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Seminar information archive
Seminar information archive ～04/30｜Today's seminar 05/01 | Future seminars 05/02～
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Ivan Cherednik (The University of North Carolina at Chapel Hill, RIMS
)
Global q,t-hypergeometric and q-Whittaker functions (ENGLISH)
Ivan Cherednik (The University of North Carolina at Chapel Hill, RIMS
)
Global q,t-hypergeometric and q-Whittaker functions (ENGLISH)
[ Abstract ]
The lectures will be devoted to the new theory of global
difference hypergeometric and Whittaker functions, one of
the major applications of the double affine Hecke algebras
and a breakthrough in the classical harmonic analysis. They
integrate the Ruijsenaars-Macdonald difference QMBP and
"Q-Toda" (any root systems), and are analytic everywhere
("global") with superb asymptotic behavior.
The definition of the global functions was suggested about
14 years ago; it is conceptually different from the definition
Heine gave in 1846, which remained unchanged and unchallenged
since then. Algebraically, the new functions are closer to
Bessel functions than to the classical hypergeometric and
Whittaker functions. The analytic theory of these functions was
completed only recently (the speaker and Jasper Stokman).
The construction is based on DAHA. The global functions are defined
as reproducing kernels of Fourier-DAHA transforms. Their
specializations are Macdonald polynomials, which is a powerful
generalization of the Shintani and Casselman-Shalika p-adic formulas.
If time permits, the connection of the Harish-Chandra theory of global
q-Whittaker functions will be discussed with the Givental-Lee formula
(Gromov-Witten invariants of flag varieties) and its generalizations due
to Braverman and Finkelberg (algebraic theory of affine flag varieties).
The lectures will be devoted to the new theory of global
difference hypergeometric and Whittaker functions, one of
the major applications of the double affine Hecke algebras
and a breakthrough in the classical harmonic analysis. They
integrate the Ruijsenaars-Macdonald difference QMBP and
"Q-Toda" (any root systems), and are analytic everywhere
("global") with superb asymptotic behavior.
The definition of the global functions was suggested about
14 years ago; it is conceptually different from the definition
Heine gave in 1846, which remained unchanged and unchallenged
since then. Algebraically, the new functions are closer to
Bessel functions than to the classical hypergeometric and
Whittaker functions. The analytic theory of these functions was
completed only recently (the speaker and Jasper Stokman).
The construction is based on DAHA. The global functions are defined
as reproducing kernels of Fourier-DAHA transforms. Their
specializations are Macdonald polynomials, which is a powerful
generalization of the Shintani and Casselman-Shalika p-adic formulas.
If time permits, the connection of the Harish-Chandra theory of global
q-Whittaker functions will be discussed with the Givental-Lee formula
(Gromov-Witten invariants of flag varieties) and its generalizations due
to Braverman and Finkelberg (algebraic theory of affine flag varieties).
2014/05/12
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Joe Kamimoto (Kyushu university)
Resolution of singularities via Newton polyhedra and its application to analysis (JAPANESE)
Joe Kamimoto (Kyushu university)
Resolution of singularities via Newton polyhedra and its application to analysis (JAPANESE)
[ Abstract ]
In the 1970s, A. N. Varchenko precisely investigated the leading term of the asymptotic expansion of an oscillatory integral with real analytic phase by using the geometry of the Newton polyhedron of the phase. Since his study, the importance of the resolution of singularities by means of Newton polyhedra has been strongly recognized. The purpose of this talk is to consider studies around this theme and to explain their relationship with some problems in several complex variables.
In the 1970s, A. N. Varchenko precisely investigated the leading term of the asymptotic expansion of an oscillatory integral with real analytic phase by using the geometry of the Newton polyhedron of the phase. Since his study, the importance of the resolution of singularities by means of Newton polyhedra has been strongly recognized. The purpose of this talk is to consider studies around this theme and to explain their relationship with some problems in several complex variables.
