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Seminar information archive
Seminar information archive ～07/26｜Today's seminar 07/27 | Future seminars 07/28～
Operator Algebra Seminars
16:30-18:00 Room #052 (Graduate School of Math. Sci. Bldg.)
Rolf Dyre Svegstrup (東大数理)
Endomorphisms of half-sided modular inclusions
Rolf Dyre Svegstrup (東大数理)
Endomorphisms of half-sided modular inclusions
2006/07/05
Seminar on Mathematics for various disciplines
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Y. H. Richard Tsai (University of Texas)
Level Set Methods and Multi-valued solutions
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
Y. H. Richard Tsai (University of Texas)
Level Set Methods and Multi-valued solutions
[ Abstract ]
We review the level set methods for computing multi-valued
solutions to a class of nonlinear first order partial differential
equations, including Hamilton-Jacobi equations, quasi-linear
hyperbolic equations, and conservative transport equations with
multi-valued transport speeds.
The multivalued solutions are embedded as the zeros of a set of scalar functions that solve the initial value problems of a time dependent partial differential equation in an augmented space.
We discuss the essential ideas behind the techniques, the coupling of these techniques to the projection of the interaction of zero level sets and a collection of applications including the omputation of the semiclassical limit for Schr\\"{o}dinger quations and the high frequency geometrical optics limits of linear wave equations.
[ Reference URL ]We review the level set methods for computing multi-valued
solutions to a class of nonlinear first order partial differential
equations, including Hamilton-Jacobi equations, quasi-linear
hyperbolic equations, and conservative transport equations with
multi-valued transport speeds.
The multivalued solutions are embedded as the zeros of a set of scalar functions that solve the initial value problems of a time dependent partial differential equation in an augmented space.
We discuss the essential ideas behind the techniques, the coupling of these techniques to the projection of the interaction of zero level sets and a collection of applications including the omputation of the semiclassical limit for Schr\\"{o}dinger quations and the high frequency geometrical optics limits of linear wave equations.
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
2006/07/04
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Alexander A. Ivanov (Imperial College (London))
Amalgams: a machinery of the modern theory of finite groups
[ Reference URL ]
http://faculty.ms.u-tokyo.ac.jp/~topology/
Alexander A. Ivanov (Imperial College (London))
Amalgams: a machinery of the modern theory of finite groups
[ Reference URL ]
http://faculty.ms.u-tokyo.ac.jp/~topology/
2006/07/03
Seminar on Geometric Complex Analysis
14:00-15:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Jörg Winkelmann (Université Henri Poincaré Nancy)
Complex Semi-Abelian Varieties II --- Compactifications and etc.
Jörg Winkelmann (Université Henri Poincaré Nancy)
Complex Semi-Abelian Varieties II --- Compactifications and etc.
2006/06/28
Number Theory Seminar
16:30-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)
原下秀士 (北海道大学・学振)
Configuration of the central streams in the moduli of abelian varieties
原下秀士 (北海道大学・学振)
Configuration of the central streams in the moduli of abelian varieties
Mathematical Finance
17:30-19:00 Room #118 (Graduate School of Math. Sci. Bldg.)
楠岡 成雄 (東京大)
転換社債の価格:均衡論的アプローチ
楠岡 成雄 (東京大)
転換社債の価格:均衡論的アプローチ
PDE Real Analysis Seminar
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Jian Zhai (Zhejiang University)
Uniqueness of Constant Anisotropic Mean Curvature Immersion of Sphere $S^2$ In $\\Bbb E^3$
Jian Zhai (Zhejiang University)
Uniqueness of Constant Anisotropic Mean Curvature Immersion of Sphere $S^2$ In $\\Bbb E^3$
[ Abstract ]
We prove that the constant anisotropic mean curvature immersion of sphere $S^2$ in $\\Bbb E^3$ is unique, provided that the energy density function $\\gamma$ satisfies some reasonable assumptions.
