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Seminar information archive
Seminar information archive ～04/23｜Today's seminar 04/24 | Future seminars 04/25～
2014/07/25
Colloquium
16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Yasuhiro Takeuchi (Aoyama Gakuin University)
Mathematical modelling of Tumor Immune System Interaction (JAPANESE)
Yasuhiro Takeuchi (Aoyama Gakuin University)
Mathematical modelling of Tumor Immune System Interaction (JAPANESE)
[ Abstract ]
We study the dynamical behavior of a tumor-immune system (T-IS) interaction model with two discrete delays,
namely the immune activation delay for effector cells (ECs) and activation delay for Helper T cells (HTCs).
By analyzing the characteristic equations, we establish the stability of two equilibria (tumor-free equilibrium and immune-control equilibrium) and the existence of Hopf bifurcations when two delays are used as the bifurcation parameter.
Our results exhibit that both delays do not affect the stability of tumor-free equilibrium.
However, they are able to destabilize the immune-control equilibrium and cause periodic solutions.
We numerically illustrate how these two delays can change the stability region of the immune-control equilibrium and display the different impacts to the control of tumors.
The numerical simulation results show that the immune activation delay for HTCs can induce heteroclinic cycles to connect the tumor-free equilibrium and immune-control equilibrium.
Furthermore, we observe that the immune activation delay for HTCs can even stabilize the unstable immune-control equilibrium.
We study the dynamical behavior of a tumor-immune system (T-IS) interaction model with two discrete delays,
namely the immune activation delay for effector cells (ECs) and activation delay for Helper T cells (HTCs).
By analyzing the characteristic equations, we establish the stability of two equilibria (tumor-free equilibrium and immune-control equilibrium) and the existence of Hopf bifurcations when two delays are used as the bifurcation parameter.
Our results exhibit that both delays do not affect the stability of tumor-free equilibrium.
However, they are able to destabilize the immune-control equilibrium and cause periodic solutions.
We numerically illustrate how these two delays can change the stability region of the immune-control equilibrium and display the different impacts to the control of tumors.
The numerical simulation results show that the immune activation delay for HTCs can induce heteroclinic cycles to connect the tumor-free equilibrium and immune-control equilibrium.
Furthermore, we observe that the immune activation delay for HTCs can even stabilize the unstable immune-control equilibrium.
thesis presentations
10:30-11:45 Room #128 (Graduate School of Math. Sci. Bldg.)
周 茂林 (東京大学大学院数理科学研究科)
On the study of front propagation in nonlinear free boundary problems(非線形自由境界問題における波面の伝播の研究) (JAPANESE)
周 茂林 (東京大学大学院数理科学研究科)
On the study of front propagation in nonlinear free boundary problems(非線形自由境界問題における波面の伝播の研究) (JAPANESE)
2014/07/24
Applied Analysis
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Nagasawa Takeyuki (Saitama University)
Decomposition of the Mobius energy (JAPANESE)
Nagasawa Takeyuki (Saitama University)
Decomposition of the Mobius energy (JAPANESE)
2014/07/23
Operator Algebra Seminars
16:30-18:00 Room #122 (Graduate School of Math. Sci. Bldg.)
George Elliott (Univ. Toronto)
The Cuntz semigroup---a critical component for classification? (ENGLISH)
George Elliott (Univ. Toronto)
The Cuntz semigroup---a critical component for classification? (ENGLISH)
Mathematical Biology Seminar
14:50-16:20 Room #128 (Graduate School of Math. Sci. Bldg.)
Naoki Masuda (University of Bristol, Department of Engineering Mathematics)
Resting-state brain networks, their energy landscapes, and sleep (JAPANESE)
Naoki Masuda (University of Bristol, Department of Engineering Mathematics)
Resting-state brain networks, their energy landscapes, and sleep (JAPANESE)
2014/07/22
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Jesse Wolfson (Northwestern University)
The Index Map and Reciprocity Laws for Contou-Carrere Symbols (ENGLISH)
Jesse Wolfson (Northwestern University)
The Index Map and Reciprocity Laws for Contou-Carrere Symbols (ENGLISH)
[ Abstract ]
In the 1960s, Atiyah and Janich constructed the families index as a natural map from the space of Fredholm operators to the classifying space of topological K-theory, and showed it to be an equivalence. In joint work with Oliver Braunling and Michael Groechenig, we construct an analogous index map in algebraic K-theory. Building on recent work of Sho Saito, we show this provides an analogue of Atiyah and Janich's equivalence. More significantly, the index map allows us to relate the Contou-Carrere symbol, a local analytic invariant of schemes, to algebraic K-theory. Using this, we provide new proofs of reciprocity laws for Contou-Carrere symbols in dimension 1 (first established by Anderson--Pablos Romo) and 2 (established recently by Osipov--Zhu). We extend these reciprocity laws to all dimensions.
