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Seminar information archive
Seminar information archive ～04/24｜Today's seminar 04/25 | Future seminars 04/26～
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Ken-ichi YOSHIKAWA (Kyoto Univ.)
Singularities and analytic torsion (JAPANESE)
Ken-ichi YOSHIKAWA (Kyoto Univ.)
Singularities and analytic torsion (JAPANESE)
2010/05/28
Classical Analysis
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Jiro Sekiguchi (Tokyo University of Agriculture and Technology)
On solutions of uniformization equations (JAPANESE)
Jiro Sekiguchi (Tokyo University of Agriculture and Technology)
On solutions of uniformization equations (JAPANESE)
2010/05/27
Operator Algebra Seminars
16:30-18:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Catherine Oikonomides (Univ. Tokyo)
The C*-algebra of codimension one foliations which are almost without holonomy (ENGLISH)
Catherine Oikonomides (Univ. Tokyo)
The C*-algebra of codimension one foliations which are almost without holonomy (ENGLISH)
2010/05/26
Seminar on Probability and Statistics
16:20-17:30 Room #000 (Graduate School of Math. Sci. Bldg.)
FUKASAWA, Masaaki (CSFI, Osaka Univ.)
Financial data analysis with R-YUIMA (JAPANESE)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/02.html
FUKASAWA, Masaaki (CSFI, Osaka Univ.)
Financial data analysis with R-YUIMA (JAPANESE)
[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/02.html
PDE Real Analysis Seminar
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Giovanni Pisante (Department of Mathematics
Hokkaido University)
A SELECTION CRITERION FOR SOLUTIONS OF A
SYSTEM OF EIKONAL EQUATIONS
(ENGLISH)
Giovanni Pisante (Department of Mathematics
Hokkaido University)
A SELECTION CRITERION FOR SOLUTIONS OF A
SYSTEM OF EIKONAL EQUATIONS
(ENGLISH)
[ Abstract ]
We deal with the system of eikonal equations |ðu/ðx1|=1, |ðu/ðx2|=1 in a planar Lipschitz domain with zero boundary condition. Exploiting the classical pyramidal construction introduced by Cellina, it is easy to prove that there exist infinitely many Lipschitz solutions. Then, the natural problem that has arisen in this framework is to find a way to select and characterize a particular meaningful class of solutions.
We propose a variational method to select the class of solutions which minimize the discontinuity set of the gradient. More precisely we select an optimal weighted measure for the jump set of the second derivatives of a given solution v of the system and we prove the existence of minimizers of the corresponding variational problem.
We deal with the system of eikonal equations |ðu/ðx1|=1, |ðu/ðx2|=1 in a planar Lipschitz domain with zero boundary condition. Exploiting the classical pyramidal construction introduced by Cellina, it is easy to prove that there exist infinitely many Lipschitz solutions. Then, the natural problem that has arisen in this framework is to find a way to select and characterize a particular meaningful class of solutions.
We propose a variational method to select the class of solutions which minimize the discontinuity set of the gradient. More precisely we select an optimal weighted measure for the jump set of the second derivatives of a given solution v of the system and we prove the existence of minimizers of the corresponding variational problem.
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Keisuke Matsuya (University of Tokyo)
Existence and non-existence of global solutions for a discrete semilinear heat equation (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Keisuke Matsuya (University of Tokyo)
Existence and non-existence of global solutions for a discrete semilinear heat equation (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
GCOE Seminars
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
松家 敬介 (東京大学大学院数理科学研究科)
Existence and non-existence of global solutions for a discrete semilinear heat equation (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
松家 敬介 (東京大学大学院数理科学研究科)
Existence and non-existence of global solutions for a discrete semilinear heat equation (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
2010/05/25
Lie Groups and Representation Theory
17:00-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Kaoru Hiraga (Kyoto University)
On endoscopy, packets, and invariants (JAPANESE)
Kaoru Hiraga (Kyoto University)
On endoscopy, packets, and invariants (JAPANESE)
[ Abstract ]
The theory of endoscopy came out of the Langlands functoriality and the trace formula.
In this talk, I will briefly explain what the endoscopy is, and talk about packet, formal degree and Whittaker normalization of transfer.
I would like to talk about the connection between these topics and the endoscopy.
The theory of endoscopy came out of the Langlands functoriality and the trace formula.
In this talk, I will briefly explain what the endoscopy is, and talk about packet, formal degree and Whittaker normalization of transfer.
I would like to talk about the connection between these topics and the endoscopy.