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Andrés Daniel Duarte (Institut de Mathématiques de Toulouse)
Higher Nash blowup on normal toric varieties and a higher order version of Nobile's theorem (ENGLISH)
Andrés Daniel Duarte (Institut de Mathématiques de Toulouse)
Higher Nash blowup on normal toric varieties and a higher order version of Nobile's theorem (ENGLISH)
[ Abstract ]
The higher Nash blowup of an algebraic variety replaces singular points with limits of certain vector spaces carrying first or higher order data associated to the variety at non-singular points. In the case of normal toric varieties, the higher Nash blowup has a combinatorial description in terms of the Gröbner fan. This description will allows us to prove a higher version of Nobile's theorem in this context: for a normal toric variety, the higher Nash blowup is an isomorphism if and only if the variety is non-singular. We will also present some further observations coming from computational experiments.
The higher Nash blowup of an algebraic variety replaces singular points with limits of certain vector spaces carrying first or higher order data associated to the variety at non-singular points. In the case of normal toric varieties, the higher Nash blowup has a combinatorial description in terms of the Gröbner fan. This description will allows us to prove a higher version of Nobile's theorem in this context: for a normal toric variety, the higher Nash blowup is an isomorphism if and only if the variety is non-singular. We will also present some further observations coming from computational experiments.
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Chien-Hong Cho (National Chung Cheng University)
On the finite difference approximation for blow-up solutions of the nonlinear wave equation (JAPANESE)
http://www.infsup.jp/utnas/
Chien-Hong Cho (National Chung Cheng University)
On the finite difference approximation for blow-up solutions of the nonlinear wave equation (JAPANESE)
[ Abstract ]
We consider in this paper the 1-dim nonlinear wave equation $u_{tt}=u_{xx}+u^{1+\\alpha}$ $(\\alpha > 0)$ and its finite difference analogue. It is known that the solutions of the current equation becomes unbounded in finite time, a phenomenon which is often called blow-up. Numerical approaches on such kind of problems are widely investigated in the last decade. However, those results are mainly about parabolic blow-up problems. Compared with the parabolic ones, there is a remarkable property for the solution of the nonlinear wave equation -- the existence of the blow-up curve. That is, even though the solution has become unbounded at certain points, the solution continues to exist at other points and blows up at later times. We are concerned in this paper as to how a finite difference scheme can reproduce such a phenomenon.
[ Reference URL ]We consider in this paper the 1-dim nonlinear wave equation $u_{tt}=u_{xx}+u^{1+\\alpha}$ $(\\alpha > 0)$ and its finite difference analogue. It is known that the solutions of the current equation becomes unbounded in finite time, a phenomenon which is often called blow-up. Numerical approaches on such kind of problems are widely investigated in the last decade. However, those results are mainly about parabolic blow-up problems. Compared with the parabolic ones, there is a remarkable property for the solution of the nonlinear wave equation -- the existence of the blow-up curve. That is, even though the solution has become unbounded at certain points, the solution continues to exist at other points and blows up at later times. We are concerned in this paper as to how a finite difference scheme can reproduce such a phenomenon.
http://www.infsup.jp/utnas/
2014/05/08
Geometry Colloquium
10:00-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Hajime Ono (Saitama University)
On non Hamiltonian volume minimizing H-stable Lagrangian tori (JAPANESE)
Hajime Ono (Saitama University)
On non Hamiltonian volume minimizing H-stable Lagrangian tori (JAPANESE)
[ Abstract ]
Y. –G. Oh investigated the volume of Lagrangian submanifolds in a Kaehler manifold and introduced the notion of Hamiltonian minimality, Hamiltonian stability and Hamiltonian volume minimizing property. For example, it is known that standard tori in complex Euclidean spaces and torus orbits in complex projective spaces are H-minimal and H-stable. In this talk I show that
1. Almost all of standard tori in the complex Euclidean space of dimension greater than two are not Hamiltonian volume minimizing.
2. There are non Hamiltonian volume minimizing torus orbits in any compact toric Kaehler manifold of dimension greater than two.