In the 1960s, Atiyah and Janich constructed the families index as a natural map from the space of Fredholm operators to the classifying space of topological K-theory, and showed it to be an equivalence. In joint work with Oliver Braunling and Michael Groechenig, we construct an analogous index map in algebraic K-theory. Building on recent work of Sho Saito, we show this provides an analogue of Atiyah and Janich's equivalence. More significantly, the index map allows us to relate the Contou-Carrere symbol, a local analytic invariant of schemes, to algebraic K-theory. Using this, we provide new proofs of reciprocity laws for Contou-Carrere symbols in dimension 1 (first established by Anderson--Pablos Romo) and 2 (established recently by Osipov--Zhu). We extend these reciprocity laws to all dimensions.
2014/07/19
Monthly Seminar on Arithmetic of Automorphic Forms
13:30-16:00 Room #123 (Graduate School of Math. Sci. Bldg.)
Yoshihiro Onishi (Miejyo University) 13:30-14:30
Hurwitz integrality of the power series expansion of the sigma function at the origin (JAPANESE)
Yoshihiro Onishi (Meijyo University) 15:00-16:00
種数 3 の trigonal curve から来る Kummer 多様体の定義方程式と Coble の超平面 (JAPANESE)
Yoshihiro Onishi (Miejyo University) 13:30-14:30
Hurwitz integrality of the power series expansion of the sigma function at the origin (JAPANESE)
Yoshihiro Onishi (Meijyo University) 15:00-16:00
種数 3 の trigonal curve から来る Kummer 多様体の定義方程式と Coble の超平面 (JAPANESE)
2014/07/17
Geometry Colloquium
10:00-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Jingyi Chen (University of British Columbia)
The space of compact shrinking solutions to Lagrangian mean curvature flow in $C^2$ (ENGLISH)
Jingyi Chen (University of British Columbia)
The space of compact shrinking solutions to Lagrangian mean curvature flow in $C^2$ (ENGLISH)
[ Abstract ]
We will discuss compactness and rigidity of compact surfaces which are shrinking solutions to Lagrangian mean curvature flow. This is recent joint work with John Ma.
We will discuss compactness and rigidity of compact surfaces which are shrinking solutions to Lagrangian mean curvature flow. This is recent joint work with John Ma.
2014/07/16
Infinite Analysis Seminar Tokyo
10:30-12:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Andrei Negut (Columbia University, Department of Mathematics)
From the Hilbert scheme to m/n Pieri rules (ENGLISH)
Andrei Negut (Columbia University, Department of Mathematics)
From the Hilbert scheme to m/n Pieri rules (ENGLISH)
[ Abstract ]
In this series of talks, we will discuss several occurrences of shuffle
algebras: in representation theory, in geometry of moduli spaces, and in
the combinatorics of symmetric functions. All the connections will be
explained in detail.
In this series of talks, we will discuss several occurrences of shuffle
algebras: in representation theory, in geometry of moduli spaces, and in
the combinatorics of symmetric functions. All the connections will be
explained in detail.
2014/07/15
Infinite Analysis Seminar Tokyo
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Andrei Negut (Columbia University, Department of Mathematics)
From the shuffle algebra to the Hilbert scheme (ENGLISH)
Andrei Negut (Columbia University, Department of Mathematics)
From the shuffle algebra to the Hilbert scheme (ENGLISH)
[ Abstract ]
In this series of talks, we will discuss several occurrences of shuffle
algebras: in representation theory, in geometry of moduli spaces, and in
the combinatorics of symmetric functions. All the connections will be
explained in detail.
