations
10:30-11:45 Room #123 (Graduate School of Math. Sci. Bldg.)
Shinichi MATSUMURA (Graduate School of Mathematical Sciences the University of Tokyo)
Studies on the asymptotic invariants of cohomology groups and the positivity in complex geometry (JAPANESE)
Shinichi MATSUMURA (Graduate School of Mathematical Sciences the University of Tokyo)
Studies on the asymptotic invariants of cohomology groups and the positivity in complex geometry (JAPANESE)
2012/08/20
thesis presentations
11:00-12:15 Room #128 (Graduate School of Math. Sci. Bldg.)
Yoshifumi MIMURA (Graduate School of Mathematical Sciences the University of Tokyo)
The variational formulation of the fully parabolic Keller-Segel system with degenerate diffusion (JAPANESE)
Yoshifumi MIMURA (Graduate School of Mathematical Sciences the University of Tokyo)
The variational formulation of the fully parabolic Keller-Segel system with degenerate diffusion (JAPANESE)
2012/07/30
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Gianluca Pacienza (Université de Strasbourg)
Log Bend-and-Break on Deligne-Mumford stacks (ENGLISH)
Gianluca Pacienza (Université de Strasbourg)
Log Bend-and-Break on Deligne-Mumford stacks (ENGLISH)
[ Abstract ]
We prove a logarithmic Bend-and-Break lemma on a LCI Deligne-Mumford stacks with projective moduli space and integral boundary divisor. As a by-product we obtain a logarithmic version of the Miyaoka-Mori numerical criterion of uniruledness for DM stacks (under additional conditions on the boundary and on the non-schematic locus) and a Cone Theorem for Deligne-Mumford stacks with boundary. These results hold on an algebraically closed field of any characteristic. This is joint work with Michael McQuillan.
We prove a logarithmic Bend-and-Break lemma on a LCI Deligne-Mumford stacks with projective moduli space and integral boundary divisor. As a by-product we obtain a logarithmic version of the Miyaoka-Mori numerical criterion of uniruledness for DM stacks (under additional conditions on the boundary and on the non-schematic locus) and a Cone Theorem for Deligne-Mumford stacks with boundary. These results hold on an algebraically closed field of any characteristic. This is joint work with Michael McQuillan.
2012/07/27
Seminar on Probability and Statistics
14:00-17:00 Room #006 (Graduate School of Math. Sci. Bldg.)
UENO, Tsuyoshi (Minato Discrete Structure Manipulation System Project, Japan Science and Technology Agency)
General approach to reinforcement learning based on statistical inference (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/06.html
UENO, Tsuyoshi (Minato Discrete Structure Manipulation System Project, Japan Science and Technology Agency)
General approach to reinforcement learning based on statistical inference (JAPANESE)
[ Reference URL ]
http://www.sigmath.es.osaka-u.ac.jp/~kamatani/statseminar/2012/06.html
2012/07/25
GCOE lecture series
16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)
George Elliott (University of Toronto)
A survey of recent results on the classification of C*-algebras (ENGLISH)
George Elliott (University of Toronto)
A survey of recent results on the classification of C*-algebras (ENGLISH)
2012/07/24
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Greg McShane (Institut Fourier, Grenoble)
Orthospectra and identities (ENGLISH)
Greg McShane (Institut Fourier, Grenoble)
Orthospectra and identities (ENGLISH)
[ Abstract ]
The orthospectra of a hyperbolic manifold with geodesic
boundary consists of the lengths of all geodesics perpendicular to the
boundary.
We discuss the properties of the orthospectra, asymptotics, multiplicity
and identities due to Basmajian, Bridgeman and Calegari. We will give
a proof that the identities of Bridgeman and Calegari are the same.
The orthospectra of a hyperbolic manifold with geodesic
boundary consists of the lengths of all geodesics perpendicular to the
boundary.
We discuss the properties of the orthospectra, asymptotics, multiplicity
and identities due to Basmajian, Bridgeman and Calegari. We will give
a proof that the identities of Bridgeman and Calegari are the same.