We prove that the constant anisotropic mean curvature immersion of sphere $S^2$ in $\\Bbb E^3$ is unique, provided that the energy density function $\\gamma$ satisfies some reasonable assumptions.
2006/06/27
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Cedric Tarquini (Ecole Nomale Superieure of Lyon)
Lorentzian foliations on 3-manifolds
Cedric Tarquini (Ecole Nomale Superieure of Lyon)
Lorentzian foliations on 3-manifolds
[ Abstract ]
a joint work with C. Boubel (Ecole Nomale Superieure of Lyon) and P. Mounoud (University of Bordeaux 1 sciences and technologies)
The aim of this work is to give a classification of transversely Lorentzian one dimensional foliations on compact manifolds of dimension three. There are the foliations which admit a transverse pseudo-Riemanniann metric of index one. It is the Lorentzian analogue of the better known Riemannian foliations and they still have rigid transverse geometry.
The Riemannian case was listed by Y. Carriere and we will see that the Lorentzian one is very different and much more complicated to classify. The difference comes form the fact that the completness of the transverse structure, which is automatic in the Riemannian case, is a very strong hypothesis for a transverse Lorentzian foliation.
We will give a classification of complete Lorentzian foliations and some examples which are not complete. As a natural corollary of this classification we will list the codimension one timelike geodesically complete totally geodesic foliations of Lorentzian compact three manifolds.
a joint work with C. Boubel (Ecole Nomale Superieure of Lyon) and P. Mounoud (University of Bordeaux 1 sciences and technologies)
The aim of this work is to give a classification of transversely Lorentzian one dimensional foliations on compact manifolds of dimension three. There are the foliations which admit a transverse pseudo-Riemanniann metric of index one. It is the Lorentzian analogue of the better known Riemannian foliations and they still have rigid transverse geometry.
The Riemannian case was listed by Y. Carriere and we will see that the Lorentzian one is very different and much more complicated to classify. The difference comes form the fact that the completness of the transverse structure, which is automatic in the Riemannian case, is a very strong hypothesis for a transverse Lorentzian foliation.
We will give a classification of complete Lorentzian foliations and some examples which are not complete. As a natural corollary of this classification we will list the codimension one timelike geodesically complete totally geodesic foliations of Lorentzian compact three manifolds.
2006/06/26
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
織田孝幸 (東大数理)
Toward construction of Green current for modular cycles in modular varieties
織田孝幸 (東大数理)
Toward construction of Green current for modular cycles in modular varieties
2006/06/23
Colloquium
17:00-18:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Robert Gompf (University of Texas at Austin)
25 years of exotic $\\mathbb{R}^4s$
Robert Gompf (University of Texas at Austin)
25 years of exotic $\\mathbb{R}^4s$
[ Abstract ]
A quarter century ago, 4-manifold theory was revolutionized by the Fields-Medal winning breakthroughs of Freedman and Donaldson, with Freedman showing that topological 4-manifolds behave like their higher dimensional counterparts, but Donaldson showing that smooth 4-manifolds behave in a completely different way. The interplay between these theories produces results unique to dimension 4: A fixed topological 4-manifold often admits infinitely many distinct smooth structures, for which no classification scheme is yet available. The quintessential example is that in contrast with other dimensions, Euclidean 4-space admits exotic smooth structures. That is, there are "exotic R^4s" homeomorphic to R4 but not diffeomorphic to it. We will survey what has been learned about these strange creatures in the last quarter century, and exhibit an explicit example.
A quarter century ago, 4-manifold theory was revolutionized by the Fields-Medal winning breakthroughs of Freedman and Donaldson, with Freedman showing that topological 4-manifolds behave like their higher dimensional counterparts, but Donaldson showing that smooth 4-manifolds behave in a completely different way. The interplay between these theories produces results unique to dimension 4: A fixed topological 4-manifold often admits infinitely many distinct smooth structures, for which no classification scheme is yet available. The quintessential example is that in contrast with other dimensions, Euclidean 4-space admits exotic smooth structures. That is, there are "exotic R^4s" homeomorphic to R4 but not diffeomorphic to it. We will survey what has been learned about these strange creatures in the last quarter century, and exhibit an explicit example.