Y. –G. Oh investigated the volume of Lagrangian submanifolds in a Kaehler manifold and introduced the notion of Hamiltonian minimality, Hamiltonian stability and Hamiltonian volume minimizing property. For example, it is known that standard tori in complex Euclidean spaces and torus orbits in complex projective spaces are H-minimal and H-stable. In this talk I show that
1. Almost all of standard tori in the complex Euclidean space of dimension greater than two are not Hamiltonian volume minimizing.
2. There are non Hamiltonian volume minimizing torus orbits in any compact toric Kaehler manifold of dimension greater than two.
2014/05/07
Mathematical Biology Seminar
14:50-16:20 Room #128 (Graduate School of Math. Sci. Bldg.)
Yoichi Enatsu (Graduate School of Mathematical Sciences, University fo Tokyo)
Asymptotic behavior of differential equation systems for age-structured epidemic models (JAPANESE)
Yoichi Enatsu (Graduate School of Mathematical Sciences, University fo Tokyo)
Asymptotic behavior of differential equation systems for age-structured epidemic models (JAPANESE)
2014/05/02
Colloquium
16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
A.P. Veselov (Loughborough, UK and Tokyo, Japan)
From hyperplane arrangements to Deligne-Mumford moduli spaces: Kohno-Drinfeld way (ENGLISH)
A.P. Veselov (Loughborough, UK and Tokyo, Japan)
From hyperplane arrangements to Deligne-Mumford moduli spaces: Kohno-Drinfeld way (ENGLISH)
[ Abstract ]
Gaudin subalgebras are abelian Lie subalgebras of maximal
dimension spanned by generators of the Kohno-Drinfeld Lie algebra t_n,
associated to A-type hyperplane arrangement.
It turns out that Gaudin subalgebras form a smooth algebraic variety
isomorphic to the Deligne-Mumford moduli space \\bar M_{0,n+1} of
stable genus zero curves with n+1 marked points.
A real version of this result allows to describe the
moduli space of integrable n-dimensional tops and
separation coordinates on the unit sphere
in terms of the geometry of Stasheff polytope.
The talk is based on joint works with L. Aguirre and G. Felder and with K.
Schoebel.
Gaudin subalgebras are abelian Lie subalgebras of maximal
dimension spanned by generators of the Kohno-Drinfeld Lie algebra t_n,
associated to A-type hyperplane arrangement.
It turns out that Gaudin subalgebras form a smooth algebraic variety
isomorphic to the Deligne-Mumford moduli space \\bar M_{0,n+1} of
stable genus zero curves with n+1 marked points.
A real version of this result allows to describe the
moduli space of integrable n-dimensional tops and
separation coordinates on the unit sphere
in terms of the geometry of Stasheff polytope.
The talk is based on joint works with L. Aguirre and G. Felder and with K.
Schoebel.
2014/04/30
Number Theory Seminar
16:40-17:40 Room #056 (Graduate School of Math. Sci. Bldg.)
Takuya Maruyama (University of Tokyo)
An effective upper bound for the number of principally polarized Abelian schemes (JAPANESE)
Takuya Maruyama (University of Tokyo)
An effective upper bound for the number of principally polarized Abelian schemes (JAPANESE)
Operator Algebra Seminars
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Narutaka Ozawa (RIMS, Kyoto University)
Noncommutative real algebraic geometry of Kazhdan's property (T) (ENGLISH)
Narutaka Ozawa (RIMS, Kyoto University)
Noncommutative real algebraic geometry of Kazhdan's property (T) (ENGLISH)
2014/04/28
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Sunsuke Saito (The University of Tokyo)
On the existence problem of Kähler-Ricci solitons (JAPANESE)
Sunsuke Saito (The University of Tokyo)
On the existence problem of Kähler-Ricci solitons (JAPANESE)
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Alexandru Dimca (Institut Universitaire de France )
Syzygies of jacobian ideals and Torelli properties (ENGLISH)
Alexandru Dimca (Institut Universitaire de France )
Syzygies of jacobian ideals and Torelli properties (ENGLISH)
[ Abstract ]
Let $C$ be a reduced complex projective plane curve defined by a homogeneous equation $f(x,y,z)=0$. We consider syzygies of the type $af_x+bf_y+cf_z=0$, where $a,b,c$ are homogeneous polynomials and $f_x,f_y,f_z$ stand for the partial derivatives of $f$. In our talk we relate such syzygies with stable or splittable rank two vector bundles on the projective plane, and to Torelli properties of plane curves in the sense of Dolgachev-Kapranov.