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Toshihisa Kubo (the University of Tokyo)
The Dynkin index and conformally invariant systems of Heisenberg parabolic type (ENGLISH)
Toshihisa Kubo (the University of Tokyo)
The Dynkin index and conformally invariant systems of Heisenberg parabolic type (ENGLISH)
[ Abstract ]
Recently, Barchini-Kable-Zierau systematically constructed conformally invariant systems of differential operators using Heisenberg parabolic subalgebras. When they built such systems, two constants, which are defined as the constant of proportionality between two expressions,played an important role. In this talk we give concrete and uniform expressions for these constants. To do so the Dynkin index of a finite dimensional representation of a complex simple Lie algebra plays a key role.
Recently, Barchini-Kable-Zierau systematically constructed conformally invariant systems of differential operators using Heisenberg parabolic subalgebras. When they built such systems, two constants, which are defined as the constant of proportionality between two expressions,played an important role. In this talk we give concrete and uniform expressions for these constants. To do so the Dynkin index of a finite dimensional representation of a complex simple Lie algebra plays a key role.
2012/07/23
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Shinnosuke Okawa (University of Tokyo)
Derived category of smooth proper Deligne-Mumford stack with p_g>0 (JAPANESE)
Shinnosuke Okawa (University of Tokyo)
Derived category of smooth proper Deligne-Mumford stack with p_g>0 (JAPANESE)
[ Abstract ]
Semiorthogonal decomposition (SOD) of the derived category of coherent sheaves reflects interesting geometry of varieties (more generally stacks), such as minimal model program. We show that the global sections of the canonical line bundle (if exists) give restrictions on the possible form of SODs. As a special case, we see that the global generation of the canonical line bundle implies the non-existence of SODs. (joint work with Kotaro Kawatani)
Semiorthogonal decomposition (SOD) of the derived category of coherent sheaves reflects interesting geometry of varieties (more generally stacks), such as minimal model program. We show that the global sections of the canonical line bundle (if exists) give restrictions on the possible form of SODs. As a special case, we see that the global generation of the canonical line bundle implies the non-existence of SODs. (joint work with Kotaro Kawatani)
Lectures
16:30-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Thomas W. Roby (University of Connecticut)
Combinatorial Ergodicity (ENGLISH)
Thomas W. Roby (University of Connecticut)
Combinatorial Ergodicity (ENGLISH)
[ Abstract ]
Many cyclic actions $\\tau$ on a finite set $S$ of
combinatorial objects, along with many natural
statistics $\\phi$ on $S$, exhibit``combinatorial ergodicity'':
the average of $\\phi$ over each $\\tau$-orbit in $S$ is
the same as the average of $\\phi$ over the whole set $S$.
One example is the case where $S$ is the set of
length $n$ binary strings $a_{1}\\dots a_{n}$
with exactly $k$ 1's,
$\\tau$ is the map that cyclically rotates them,
and $\\phi$ is the number of \\textit{inversions}
(i.e, pairs $(a_{i},a_{j})=(1,0)$ for $iJ$ less than $j$).
This phenomenon was first noticed by Panyushev
in 2007 in the context of antichains in root posets;
Armstrong, Stump, and Thomas proved his
conjecture in 2011.
We describe a theoretical framework for results of this kind,
and discuss old and new results for products of two chains.
This is joint work with Jim Propp.
Many cyclic actions $\\tau$ on a finite set $S$ of
combinatorial objects, along with many natural
statistics $\\phi$ on $S$, exhibit``combinatorial ergodicity'':
the average of $\\phi$ over each $\\tau$-orbit in $S$ is
the same as the average of $\\phi$ over the whole set $S$.
One example is the case where $S$ is the set of
length $n$ binary strings $a_{1}\\dots a_{n}$
with exactly $k$ 1's,
$\\tau$ is the map that cyclically rotates them,
and $\\phi$ is the number of \\textit{inversions}
(i.e, pairs $(a_{i},a_{j})=(1,0)$ for $iJ$ less than $j$).
This phenomenon was first noticed by Panyushev
in 2007 in the context of antichains in root posets;
Armstrong, Stump, and Thomas proved his
conjecture in 2011.
We describe a theoretical framework for results of this kind,
and discuss old and new results for products of two chains.
This is joint work with Jim Propp.