2010/05/24
Algebraic Geometry Seminar
16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)
Hokuto Uehara (Tokyo Metropolitan University)
A counterexample of the birational Torelli problem via Fourier--Mukai transforms (JAPANESE)
Hokuto Uehara (Tokyo Metropolitan University)
A counterexample of the birational Torelli problem via Fourier--Mukai transforms (JAPANESE)
[ Abstract ]
We study the Fourier--Mukai numbers of rational elliptic surfaces. As
its application, we give an example of a pair of minimal 3-folds $X$
with Kodaira dimensions 1, $h^1(O_X)=h^2(O_X)=0$ such that they are
mutually derived equivalent, deformation equivalent, but not
birationally equivalent. It also supplies a counterexample of the
birational Torelli problem.
We study the Fourier--Mukai numbers of rational elliptic surfaces. As
its application, we give an example of a pair of minimal 3-folds $X$
with Kodaira dimensions 1, $h^1(O_X)=h^2(O_X)=0$ such that they are
mutually derived equivalent, deformation equivalent, but not
birationally equivalent. It also supplies a counterexample of the
birational Torelli problem.
2010/05/19
Seminar on Mathematics for various disciplines
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Hiroshi Suito (Okayama University)
Mathematical sciences collaborating with clinical medicine (JAPANESE)
Hiroshi Suito (Okayama University)
Mathematical sciences collaborating with clinical medicine (JAPANESE)
Seminar on Probability and Statistics
15:00-16:10 Room #002 (Graduate School of Math. Sci. Bldg.)
YOSHIDA, Nakahiro (University of Tokyo)
Estimation of the variance-covariance structure for stochastic processes and applications of YUIMA (JAPANESE)
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/01.html
YOSHIDA, Nakahiro (University of Tokyo)
Estimation of the variance-covariance structure for stochastic processes and applications of YUIMA (JAPANESE)
[ Abstract ]
We discuss limit theorems and asymptotic expansions in estimation of the variance-covariance structure for Ito processes. We will show some numerical examples by YUIMA, a package for statistical analysis and simulation of stochastic differential equations.
[ Reference URL ]We discuss limit theorems and asymptotic expansions in estimation of the variance-covariance structure for Ito processes. We will show some numerical examples by YUIMA, a package for statistical analysis and simulation of stochastic differential equations.
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2010/01.html
2010/05/18
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Naoyuki Monden (Osaka University)
On roots of Dehn twists (JAPANESE)
Naoyuki Monden (Osaka University)
On roots of Dehn twists (JAPANESE)
[ Abstract ]
Let $t_{c}$ be the Dehn twist about a nonseparating simple closed curve
$c$ in a closed orientable surface. If a mapping class $f$ satisfies
$t_{c}=f^{n}$ in mapping class group, we call $f$ a root of $t_{c}$ of
degree $n$. In 2009, Margalit and Schleimer constructed roots of $t_{c}$.
In this talk, I will explain the data set which determine a root of
$t_{c}$ up to conjugacy. Moreover, I will explain the minimal and the
maximal degree.
Let $t_{c}$ be the Dehn twist about a nonseparating simple closed curve
$c$ in a closed orientable surface. If a mapping class $f$ satisfies
$t_{c}=f^{n}$ in mapping class group, we call $f$ a root of $t_{c}$ of
degree $n$. In 2009, Margalit and Schleimer constructed roots of $t_{c}$.
In this talk, I will explain the data set which determine a root of
$t_{c}$ up to conjugacy. Moreover, I will explain the minimal and the
maximal degree.
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
B. Speh (Cornel University)
On the eigenvalues of the Laplacian on locally symmetric hyperbolic spaces (ENGLISH)
B. Speh (Cornel University)
On the eigenvalues of the Laplacian on locally symmetric hyperbolic spaces (ENGLISH)
[ Abstract ]
A famous Theorem of Selberg says that the non-zero eigenvalues of the Laplacian acting on functions on quotients of the upper half plane H by congruence subgroups of the integral modular group, are bounded away from zero, as the congruence subgroup varies. Analogous questions on Laplacians acting on differential forms of higher degree on locally symmetric spaces (functions may be thought of as differential forms of degree zero) have geometric implications for the cohomology of the locally symmetric space.
Let $X$ be the real hyperbolic n-space and $\\Gamma \\subset $ SO(n, 1) a congruence arithmetic subgroup. Bergeron conjectured that the eigenvalues of the Laplacian acting on the differential forms on $ X / \\Gamma $ are bounded from the below by a constant independent of the congruence subgroup. In the lecture I will show how one can use representation theory to show that this conjecture is true provided that it is true in the middle degree.