Let $C$ be a reduced complex projective plane curve defined by a homogeneous equation $f(x,y,z)=0$. We consider syzygies of the type $af_x+bf_y+cf_z=0$, where $a,b,c$ are homogeneous polynomials and $f_x,f_y,f_z$ stand for the partial derivatives of $f$. In our talk we relate such syzygies with stable or splittable rank two vector bundles on the projective plane, and to Torelli properties of plane curves in the sense of Dolgachev-Kapranov.
2014/04/26
Monthly Seminar on Arithmetic of Automorphic Forms
13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Ryutarou Okazaki (Doushisha Univ. until March, 2014) 13:30-14:30
The estimate of integral points of F(X,Y)=1, with F being a integral homogeneous quartic form F of degree 4 (JAPANESE)
Ryutarou Okazaki (Doushisha Univ. until March, 2014) 15:00-16:00
Moduli of teh pairs of algebraic curve of genus 2 and its unramified cover of degree 7 (joint work with Hoffmann) (JAPANESE)
Ryutarou Okazaki (Doushisha Univ. until March, 2014) 13:30-14:30
The estimate of integral points of F(X,Y)=1, with F being a integral homogeneous quartic form F of degree 4 (JAPANESE)
Ryutarou Okazaki (Doushisha Univ. until March, 2014) 15:00-16:00
Moduli of teh pairs of algebraic curve of genus 2 and its unramified cover of degree 7 (joint work with Hoffmann) (JAPANESE)
2014/04/24
Geometry Colloquium
10:00-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Hiraku Nozawa (Ritsumeikan University)
On rigidity of Lie foliations (JAPANESE)
Hiraku Nozawa (Ritsumeikan University)
On rigidity of Lie foliations (JAPANESE)
[ Abstract ]
If the leaves of a Lie foliation are isometric to a symmetric space of noncompact type of higher rank, then, by a theorem of Zimmer, the holonomy group of the Lie foliation has rigidity similar to that of lattices of semisimple Lie groups of higher rank. The main result of this talk is a generalization of Zimmer's theorem including the case of real rank one based on an application of a variant of Mostow rigidity. (This talk is based on a joint work with Ga¥"el Meigniez.)
If the leaves of a Lie foliation are isometric to a symmetric space of noncompact type of higher rank, then, by a theorem of Zimmer, the holonomy group of the Lie foliation has rigidity similar to that of lattices of semisimple Lie groups of higher rank. The main result of this talk is a generalization of Zimmer's theorem including the case of real rank one based on an application of a variant of Mostow rigidity. (This talk is based on a joint work with Ga¥"el Meigniez.)
2014/04/23
Operator Algebra Seminars
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Takuya Takeishi (Univ. Tokyo)
Bost-Connes system for local fields of characteristic zero (ENGLISH)
Takuya Takeishi (Univ. Tokyo)
Bost-Connes system for local fields of characteristic zero (ENGLISH)
Number Theory Seminar
16:40-17:40 Room #002 (Graduate School of Math. Sci. Bldg.)
Yoichi Mieda (University of Tokyo)
Non-tempered A-packets and the Rapoport-Zink spaces (JAPANESE)
Yoichi Mieda (University of Tokyo)
Non-tempered A-packets and the Rapoport-Zink spaces (JAPANESE)
Mathematical Biology Seminar
14:50-16:20 Room #128 (Graduate School of Math. Sci. Bldg.)