2012/07/21
Monthly Seminar on Arithmetic of Automorphic Forms
13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)
S. Takemori (Kyoto Univ., School of Science) 13:30-14:30
On Fourier coefficients of Siegel-Eisenstein series of degree n. (JAPANESE)
Polylogarithms revisited from the viewpoint of the irrationality (JAPANESE)
S. Takemori (Kyoto Univ., School of Science) 13:30-14:30
On Fourier coefficients of Siegel-Eisenstein series of degree n. (JAPANESE)
[ Abstract ]
We define an Siegel-Eisenstein series G_{k,\\chi} of degree n and talk about an explicit formula of the Fourier coefficients. This Eisenstein series is different from ordinarily defined Eisenstein series E_{k,\\chi}, but if \\chi satisfies a certain condition, we can obtain an explicit formula of Fourier coefficients of E_{k,\\chi}.
Noriko HIRATA-Kohno (Nihon University) 15:00-16:00We define an Siegel-Eisenstein series G_{k,\\chi} of degree n and talk about an explicit formula of the Fourier coefficients. This Eisenstein series is different from ordinarily defined Eisenstein series E_{k,\\chi}, but if \\chi satisfies a certain condition, we can obtain an explicit formula of Fourier coefficients of E_{k,\\chi}.
Polylogarithms revisited from the viewpoint of the irrationality (JAPANESE)
[ Abstract ]
In this report, we consider a polylogarithmic function to give a lower bound for the dimension of the linear space over the rationals spanned by $1$ and values of the function. Our proof uses Pad\\'e approximation and a criterion due to Yu. V. Nesterenko. We also describe what happens in the $p$-adic case and in the elliptic one.
In this report, we consider a polylogarithmic function to give a lower bound for the dimension of the linear space over the rationals spanned by $1$ and values of the function. Our proof uses Pad\\'e approximation and a criterion due to Yu. V. Nesterenko. We also describe what happens in the $p$-adic case and in the elliptic one.
2012/07/19
GCOE Seminars
17:00-18:00 Room #370 (Graduate School of Math. Sci. Bldg.)
Oleg Emanouilov (Colorado State Univ.)
Inverse boundary value problem for Schroedinger equation in two dimensions (ENGLISH)
Oleg Emanouilov (Colorado State Univ.)
Inverse boundary value problem for Schroedinger equation in two dimensions (ENGLISH)
[ Abstract ]
We consider the Dirichlet-to-Neumann map for determining potential in two-dimensional Schroedinger equation. We relax the regularity condition on potentials and establish the uniqueness within L^p class with p > 2.
We consider the Dirichlet-to-Neumann map for determining potential in two-dimensional Schroedinger equation. We relax the regularity condition on potentials and establish the uniqueness within L^p class with p > 2.
2012/07/18
Number Theory Seminar
16:40-17:40 Room #056 (Graduate School of Math. Sci. Bldg.)
Shane Kelly (Australian National University)
Voevodsky motives and a theorem of Gabber (ENGLISH)
Shane Kelly (Australian National University)
Voevodsky motives and a theorem of Gabber (ENGLISH)
[ Abstract ]
The assumption that the base field satisfies resolution of singularities litters Voevodsky's work on motives. While we don't have resolution of singularities in positive characteristic p, there is a theorem of Gabber on alterations which may be used as a substitute if we are willing to work with Z[1/p] coefficients. We will discuss how this theorem of Gabber may be applied in the context of Voevodsky's work and mention some consequences.
The assumption that the base field satisfies resolution of singularities litters Voevodsky's work on motives. While we don't have resolution of singularities in positive characteristic p, there is a theorem of Gabber on alterations which may be used as a substitute if we are willing to work with Z[1/p] coefficients. We will discuss how this theorem of Gabber may be applied in the context of Voevodsky's work and mention some consequences.
Classical Analysis
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Jiro Sekiguchi (Tokyo University of Agriculture and Technology)
Free divisors, holonomic systems and algebraic Painlev\\'{e} sixth solutions (ENGLISH)
Jiro Sekiguchi (Tokyo University of Agriculture and Technology)
Free divisors, holonomic systems and algebraic Painlev\\'{e} sixth solutions (ENGLISH)
[ Abstract ]
In this talk, I will report an attempt to treat algebraic solutions of Painlev\\'{e} VI equation in a unified manner.
A classification of algebraic solutions of Painlev\\'{e} VI equation was accomplished by O. Lisovyy and Y. Tykhyy after efforts on the construction of such solutions by many authors, K. Iwasaki N. J. Hitchin, P. Boalch, B. Dubrovin, M. Mazzocco, A. V. Kitaev, R. Vidunas and others.
The outline of my approach is as follows.