This is joint work with T.N. Venkataramana
A famous Theorem of Selberg says that the non-zero eigenvalues of the Laplacian acting on functions on quotients of the upper half plane H by congruence subgroups of the integral modular group, are bounded away from zero, as the congruence subgroup varies. Analogous questions on Laplacians acting on differential forms of higher degree on locally symmetric spaces (functions may be thought of as differential forms of degree zero) have geometric implications for the cohomology of the locally symmetric space.
Let $X$ be the real hyperbolic n-space and $\\Gamma \\subset $ SO(n, 1) a congruence arithmetic subgroup. Bergeron conjectured that the eigenvalues of the Laplacian acting on the differential forms on $ X / \\Gamma $ are bounded from the below by a constant independent of the congruence subgroup. In the lecture I will show how one can use representation theory to show that this conjecture is true provided that it is true in the middle degree.
This is joint work with T.N. Venkataramana
2010/05/17
Algebraic Geometry Seminar
16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)
Yuji Odaka (Research Institute for Mathematical Sciences)
On the GIT stability of Polarized Varieties (JAPANESE)
Yuji Odaka (Research Institute for Mathematical Sciences)
On the GIT stability of Polarized Varieties (JAPANESE)
[ Abstract ]
Background:
Original GIT-stability notion for polarized variety is
"asymptotic stability", studied by Mumford, Gieseker etc around 1970s.
Recently a version appeared, so-called "K-stability", introduced by
Tian(1997) and reformulated by Donaldson(2002), by the way of seeking
the analogue of Kobayashi-Hitchin correspondence, which gives
"differential geometric" interpretation of "stability". These two have
subtle but interesting differences in dimension higher than 1.
Contents:
(1*) Any semistable (in any sense) polarized variety should have only
"semi-log-canonical" singularities. (Partly observed around 1970s)
(2) On the other hand, we proved some stabilities, which corresponds to
"Calabi conjecture", also with admitting mild singularities.
As applications these yield
(3*) Compact moduli spaces with GIT interpretations.
(4) Many counterexamples (as orbifolds) to folklore conjecture:
"K-stability implies asymptotic stability".
(*: Some technical points are yet to be settled.
Some parts for (1)(2) are available on arXiv:0910.1794.)
Background:
Original GIT-stability notion for polarized variety is
"asymptotic stability", studied by Mumford, Gieseker etc around 1970s.
Recently a version appeared, so-called "K-stability", introduced by
Tian(1997) and reformulated by Donaldson(2002), by the way of seeking
the analogue of Kobayashi-Hitchin correspondence, which gives
"differential geometric" interpretation of "stability". These two have
subtle but interesting differences in dimension higher than 1.
Contents:
(1*) Any semistable (in any sense) polarized variety should have only
"semi-log-canonical" singularities. (Partly observed around 1970s)
(2) On the other hand, we proved some stabilities, which corresponds to
"Calabi conjecture", also with admitting mild singularities.
As applications these yield
(3*) Compact moduli spaces with GIT interpretations.
(4) Many counterexamples (as orbifolds) to folklore conjecture:
"K-stability implies asymptotic stability".
(*: Some technical points are yet to be settled.
Some parts for (1)(2) are available on arXiv:0910.1794.)
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Masaharu TANABE (Tokyo Inst. Tech.)
On the norm defined on the holomorphic maps of compact Riemann surfaces (JAPANESE)
Masaharu TANABE (Tokyo Inst. Tech.)
On the norm defined on the holomorphic maps of compact Riemann surfaces (JAPANESE)
2010/05/15
Monthly Seminar on Arithmetic of Automorphic Forms
13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)
NARITA, Hiroaki (Kumamoto University, Fac. of Science) 13:30-14:30
Strict positivity of the central values of some Rankin-Selberg
L-functions (JAPANESE)
Calabi-Yau manifolds associated to hypergeometric sheaves and their application
Osaka Pref. Univ. (JAPANESE)
NARITA, Hiroaki (Kumamoto University, Fac. of Science) 13:30-14:30
Strict positivity of the central values of some Rankin-Selberg
L-functions (JAPANESE)
[ Abstract ]
We consider the Arakawa lift which is an automprphic form on an inner twist of $GSp(2)$. We construct examples the case when the central values of the $L$-functions of Rankin-Selberg type with degree 8 Euler factors take positive values. ....