Yukihiko Nakata (Graduate School of Mathematical Sciences, University of Tokyo)
Age-structured epidemic model with infection during transportation (JAPANESE)
Yukihiko Nakata (Graduate School of Mathematical Sciences, University of Tokyo)
Age-structured epidemic model with infection during transportation (JAPANESE)
2014/04/22
Tuesday Seminar of Analysis
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yohei Tsutsui (The University of Tokyo)
Bounded small solutions to a chemotaxis system with
non-diffusive chemical (JAPANESE)
Yohei Tsutsui (The University of Tokyo)
Bounded small solutions to a chemotaxis system with
non-diffusive chemical (JAPANESE)
[ Abstract ]
We consider a chemotaxis system with a logarithmic
sensitivity and a non-diffusive chemical substance. For some chemotactic
sensitivity constants, Ahn and Kang proved the existence of bounded
global solutions to the system. An entropy functional was used in their
argument to control the cell density by the density of the chemical
substance. Our purpose is to show the existence of bounded global
solutions for all the chemotactic sensitivity constants. Assuming the
smallness on the initial data in some sense, we can get uniform
estimates for time. These estimates are used to extend local solutions.
This talk is partially based on joint work with Yoshie Sugiyama (Kyusyu
Univ.) and Juan J. L. Vel\\'azquez (Univ. of Bonn).
We consider a chemotaxis system with a logarithmic
sensitivity and a non-diffusive chemical substance. For some chemotactic
sensitivity constants, Ahn and Kang proved the existence of bounded
global solutions to the system. An entropy functional was used in their
argument to control the cell density by the density of the chemical
substance. Our purpose is to show the existence of bounded global
solutions for all the chemotactic sensitivity constants. Assuming the
smallness on the initial data in some sense, we can get uniform
estimates for time. These estimates are used to extend local solutions.
This talk is partially based on joint work with Yoshie Sugiyama (Kyusyu
Univ.) and Juan J. L. Vel\\'azquez (Univ. of Bonn).
2014/04/21
Numerical Analysis Seminar
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Takashi Nakazawa (Tohoku University)
Shape optimization problems for time-periodic solutions of the Navier-Stokes equations (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Takashi Nakazawa (Tohoku University)
Shape optimization problems for time-periodic solutions of the Navier-Stokes equations (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Hikaru Yamamoto (The University of Tokyo)
Lagrangian mean curvature flows and some examples (JAPANESE)
Hikaru Yamamoto (The University of Tokyo)
Lagrangian mean curvature flows and some examples (JAPANESE)
2014/04/19
Harmonic Analysis Komaba Seminar
13:30-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Ryo Takada (Tohoku University) 13:30-15:00
Strichartz estimates for incompressible rotating fluids (JAPANESE)
Masami Okada (Tokyo Metropolitan Unversity) 15:30-16:30
On the interpolation of functions for scattered data on random infinite points with a sharp error estimate (JAPANESE)
Ryo Takada (Tohoku University) 13:30-15:00
Strichartz estimates for incompressible rotating fluids (JAPANESE)
Masami Okada (Tokyo Metropolitan Unversity) 15:30-16:30
On the interpolation of functions for scattered data on random infinite points with a sharp error estimate (JAPANESE)
2014/04/16
Number Theory Seminar
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Olivier Wittenberg (ENS and CNRS)
On the cycle class map for zero-cycles over local fields (ENGLISH)
Olivier Wittenberg (ENS and CNRS)
On the cycle class map for zero-cycles over local fields (ENGLISH)
[ Abstract ]
The Chow group of zero-cycles of a smooth and projective variety defined over a field k is an invariant of an arithmetic and geometric nature which is well understood only when k is a finite field (by higher-dimensional class field theory). In this talk, we will discuss the case of local and strictly local fields. We prove in particular the injectivity of the cycle class map to integral l-adic cohomology for a large class of surfaces with positive geometric genus over p-adic fields. The same statement holds for semistable K3 surfaces over C((t)), but does not hold in general for surfaces over C((t)) or over the maximal unramified extension of a p-adic field. This is a joint work with Hélène Esnault.