Let $t$ be a variable and let $w$ be its algebraic function such that $w$ is a solution of Painlev\\'{e} sixth equation. Suppose that both $t$ and $w$ are rational functions of a parameter. Namely $(t,w)$ defines a rational curve.
(1) Find a polynomial $P(u)$ such that $t=\\frac{P(-u)}{P(u)}$.
(2) From $P(u)$, define a weighted homogeneous polynomial $f(x_1,x_2,x_3)=x_3f_1(x_1,x_2,x_3)$ of three variables $x_1,x_2,x_3$, where $(1,2,n)$ is the weight system of $(x_1,x_2,x_3)$ with $n=\\deg P(u)$. The hypersurface $D:f(x)=0$ is a free divisor in ${\\bf C}^3$. Note that $\\deg_{x_3}f_1=2$.
(3) Construct a holonomic system ${\\sl M}$ on ${\\bf C}^3$ of rank two with singularities along $D$.
(4) Construct an ordinary differential equation from the holonomic system ${\\sl M}$ with respect to $x_3$. This differential equation has three singular points $z_0,z_1,a_s$ in $x_3$-line.
(5) Putting $t=\\frac{z_1}{z_0},\\lambda=\\frac{a_s}{z_0}$, we conclude that $(t,\\lambda)$ is equivalent to the pair $(t,w)$.
Our study starts with showing the existence of $P(u)$ in (1). From the classification by Losovyy and Tykhyy, I find that the existence of $P(u)$ is guaranteed for Solutions III, IV, Solutions $k$ ($1\\le k\\le 21$, $k\\not= 4,13,14,20$) and Solution 30. We checked whether (1)-(5) are true or not in these cases separately and as a consequence (1)-(5) hold for the all these cases except Solutions 19, 21.
In this talk, I will report an attempt to treat algebraic solutions of Painlev\\'{e} VI equation in a unified manner.
A classification of algebraic solutions of Painlev\\'{e} VI equation was accomplished by O. Lisovyy and Y. Tykhyy after efforts on the construction of such solutions by many authors, K. Iwasaki N. J. Hitchin, P. Boalch, B. Dubrovin, M. Mazzocco, A. V. Kitaev, R. Vidunas and others.
The outline of my approach is as follows.
Let $t$ be a variable and let $w$ be its algebraic function such that $w$ is a solution of Painlev\\'{e} sixth equation. Suppose that both $t$ and $w$ are rational functions of a parameter. Namely $(t,w)$ defines a rational curve.
(1) Find a polynomial $P(u)$ such that $t=\\frac{P(-u)}{P(u)}$.
(2) From $P(u)$, define a weighted homogeneous polynomial $f(x_1,x_2,x_3)=x_3f_1(x_1,x_2,x_3)$ of three variables $x_1,x_2,x_3$, where $(1,2,n)$ is the weight system of $(x_1,x_2,x_3)$ with $n=\\deg P(u)$. The hypersurface $D:f(x)=0$ is a free divisor in ${\\bf C}^3$. Note that $\\deg_{x_3}f_1=2$.
(3) Construct a holonomic system ${\\sl M}$ on ${\\bf C}^3$ of rank two with singularities along $D$.
(4) Construct an ordinary differential equation from the holonomic system ${\\sl M}$ with respect to $x_3$. This differential equation has three singular points $z_0,z_1,a_s$ in $x_3$-line.
(5) Putting $t=\\frac{z_1}{z_0},\\lambda=\\frac{a_s}{z_0}$, we conclude that $(t,\\lambda)$ is equivalent to the pair $(t,w)$.
Our study starts with showing the existence of $P(u)$ in (1). From the classification by Losovyy and Tykhyy, I find that the existence of $P(u)$ is guaranteed for Solutions III, IV, Solutions $k$ ($1\\le k\\le 21$, $k\\not= 4,13,14,20$) and Solution 30. We checked whether (1)-(5) are true or not in these cases separately and as a consequence (1)-(5) hold for the all these cases except Solutions 19, 21.
2012/07/17
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Mutsuo Oka (Tokyo University of Science)
Contact structure of mixed links (JAPANESE)
Mutsuo Oka (Tokyo University of Science)
Contact structure of mixed links (JAPANESE)
[ Abstract ]
A strongly non-degenerate mixed function has a Milnor open book
structures on a sufficiently small sphere. We introduce the notion of
{\\em a holomorphic-like} mixed function
and we will show that a link defined by such a mixed function has a
canonical contact structure.