YAMAUCHI, Takuya (Osaka Pref. Univ. ) 15:00-16:00We consider the Arakawa lift which is an automprphic form on an inner twist of $GSp(2)$. We construct examples the case when the central values of the $L$-functions of Rankin-Selberg type with degree 8 Euler factors take positive values. ....
Calabi-Yau manifolds associated to hypergeometric sheaves and their application
Osaka Pref. Univ. (JAPANESE)
[ Abstract ]
Let U be the P_1 munus 3 points, and form hypergeometric sheaves on U, by iterative convolutions of certain local sysytem of rank 1 on U. We construct certain families of Calabi-Yau manifolds whose cohomology groups of middle degree are these hypergeometric sheaves. We discuss the potential-modularity of these varieties and unit root formula. This is a joint work with Michio Tsuzuki. (trans. by the organizer of the seminar)
Let U be the P_1 munus 3 points, and form hypergeometric sheaves on U, by iterative convolutions of certain local sysytem of rank 1 on U. We construct certain families of Calabi-Yau manifolds whose cohomology groups of middle degree are these hypergeometric sheaves. We discuss the potential-modularity of these varieties and unit root formula. This is a joint work with Michio Tsuzuki. (trans. by the organizer of the seminar)
2010/05/12
Lectures
15:30-17:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Luc Illusie (東京大学/Paris南大学)
Independence of families of $\\ell$-adic representations and uniform constructibility (ENGLISH)
Luc Illusie (東京大学/Paris南大学)
Independence of families of $\\ell$-adic representations and uniform constructibility (ENGLISH)
[ Abstract ]
Let $k$ be a number field, $\\overline{k}$ an algebraic closure of $k$, $\\Gamma_k = \\mathrm{Gal}(\\overline{k}/k)$. A family of continuous homomorphisms $\\rho_{\\ell} : \\Gamma_k \\rightarrow G_{\\ell}$, indexed by prime numbers $\\ell$, where $G_{\\ell}$ is a locally compact $\\ell$-adic Lie group, is said to be independent if $\\rho(\\Gamma_k) = \\prod \\rho_{\\ell}(\\Gamma_k)$, where $\\rho = (\\rho_{\\ell}) : \\Gamma_k \\rightarrow \\prod G_{\\ell}$. Serre gave a criterion for such a family to become independent after a finite extension of $k$. We will explain Serre's criterion and show that it applies to families coming from the $\\ell$-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over $k$. This application uses a variant of Deligne's generic constructibility theorem with uniformity in $\\ell$.
Let $k$ be a number field, $\\overline{k}$ an algebraic closure of $k$, $\\Gamma_k = \\mathrm{Gal}(\\overline{k}/k)$. A family of continuous homomorphisms $\\rho_{\\ell} : \\Gamma_k \\rightarrow G_{\\ell}$, indexed by prime numbers $\\ell$, where $G_{\\ell}$ is a locally compact $\\ell$-adic Lie group, is said to be independent if $\\rho(\\Gamma_k) = \\prod \\rho_{\\ell}(\\Gamma_k)$, where $\\rho = (\\rho_{\\ell}) : \\Gamma_k \\rightarrow \\prod G_{\\ell}$. Serre gave a criterion for such a family to become independent after a finite extension of $k$. We will explain Serre's criterion and show that it applies to families coming from the $\\ell$-adic cohomology (or cohomology with compact support) of schemes separated and of finite type over $k$. This application uses a variant of Deligne's generic constructibility theorem with uniformity in $\\ell$.
Number Theory Seminar
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Makoto Matsumoto (University of Tokyo)
Differences between
Galois representations in outer-automorphisms
of the fundamental groups and those in automorphisms, implied by
topology of moduli spaces (ENGLISH)
Makoto Matsumoto (University of Tokyo)
Differences between
Galois representations in outer-automorphisms
of the fundamental groups and those in automorphisms, implied by
topology of moduli spaces (ENGLISH)
[ Abstract ]
Fix a prime l. Let C be a proper smooth geometrically connected curve over a number field K, and x be its closed point. Let Π denote the pro-l completion of the geometric fundamental group of C with geometric base point over x. We have two non-abelian Galois representations:
ρA : Galk(x) → Aut(Π),ρO : GalK → Out(Π).
Our question is: in the natural inclusion Ker(ρA) ⊂ Ker(ρO) ∩ Galk(x), whether the equality holds or not. Theorem: Assume that g ≥ 3, l divides 2g -2. Then, there are infinitely many pairs (C, K) with the following property. If l does not divide the extension degree [k(x): K], then Ker(ρA) = (Ker(ρO) ∩ Galk(x)) holds.