2006/06/22
Operator Algebra Seminars
16:30-18:00 Room #052 (Graduate School of Math. Sci. Bldg.)
Detlev Buchholz (Univ. Göttingen)
Integrable models and operator algebras
Detlev Buchholz (Univ. Göttingen)
Integrable models and operator algebras
[ Abstract ]
Recently, it has been possible to establish rigorously the existence of an abundance of 1+1-dimensional local nets of von Neumann algebras describing an interacting massive particle with factorizing scattering matrix. This novel approach is based on structural results in algebraic quantum field theory concerning the modular structure of such theories. It is thus complementary to the older methods of constructive quantum field theory and settles some longstanding questions in the context of integrable models (form-factor program). In this talk, a survey is given on basic ideas, results and perspectives of this promising new approach.
Recently, it has been possible to establish rigorously the existence of an abundance of 1+1-dimensional local nets of von Neumann algebras describing an interacting massive particle with factorizing scattering matrix. This novel approach is based on structural results in algebraic quantum field theory concerning the modular structure of such theories. It is thus complementary to the older methods of constructive quantum field theory and settles some longstanding questions in the context of integrable models (form-factor program). In this talk, a survey is given on basic ideas, results and perspectives of this promising new approach.
2006/06/21
Seminar on Probability and Statistics
16:20-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
石川 保志 (愛媛大学理学部)
Malliavin calculus applied to mathematical finance and a new formulation of the intgration-by-parts
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/05.html
石川 保志 (愛媛大学理学部)
Malliavin calculus applied to mathematical finance and a new formulation of the intgration-by-parts
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2006/05.html
2006/06/19
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
後藤竜司 (大阪大学)
Deformations and smoothing of (generalized) holomorphic symplectic structures
後藤竜司 (大阪大学)
Deformations and smoothing of (generalized) holomorphic symplectic structures
2006/06/15
Applied Analysis
16:00-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Mark Bowen (東京大学大学院数理科学研究科/日本学術振興会)
Spreading and draining in thin fluid films
Mark Bowen (東京大学大学院数理科学研究科/日本学術振興会)
Spreading and draining in thin fluid films
[ Abstract ]
The surface tension driven flow of a thin fluid film arises in a number of contexts. In this talk, we will begin with an overview of thin film theory and present a number of examples from the natural sciences and industrial process engineering. Similarity solutions play an important role in understanding the dynamics of general thin film motion and we shall use them to investigate the dynamics of an archetypal (degenerate high-order parabolic) thin film equation. In this context, we will encounter self-similarity of the first and second kind, undertake an investigation of a four-dimensional phase space and discover a surprisingly rich set of stable sign-changing solutions for the intermediate asymptotics of a generalised problem.
The surface tension driven flow of a thin fluid film arises in a number of contexts. In this talk, we will begin with an overview of thin film theory and present a number of examples from the natural sciences and industrial process engineering. Similarity solutions play an important role in understanding the dynamics of general thin film motion and we shall use them to investigate the dynamics of an archetypal (degenerate high-order parabolic) thin film equation. In this context, we will encounter self-similarity of the first and second kind, undertake an investigation of a four-dimensional phase space and discover a surprisingly rich set of stable sign-changing solutions for the intermediate asymptotics of a generalised problem.
2006/06/14
PDE Real Analysis Seminar
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Qing-Ming Cheng (Saga University)
Bounds on eigenvalues of Dirichlet aplacian
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
Qing-Ming Cheng (Saga University)
Bounds on eigenvalues of Dirichlet aplacian
[ Abstract ]
In this talk, I shall consider the eigenvalue problem of the Dirichlet Laplacian. I shall mention the Weyl asymptotic formula,
Polya conjecture and its partial solution. Furthermore, I shall talk about Bochner-Kac problem.