In this series of talks, we will discuss several occurrences of shuffle
algebras: in representation theory, in geometry of moduli spaces, and in
the combinatorics of symmetric functions. All the connections will be
explained in detail.
2014/07/14
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Gopal Prasad (University of Michigan)
Higher dimensional analogues of fake projective planes (ENGLISH)
Gopal Prasad (University of Michigan)
Higher dimensional analogues of fake projective planes (ENGLISH)
[ Abstract ]
A fake projective plane is a smooth projective complex algebraic surface which is not isomorphic to the complex projective plane but whose Betti numbers are that of the complex projective plane. The fake projective planes are algebraic surfaces of general type and have smallest possible Euler-Poincare characteristic among them. The first fake projective plane was constructed by D. Mumford using p-adic uniformization, and it was known that there can only be finitely many of them. A complete classification of the fake projective planes was obtained by Sai-Kee Yeung and myself. We showed that there are 28 classes of them, and constructed at least one explicit example in each class. Later, using long computer assisted computations, D. Cartwright and Tim Steger found that the 28 families altogether contain precisely 100 fake projective planes. Using our work, they also found a very interesting smooth projective complex algebraic surface whose Euler-Poincare characteristic is 3 but whose first Betti
number is 2. We have a natural notion of higher dimensional analogues of fake projective planes and to a large extent determined them. My talk will be devoted to an exposition of this work.
A fake projective plane is a smooth projective complex algebraic surface which is not isomorphic to the complex projective plane but whose Betti numbers are that of the complex projective plane. The fake projective planes are algebraic surfaces of general type and have smallest possible Euler-Poincare characteristic among them. The first fake projective plane was constructed by D. Mumford using p-adic uniformization, and it was known that there can only be finitely many of them. A complete classification of the fake projective planes was obtained by Sai-Kee Yeung and myself. We showed that there are 28 classes of them, and constructed at least one explicit example in each class. Later, using long computer assisted computations, D. Cartwright and Tim Steger found that the 28 families altogether contain precisely 100 fake projective planes. Using our work, they also found a very interesting smooth projective complex algebraic surface whose Euler-Poincare characteristic is 3 but whose first Betti
number is 2. We have a natural notion of higher dimensional analogues of fake projective planes and to a large extent determined them. My talk will be devoted to an exposition of this work.
2014/07/13
Infinite Analysis Seminar Tokyo
14:00-15:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Andrei Negut (Columbia University, Department of Mathematics)
From vertex operators to the shuffle algebra (ENGLISH)
Andrei Negut (Columbia University, Department of Mathematics)
From vertex operators to the shuffle algebra (ENGLISH)
[ Abstract ]
In this series of talks, we will discuss several occurrences of shuffle
algebras: in representation theory, in geometry of moduli spaces, and in
the combinatorics of symmetric functions. All the connections will be
explained in detail.
In this series of talks, we will discuss several occurrences of shuffle
algebras: in representation theory, in geometry of moduli spaces, and in
the combinatorics of symmetric functions. All the connections will be
explained in detail.
2014/07/12
Lie Groups and Representation Theory
13:20-17:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Mikhail Kapranov (Kavli IPMU) 13:20-14:20
Perverse sheaves on hyperplane arrangements (ENGLISH)
Upper global nasis, cluster algebra and simplicity of tensor products of simple modules (ENGLISH)
Branching Problems of Representations of Real Reductive Groups (ENGLISH)
Mikhail Kapranov (Kavli IPMU) 13:20-14:20
Perverse sheaves on hyperplane arrangements (ENGLISH)
[ Abstract ]
Given an arrangement of hyperplanes in $R^n$, one has the complexified arrangement in $C^n$ and the corresponding category of perverse sheaves (smooth along the strata of the natural stratification).
The talk, based in a joint work with V. Schechtman, will present an explicit description of this category in terms of data associated to the face complex of the real arrangement. Such a description suggests a possibility of categorifying the concept of a oerverse sheaf in this and possibly in more general cases.
Masaki Kashiwara (RIMS) 14:40-15:40Given an arrangement of hyperplanes in $R^n$, one has the complexified arrangement in $C^n$ and the corresponding category of perverse sheaves (smooth along the strata of the natural stratification).