The Chow group of zero-cycles of a smooth and projective variety defined over a field k is an invariant of an arithmetic and geometric nature which is well understood only when k is a finite field (by higher-dimensional class field theory). In this talk, we will discuss the case of local and strictly local fields. We prove in particular the injectivity of the cycle class map to integral l-adic cohomology for a large class of surfaces with positive geometric genus over p-adic fields. The same statement holds for semistable K3 surfaces over C((t)), but does not hold in general for surfaces over C((t)) or over the maximal unramified extension of a p-adic field. This is a joint work with Hélène Esnault.
2014/04/15
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Takahito Naito (The University of Tokyo)
On the rational string operations of classifying spaces and the
Hochschild cohomology (JAPANESE)
Takahito Naito (The University of Tokyo)
On the rational string operations of classifying spaces and the
Hochschild cohomology (JAPANESE)
[ Abstract ]
Chataur and Menichi initiated the theory of string topology of
classifying spaces.
In particular, the cohomology of the free loop space of a classifying
space is endowed with a product
called the dual loop coproduct. In this talk, I will discuss the
algebraic structure and relate the rational dual loop coproduct to the
cup product on the Hochschild cohomology via the Van den Bergh isomorphism.
Chataur and Menichi initiated the theory of string topology of
classifying spaces.
In particular, the cohomology of the free loop space of a classifying
space is endowed with a product
called the dual loop coproduct. In this talk, I will discuss the
algebraic structure and relate the rational dual loop coproduct to the
cup product on the Hochschild cohomology via the Van den Bergh isomorphism.
PDE Real Analysis Seminar
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Yohei Tsutsui (The University of Tokyo)
An application of weighted Hardy spaces to the Navier-Stokes equations (JAPANESE)
Yohei Tsutsui (The University of Tokyo)
An application of weighted Hardy spaces to the Navier-Stokes equations (JAPANESE)
[ Abstract ]
The purpose of this talk is to investigate decay orders of the L^2 energy of solutions to the incompressible homogeneous Navier-Stokes equations on the whole spaces by the aid of the theory of weighted Hardy spaces. The main estimates are two weighted inequalities for heat semigroup on weighted Hardy spaces and a weighted version of the div-curl lemma due to Coifman-Lions-Meyer-Semmes. It turns out that because of the use of weighted Hardy spaces, our decay orders of the energy can be close to the critical one of Wiegner.
The purpose of this talk is to investigate decay orders of the L^2 energy of solutions to the incompressible homogeneous Navier-Stokes equations on the whole spaces by the aid of the theory of weighted Hardy spaces. The main estimates are two weighted inequalities for heat semigroup on weighted Hardy spaces and a weighted version of the div-curl lemma due to Coifman-Lions-Meyer-Semmes. It turns out that because of the use of weighted Hardy spaces, our decay orders of the energy can be close to the critical one of Wiegner.
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Shunsuke Tsuchioka (the University of Tokyo)
Toward the graded Cartan invariants of the symmetric groups (JAPANESE)
Shunsuke Tsuchioka (the University of Tokyo)
Toward the graded Cartan invariants of the symmetric groups (JAPANESE)
[ Abstract ]
We propose a graded analog of Hill's conjecture which is equivalent to K\\"ulshammer-Olsson-Robinson's conjecture on the generalized Cartan invariants of the symmetric groups.
We give justifications for it and discuss implications between the variants.
Some materials are based on the joint work with Anton Evseev.
We propose a graded analog of Hill's conjecture which is equivalent to K\\"ulshammer-Olsson-Robinson's conjecture on the generalized Cartan invariants of the symmetric groups.
We give justifications for it and discuss implications between the variants.
Some materials are based on the joint work with Anton Evseev.
2014/04/14
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Katsutoshi Yamanoi (Tokyo Institute of Technology)
Alternative proof of the geometric vrsion of Lemma on logarithmic derivatives (JAPANESE)
Katsutoshi Yamanoi (Tokyo Institute of Technology)
Alternative proof of the geometric vrsion of Lemma on logarithmic derivatives (JAPANESE)
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