For universal inequalities for eigenvalues, I shall consider
conjectures of Payne, Polya and Weinberger and their development. In the final, I shall talk the universal bounds for eigenvalues as main part of my talk, which is my recent joint work with rofessor Yang.
[ Reference URL ]In this talk, I shall consider the eigenvalue problem of the Dirichlet Laplacian. I shall mention the Weyl asymptotic formula,
Polya conjecture and its partial solution. Furthermore, I shall talk about Bochner-Kac problem.
For universal inequalities for eigenvalues, I shall consider
conjectures of Payne, Polya and Weinberger and their development. In the final, I shall talk the universal bounds for eigenvalues as main part of my talk, which is my recent joint work with rofessor Yang.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/index.html
2006/06/13
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
田中 心 (東京大学大学院数理科学研究科)
A note on C1-moves
田中 心 (東京大学大学院数理科学研究科)
A note on C1-moves
[ Abstract ]
鎌田氏によりチャートという概念が定義された。これは二次元円板上の 有向ラベル付きグラフであり、二次元ブレイドを記述する際に用いられる。 彼はチャートに対してC変形と呼ばれる三種類の変形(C1変形、C2変形、C3変形) を定義し、曲面ブレイドの同値類とチャートのC変形同値類の間に一対一対応が ある事を示した。 カーター氏と斎藤氏は、任意のC1変形は七種類の基本C1変形の列で得られる 事を示したが、その証明には曖昧な部分がある事が知られていた。本講演では 彼らとは異なるアプローチにより、彼らの主張に対して正しい証明を与える。
鎌田氏によりチャートという概念が定義された。これは二次元円板上の 有向ラベル付きグラフであり、二次元ブレイドを記述する際に用いられる。 彼はチャートに対してC変形と呼ばれる三種類の変形(C1変形、C2変形、C3変形) を定義し、曲面ブレイドの同値類とチャートのC変形同値類の間に一対一対応が ある事を示した。 カーター氏と斎藤氏は、任意のC1変形は七種類の基本C1変形の列で得られる 事を示したが、その証明には曖昧な部分がある事が知られていた。本講演では 彼らとは異なるアプローチにより、彼らの主張に対して正しい証明を与える。
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
織田 寛 (拓殖大学工学部)
古典型複素Lie環の一般Verma加群に対する最小多項式
織田 寛 (拓殖大学工学部)
古典型複素Lie環の一般Verma加群に対する最小多項式
[ Abstract ]
古典型複素Lie環 g の自然表現から自然に定まる U(g) 係数の正方行列を F とする.g のスカラー一般Verma加群 $M_Θ(λ)$ に対して,複素モニック多項式 q(x) で q(F) の各成分が全て Ann $M_Θ(λ)$ に属するような最小次数のものを “$M_Θ(λ)$ の最小多項式” とよぶ.M(λ) を $M_Θ(λ)$ を商加群とするVerma加群とし,q(F) の各成分と Ann M(λ) が生成する U(g) の両側イデアルを $I_Θ(λ)$ とすると,最近
(1) 各λに対する $M_Θ(λ)$ の最小多項式の明示公式
(2) $M_Θ(λ)= M(λ)/I_Θ(λ)M(λ)$ が成り立つためのλの 必要十分条件
が得られた(これらは大島により g = gln の場合には既に得られている).セミナーでは(2)を示すための q(F) の各成分の Harish-Chandra 準同型像の計算法を主に説明する.
古典型複素Lie環 g の自然表現から自然に定まる U(g) 係数の正方行列を F とする.g のスカラー一般Verma加群 $M_Θ(λ)$ に対して,複素モニック多項式 q(x) で q(F) の各成分が全て Ann $M_Θ(λ)$ に属するような最小次数のものを “$M_Θ(λ)$ の最小多項式” とよぶ.M(λ) を $M_Θ(λ)$ を商加群とするVerma加群とし,q(F) の各成分と Ann M(λ) が生成する U(g) の両側イデアルを $I_Θ(λ)$ とすると,最近
(1) 各λに対する $M_Θ(λ)$ の最小多項式の明示公式
(2) $M_Θ(λ)= M(λ)/I_Θ(λ)M(λ)$ が成り立つためのλの 必要十分条件
が得られた(これらは大島により g = gln の場合には既に得られている).セミナーでは(2)を示すための q(F) の各成分の Harish-Chandra 準同型像の計算法を主に説明する.