Then we will show that this contact structure for a certain
holomorphic-like mixed function
is carried by the Milnor open book.
A strongly non-degenerate mixed function has a Milnor open book
structures on a sufficiently small sphere. We introduce the notion of
{\\em a holomorphic-like} mixed function
and we will show that a link defined by such a mixed function has a
canonical contact structure.
Then we will show that this contact structure for a certain
holomorphic-like mixed function
is carried by the Milnor open book.
GCOE lecture series
16:30-18:00 Room #118 (Graduate School of Math. Sci. Bldg.)
George Elliott (University of Toronto)
An introduction to C*-algebra classification theory (ENGLISH)
George Elliott (University of Toronto)
An introduction to C*-algebra classification theory (ENGLISH)
Tuesday Seminar of Analysis
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Toru Kan (Mathematical institute, Tohoku University)
On non-radially symmetric solutions of the Liouville-Gel'fand equation on a two-dimensional annular domain (JAPANESE)
Toru Kan (Mathematical institute, Tohoku University)
On non-radially symmetric solutions of the Liouville-Gel'fand equation on a two-dimensional annular domain (JAPANESE)
[ Abstract ]
指数関数を非線形項に持つ非線形楕円型方程式(Liouville-Gel'fand方程式)について考察する。特に2次元の円環領域では、この方程式の非球対称な解が球対称解から分岐する形で現れる。本講演では、この分岐解の分岐図上での大域的な構造に関して得られた結果を紹介する。
指数関数を非線形項に持つ非線形楕円型方程式(Liouville-Gel'fand方程式)について考察する。特に2次元の円環領域では、この方程式の非球対称な解が球対称解から分岐する形で現れる。本講演では、この分岐解の分岐図上での大域的な構造に関して得られた結果を紹介する。
Lie Groups and Representation Theory
17:00-18:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Eric Opdam (Universiteit van Amsterdam)
Dirac induction for graded affine Hecke algebras (ENGLISH)
Eric Opdam (Universiteit van Amsterdam)
Dirac induction for graded affine Hecke algebras (ENGLISH)
[ Abstract ]
In recent joint work with Dan Ciubotaru and Peter Trapa we
constructed a model for the discrete series representations of graded affine Hecke algebras as the index of a Dirac operator.
We discuss the K-theoretic meaning of this result, and the remarkable relation between elliptic character theory of a Weyl group and the ordinary character theory of its Pin cover.
In recent joint work with Dan Ciubotaru and Peter Trapa we
constructed a model for the discrete series representations of graded affine Hecke algebras as the index of a Dirac operator.
We discuss the K-theoretic meaning of this result, and the remarkable relation between elliptic character theory of a Weyl group and the ordinary character theory of its Pin cover.
2012/07/14
Harmonic Analysis Komaba Seminar
13:30-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Hidemitsu Wadade (Gifu University) 13:30-15:00
On various inequalities characterizing critical Sobolev-Lorentz spaces (JAPANESE)
Yoshihiro Sawano (Tokyo Metropolitan University) 15:30-17:00
Boundedness of operators on Hardy spaces with variable exponents
(JAPANESE)
Hidemitsu Wadade (Gifu University) 13:30-15:00
On various inequalities characterizing critical Sobolev-Lorentz spaces (JAPANESE)
Yoshihiro Sawano (Tokyo Metropolitan University) 15:30-17:00
Boundedness of operators on Hardy spaces with variable exponents
(JAPANESE)
[ Abstract ]
In this talk, as an off-spring, we will discuss the boundedness of various operators. Our plan of the talk is as follows:
First we recall the definition of Hardy spaces with variable exponents and then we describe the atomic decomposition.
Based upon the atomic decomposition, I define linear operators such as singular integral operators and commutators.
After the definition, I will state the boundedness results and outline the proof of the boundedness of these operators.
In this talk, as an off-spring, we will discuss the boundedness of various operators. Our plan of the talk is as follows:
First we recall the definition of Hardy spaces with variable exponents and then we describe the atomic decomposition.
Based upon the atomic decomposition, I define linear operators such as singular integral operators and commutators.
After the definition, I will state the boundedness results and outline the proof of the boundedness of these operators.
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