The talk, based in a joint work with V. Schechtman, will present an explicit description of this category in terms of data associated to the face complex of the real arrangement. Such a description suggests a possibility of categorifying the concept of a oerverse sheaf in this and possibly in more general cases.
Upper global nasis, cluster algebra and simplicity of tensor products of simple modules (ENGLISH)
[ Abstract ]
One of the motivation of cluster algebras introduced by
Fomin and Zelevinsky is
multiplicative properties of upper global basis.
In this talk, I explain their relations, related conjectures by Besrnard Leclerc and the recent progress by the speaker with Seok-Jin Kang, Myungho Kima and Sejin Oh.
Toshiyuki Kobayashi (the University of Tokyo) 16:00-17:00One of the motivation of cluster algebras introduced by
Fomin and Zelevinsky is
multiplicative properties of upper global basis.
In this talk, I explain their relations, related conjectures by Besrnard Leclerc and the recent progress by the speaker with Seok-Jin Kang, Myungho Kima and Sejin Oh.
Branching Problems of Representations of Real Reductive Groups (ENGLISH)
[ Abstract ]
Branching problems ask how irreducible representations π of groups G "decompose" when restricted to subgroups G'.
For real reductive groups, branching problems include various important special cases, however, it is notorious that "infinite multiplicities" and "continuous spectra" may well happen in general even if (G,G') are natural pairs such as symmetric pairs.
By using analysis on (real) spherical varieties, we give a necessary and sufficient condition on the pair of reductive groups for the multiplicities to be always finite (and also to be of uniformly bounded). Further, we discuss "discretely decomposable restrictions" which allows us to apply algebraic tools in branching problems. Some classification results will be also presented.
If time permits, I will discuss some applications of branching laws of Zuckerman's derived functor modules to analysis on locally symmetric spaces with indefinite metric.
Branching problems ask how irreducible representations π of groups G "decompose" when restricted to subgroups G'.
For real reductive groups, branching problems include various important special cases, however, it is notorious that "infinite multiplicities" and "continuous spectra" may well happen in general even if (G,G') are natural pairs such as symmetric pairs.
By using analysis on (real) spherical varieties, we give a necessary and sufficient condition on the pair of reductive groups for the multiplicities to be always finite (and also to be of uniformly bounded). Further, we discuss "discretely decomposable restrictions" which allows us to apply algebraic tools in branching problems. Some classification results will be also presented.
If time permits, I will discuss some applications of branching laws of Zuckerman's derived functor modules to analysis on locally symmetric spaces with indefinite metric.
Lie Groups and Representation Theory
09:30-11:45 Room #126 (Graduate School of Math. Sci. Bldg.)
Toshio Oshima (Josai University) 09:30-10:30
Hypergeometric systems and Kac-Moody root systems (ENGLISH)
Gordan Savin (the University of Utah) 10:45-11:45
Representations of covering groups with multiplicity free K-types (ENGLISH)
Toshio Oshima (Josai University) 09:30-10:30
Hypergeometric systems and Kac-Moody root systems (ENGLISH)
Gordan Savin (the University of Utah) 10:45-11:45
Representations of covering groups with multiplicity free K-types (ENGLISH)
[ Abstract ]
Let g be a simple Lie algebra over complex numbers. McGovern has
described an ideal J in the enveloping algebra U such that U/J, considered as a g-module under the adjoint action, is a sum of all self-dual representations of g with multiplicity one. In a joint work with Loke, we prove that all (g,K)-modules annihilated by J have multiplicity free K-types, where K is defined by the Chevalley involution.
Let g be a simple Lie algebra over complex numbers. McGovern has
described an ideal J in the enveloping algebra U such that U/J, considered as a g-module under the adjoint action, is a sum of all self-dual representations of g with multiplicity one. In a joint work with Loke, we prove that all (g,K)-modules annihilated by J have multiplicity free K-types, where K is defined by the Chevalley involution.
2014/07/11
Colloquium
16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Toshiyuki Kobayashi (Graduate School of Mathematical Sciences, University of Tokyo)
Global Geometry and Analysis on Locally Symmetric Spaces with
Indefinite-metric (JAPANESE)
Toshiyuki Kobayashi (Graduate School of Mathematical Sciences, University of Tokyo)
Global Geometry and Analysis on Locally Symmetric Spaces with
Indefinite-metric (JAPANESE)
[ Abstract ]
The local to global study of geometries was a major trend of 20th
century geometry,
with remarkable developments achieved particularly in Riemannian geometry.