2006/06/12
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
赤堀隆夫 (兵庫県立大学)
The Rumin complex and Hamiltonian mechanism
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~hirachi/scv/akahori.pdf
赤堀隆夫 (兵庫県立大学)
The Rumin complex and Hamiltonian mechanism
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~hirachi/scv/akahori.pdf
2006/06/10
Infinite Analysis Seminar Tokyo
13:30-16:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Boris Feigin (Landau Institute for Theoretical Physics) 13:30-14:30
"Critical" level for Vertex Algebras
酸化物非線形素子とその展開
Boris Feigin (Landau Institute for Theoretical Physics) 13:30-14:30
"Critical" level for Vertex Algebras
[ Abstract ]
In the talk I present the construction of "VOA" on a critical level using fermionic screenings.Then I discuss the geometric background behind such algebras and applications - Langlands correspondence and related things
坂井 穣 (北陸先端科学技術大学院大学) 15:00-16:00In the talk I present the construction of "VOA" on a critical level using fermionic screenings.Then I discuss the geometric background behind such algebras and applications - Langlands correspondence and related things
酸化物非線形素子とその展開
[ Abstract ]
半導体からなるダイオード、超伝導体からなるジョセフソン素子 などは、それぞれに特徴的な非線形電流電圧 (I-V) 特性をもつがゆえに素子としての機能を発現する。本講演では、主にセラミックス 材料からなるいくつかの薄膜素子において最近観測された、電界誘起金 属転移や不揮発性抵抗変化といった興味深い非線形 I-V 特性を 紹介し、それらをメモリやロジック素子へ展開する可能性を探る。
半導体からなるダイオード、超伝導体からなるジョセフソン素子 などは、それぞれに特徴的な非線形電流電圧 (I-V) 特性をもつがゆえに素子としての機能を発現する。本講演では、主にセラミックス 材料からなるいくつかの薄膜素子において最近観測された、電界誘起金 属転移や不揮発性抵抗変化といった興味深い非線形 I-V 特性を 紹介し、それらをメモリやロジック素子へ展開する可能性を探る。
2006/06/07
Infinite Analysis Seminar Tokyo
14:00-15:00 Room #270 (Graduate School of Math. Sci. Bldg.)
Youjin Zhang (Tsinghua Univ.)
On deformations of bihamiltonian structures of hydrodynamic type
Youjin Zhang (Tsinghua Univ.)
On deformations of bihamiltonian structures of hydrodynamic type
[ Abstract ]
I will talk about the properties of deformations bihamiltonian structures of hydrodynamic type and the related integrable hierarchies, and the problem of classification of such deformations.
I will talk about the properties of deformations bihamiltonian structures of hydrodynamic type and the related integrable hierarchies, and the problem of classification of such deformations.
PDE Real Analysis Seminar
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
高坂 良史 (室蘭工業大学)
On phase boundary motion by surface diffusion with triple junction
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/022.html
高坂 良史 (室蘭工業大学)
On phase boundary motion by surface diffusion with triple junction
[ Abstract ]
The phase boundary motion by a geometrical evolution law in a bounded domain is studied in this talk. We consider the surface diffusion flow equation, which has the gradient flow structure with respect to $H^{-1}$-inner product and the area-preserving property. This equation was derived by Mullins to model the motion of interfaces in the case that the motion of interfaces is governed purely by mass diffusion within the interfaces. We study the three-phase problem with triple junction in a bounded domain and analyze the stability of the stationary solutions for this problem.