This is in contrast to the case of the projective line minus three points and its canonical tangential base points, where the equality holds (a result of Deligne and Ihara).
There are two ingredients in the proof: (1) Galois representations often contain the image of the geometric monodromy (namely, the mapping class group) [M-Tamagawa 2000] (2) A topological result [S. Morita 98] [Hain-Reed 2000] on the cohomological obstruction of lifting the outer action of the mapping class group to automorphisms.
(This lecture is held as `Arithmetic Geometry Seminar Tokyo-Paris' and it is transmitted to IHES by the internet.)
Fix a prime l. Let C be a proper smooth geometrically connected curve over a number field K, and x be its closed point. Let Π denote the pro-l completion of the geometric fundamental group of C with geometric base point over x. We have two non-abelian Galois representations:
ρA : Galk(x) → Aut(Π),ρO : GalK → Out(Π).
Our question is: in the natural inclusion Ker(ρA) ⊂ Ker(ρO) ∩ Galk(x), whether the equality holds or not. Theorem: Assume that g ≥ 3, l divides 2g -2. Then, there are infinitely many pairs (C, K) with the following property. If l does not divide the extension degree [k(x): K], then Ker(ρA) = (Ker(ρO) ∩ Galk(x)) holds.
This is in contrast to the case of the projective line minus three points and its canonical tangential base points, where the equality holds (a result of Deligne and Ihara).
There are two ingredients in the proof: (1) Galois representations often contain the image of the geometric monodromy (namely, the mapping class group) [M-Tamagawa 2000] (2) A topological result [S. Morita 98] [Hain-Reed 2000] on the cohomological obstruction of lifting the outer action of the mapping class group to automorphisms.
(This lecture is held as `Arithmetic Geometry Seminar Tokyo-Paris' and it is transmitted to IHES by the internet.)
PDE Real Analysis Seminar
10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Jean-Pierre Puel (Graduate School of Mathematical Sciences
The University of Tokyo)
Exact controllability for incompressible fluids (ENGLISH)
Jean-Pierre Puel (Graduate School of Mathematical Sciences
The University of Tokyo)
Exact controllability for incompressible fluids (ENGLISH)
[ Abstract ]
After a short presentation of J.-M. Coron's results for Euler equation, we will give the good notions of controllability for Navier-Stokes equations, namely the exact controllability to trajectories.
We will outline the strategy for obtaining local results, based on a fixed point argument following the study of null controllability for the linearized problem. This is equivalent to an observability inequality for the adjoint system, which requires a global Carleman estimate for linearized Navier-Stokes equations. We will explain this estimate and the different steps for obtaining it along the lines of the articles by E.Fernadez-Cara, S.Guerrero, O.Imanuvilov and J.-P.Puel (JMPA, 2004) and M.Gonzalez-Burgos, S.Guerrero and J.-P.Puel (CPAA, 2009).
We will end up with some important open problems.
After a short presentation of J.-M. Coron's results for Euler equation, we will give the good notions of controllability for Navier-Stokes equations, namely the exact controllability to trajectories.
We will outline the strategy for obtaining local results, based on a fixed point argument following the study of null controllability for the linearized problem. This is equivalent to an observability inequality for the adjoint system, which requires a global Carleman estimate for linearized Navier-Stokes equations. We will explain this estimate and the different steps for obtaining it along the lines of the articles by E.Fernadez-Cara, S.Guerrero, O.Imanuvilov and J.-P.Puel (JMPA, 2004) and M.Gonzalez-Burgos, S.Guerrero and J.-P.Puel (CPAA, 2009).
We will end up with some important open problems.
Numerical Analysis Seminar
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Takeshi Ogita (Tokyo Woman's Christian University)
Accurate factorizations of ill-conditioned matrices and applications (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
Takeshi Ogita (Tokyo Woman's Christian University)
Accurate factorizations of ill-conditioned matrices and applications (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
GCOE Seminars
16:30-18:00 Room #002 (Graduate School of Math. Sci. Bldg.)
荻田 武史 (東京女子大学現代教養学部)
悪条件行列の高精度な分解法とその応用 (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
荻田 武史 (東京女子大学現代教養学部)
悪条件行列の高精度な分解法とその応用 (JAPANESE)
[ Reference URL ]
http://www.infsup.jp/utnas/
2010/05/11
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Nariya Kawazumi (The University of Tokyo)
The logarithms of Dehn twists (JAPANESE)
Nariya Kawazumi (The University of Tokyo)
The logarithms of Dehn twists (JAPANESE)
[ Abstract ]
We establish an explicit formula for the action of (non-separating and
separating) Dehn twists on the complete group ring of the fundamental group of a
surface. It generalizes the classical transvection formula on the first homology.