[ Reference URL ]The phase boundary motion by a geometrical evolution law in a bounded domain is studied in this talk. We consider the surface diffusion flow equation, which has the gradient flow structure with respect to $H^{-1}$-inner product and the area-preserving property. This equation was derived by Mullins to model the motion of interfaces in the case that the motion of interfaces is governed purely by mass diffusion within the interfaces. We study the three-phase problem with triple junction in a bounded domain and analyze the stability of the stationary solutions for this problem.
http://coe.math.sci.hokudai.ac.jp/sympo/pde_ra/022.html
Number Theory Seminar
16:30-17:30 Room #117 (Graduate School of Math. Sci. Bldg.)
廣惠 一希 (東京大学大学院数理科学研究科)
Hecke-Siegel's pull back formula for the Epstein zeta function with spherical
廣惠 一希 (東京大学大学院数理科学研究科)
Hecke-Siegel's pull back formula for the Epstein zeta function with spherical
Applied Analysis
16:00-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Marek FILA (Bratislava, スロバキア) 16:00-17:00
Slow convergence to zero for a supercritical parabolic equation
柴田 良弘 (早稲田大学・理工学部数理科学科) 17:00-18:00
未定
Marek FILA (Bratislava, スロバキア) 16:00-17:00
Slow convergence to zero for a supercritical parabolic equation
柴田 良弘 (早稲田大学・理工学部数理科学科) 17:00-18:00
未定
2006/06/06
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
三好 重明 (中央大学理工学部)
Thurston's inequality for a foliation with Reeb components
三好 重明 (中央大学理工学部)
Thurston's inequality for a foliation with Reeb components
[ Abstract ]
The Euler class of a Reebless foliation or a tight contact structure on a closed 3-manifold satisfies Thurston's inequality, i.e. its (dual) Thurston norm is less than or equal to 1. It should be significant to study Thurston's inequality in both of foliation theory and contact topology. We investigate conditions for a spinnable foliation one of which assures that Thurston's inequality holds and also another of which implies the violation of the inequality.
The Euler class of a Reebless foliation or a tight contact structure on a closed 3-manifold satisfies Thurston's inequality, i.e. its (dual) Thurston norm is less than or equal to 1. It should be significant to study Thurston's inequality in both of foliation theory and contact topology. We investigate conditions for a spinnable foliation one of which assures that Thurston's inequality holds and also another of which implies the violation of the inequality.
Infinite Analysis Seminar Tokyo
13:30-14:30 Room #117 (Graduate School of Math. Sci. Bldg.)
Leon Takhtajan (SUNY)
A local index theorem for families of $\\bar\\partial$-operators and moduli of parabolic vector bundles
Leon Takhtajan (SUNY)
A local index theorem for families of $\\bar\\partial$-operators and moduli of parabolic vector bundles
[ Abstract ]
We extend our previous work on local index theorem for families of $\\bar\\partial$-operators on punctured Riemann surfaces (Comm. Math. Phys. 137 (1991), 399-426) and for families of $\\bar\\partial$-operators on endomorphism bundles of stable vector bundles over a compact Riemann surface (Math. USSR Izvestia 35 (1990), 83-100) to the case of stable parabolic vector bundles over a Riemann surface. The result is an explicit formula for the first Chern form of the canonical line bundle to the moduli space stable parabolic bundles with the Quillen's type metric. The derivation uses Mehta-Seshadri theorem and spectral theory of automorphic functions on the Lobatchevsky plane with the unitary representation. This is a joint work with P. Zograf.
We extend our previous work on local index theorem for families of $\\bar\\partial$-operators on punctured Riemann surfaces (Comm. Math. Phys. 137 (1991), 399-426) and for families of $\\bar\\partial$-operators on endomorphism bundles of stable vector bundles over a compact Riemann surface (Math. USSR Izvestia 35 (1990), 83-100) to the case of stable parabolic vector bundles over a Riemann surface. The result is an explicit formula for the first Chern form of the canonical line bundle to the moduli space stable parabolic bundles with the Quillen's type metric. The derivation uses Mehta-Seshadri theorem and spectral theory of automorphic functions on the Lobatchevsky plane with the unitary representation. This is a joint work with P. Zograf.
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