The proof is involved with a homological interpretation of the Goldman
Lie algebra. This talk is based on a jointwork with Yusuke Kuno (Hiroshima U./JSPS).
We establish an explicit formula for the action of (non-separating and
separating) Dehn twists on the complete group ring of the fundamental group of a
surface. It generalizes the classical transvection formula on the first homology.
The proof is involved with a homological interpretation of the Goldman
Lie algebra. This talk is based on a jointwork with Yusuke Kuno (Hiroshima U./JSPS).
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Hisayosi Matumoto (the University of Tokyo)
On a finite $W$-algebra module structure on the space of
continuous Whittaker vectors for an irreducible Harish-Chandra module (ENGLISH)
Hisayosi Matumoto (the University of Tokyo)
On a finite $W$-algebra module structure on the space of
continuous Whittaker vectors for an irreducible Harish-Chandra module (ENGLISH)
[ Abstract ]
Let $G$ be a real reductive Lie group. The space of continuous Whittaker vectors for an irreducible Harish-Chandra module has a structure of a module over a finite $W$-algebra. We have seen such modules are irreducible for groups of type A. However, there is a counterexample to the naive conjecture. We discuss a refined version of the conjecture and further examples in this talk.
Let $G$ be a real reductive Lie group. The space of continuous Whittaker vectors for an irreducible Harish-Chandra module has a structure of a module over a finite $W$-algebra. We have seen such modules are irreducible for groups of type A. However, there is a counterexample to the naive conjecture. We discuss a refined version of the conjecture and further examples in this talk.
2010/05/10
Algebraic Geometry Seminar
16:40-18:10 Room #126 (Graduate School of Math. Sci. Bldg.)
Makoto Miura
(The University of Tokyo)
Toric degenerations of Grassmannians and mirror symmetry (JAPANESE)
Makoto Miura
(The University of Tokyo)
Toric degenerations of Grassmannians and mirror symmetry (JAPANESE)
[ Abstract ]
I will talk about toric degenerarions of Grassmannians and
an application to the mirror constructions for complete intersection
Calabi-Yau manifolds in Grassmannians.
In particular, if we focus on toric degenerations by term orderings on
polynomial rings,
we have to choose a term ordering for which the coordinate ring has an
uniformly homogeneous sagbi basis.
We discuss this condition for some examples of ordinary Grassmannians
and a spinor variety.
I will talk about toric degenerarions of Grassmannians and
an application to the mirror constructions for complete intersection
Calabi-Yau manifolds in Grassmannians.
In particular, if we focus on toric degenerations by term orderings on
polynomial rings,
we have to choose a term ordering for which the coordinate ring has an
uniformly homogeneous sagbi basis.
We discuss this condition for some examples of ordinary Grassmannians
and a spinor variety.
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yoshihiko MATSUMOTO (Univ. of Tokyo)
Asymptotics of ACH-Einstein metrics, and an invariant tensor of partially-integrable almost CR manifolds (JAPANESE)
Yoshihiko MATSUMOTO (Univ. of Tokyo)
Asymptotics of ACH-Einstein metrics, and an invariant tensor of partially-integrable almost CR manifolds (JAPANESE)
[ Abstract ]
To investigate strictly pseudoconvex partially-integrable almost CR manifolds as boundaries at infinity of noncompact complete Riemannian spaces, we study the Einstein equation for ACH metrics. At the jet level (of a certain order that depends only on the dimension) along the boundary, a solution uniquely exists up to the action of boundary-preserving diffeomorphisms. If we further consider higher-order solutions, without logarithmic singularities, in general we encounter an obstruction for construction, which is a local invariant tensor of the boundary. Some properties of that invariant tensor are also mentioned.
To investigate strictly pseudoconvex partially-integrable almost CR manifolds as boundaries at infinity of noncompact complete Riemannian spaces, we study the Einstein equation for ACH metrics. At the jet level (of a certain order that depends only on the dimension) along the boundary, a solution uniquely exists up to the action of boundary-preserving diffeomorphisms. If we further consider higher-order solutions, without logarithmic singularities, in general we encounter an obstruction for construction, which is a local invariant tensor of the boundary. Some properties of that invariant tensor are also mentioned.
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