In contrast, in areas such as pseudo-Riemannian geometry, familiar to us
as the space-time of relativity theory, and more generally in
pseudo-Riemannian geometry of general signature, surprising little is
known about global properties of the geometry even if we impose a
locally homogeneous structure.
I plan to explain two programs:
1. (global shape) Existence problem of compact locally homogeneous spaces,
and deformation theory.
2. (spectral analysis) Construction of the spectrum of the Laplacian,
and its stability under the deformation of the geometric structure.
by taking anti-de Sitter manifolds as a typical example.
The local to global study of geometries was a major trend of 20th
century geometry,
with remarkable developments achieved particularly in Riemannian geometry.
In contrast, in areas such as pseudo-Riemannian geometry, familiar to us
as the space-time of relativity theory, and more generally in
pseudo-Riemannian geometry of general signature, surprising little is
known about global properties of the geometry even if we impose a
locally homogeneous structure.
I plan to explain two programs:
1. (global shape) Existence problem of compact locally homogeneous spaces,
and deformation theory.
2. (spectral analysis) Construction of the spectrum of the Laplacian,
and its stability under the deformation of the geometric structure.
by taking anti-de Sitter manifolds as a typical example.
FMSP Lectures
15:00-16:00 Room #270 (Graduate School of Math. Sci. Bldg.)
Oleg Emanouilov (Colorado State Univ.)
Conditional stability estimate for the Calderon's problem in two dimensional case (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Emanouilov140711.pdf
Oleg Emanouilov (Colorado State Univ.)
Conditional stability estimate for the Calderon's problem in two dimensional case (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Emanouilov140711.pdf
2014/07/08
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Ingrid Irmer (JSPS, the University of Tokyo)
The Johnson homomorphism and a family of curve graphs (ENGLISH)
Ingrid Irmer (JSPS, the University of Tokyo)
The Johnson homomorphism and a family of curve graphs (ENGLISH)
[ Abstract ]
Abstract: A family of curve graphs of an oriented surface $S_{g,1}$ will be defined on which there exists a natural orientation, coming from the orientation of subsurfaces. Distances in these graphs represent commutator lengths in $\\pi_{1}(S_{g,1})$. The displacement of vertices in the graphs under the action of the Torelli group is used to give a combinatorial description of the Johnson homomorphism."
Abstract: A family of curve graphs of an oriented surface $S_{g,1}$ will be defined on which there exists a natural orientation, coming from the orientation of subsurfaces. Distances in these graphs represent commutator lengths in $\\pi_{1}(S_{g,1})$. The displacement of vertices in the graphs under the action of the Torelli group is used to give a combinatorial description of the Johnson homomorphism."
Classical Analysis
16:00-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Nakazono Nobutaka (University of Sydney)
ABS equations arising from q-P((A2+A1)^{(1)}) (JAPANESE)
Nakazono Nobutaka (University of Sydney)
ABS equations arising from q-P((A2+A1)^{(1)}) (JAPANESE)
[ Abstract ]
The study of periodic reductions from ABS equations to discrete Painlevé equations have been investigated by many groups. However, there still remain open questions:
(i) How do we identify the discrete Painlevé equation that would result from applying a periodic reduction to an ABS equation?
(ii) Discrete Painlevé equations obtained by periodic reductions often have insufficient number of parameters. How do we obtain the general case with all essential parameters?
To solve these problems, we investigated the periodic reductions from the viewpoint of Painlevé systems.
In this talk, we show how to construct a lattice where ABS equations arise from relationships between $\\tau$ functions of Painlevé systems and explain how this lattice relates to a hyper cube associated with an ABS equation on each face.
In particular, we consider the $q$-Painlevé equations, which have the affine Weyl group symmetry of type $(A_2+A_1)^{(1)}$.
The study of periodic reductions from ABS equations to discrete Painlevé equations have been investigated by many groups. However, there still remain open questions:
(i) How do we identify the discrete Painlevé equation that would result from applying a periodic reduction to an ABS equation?
(ii) Discrete Painlevé equations obtained by periodic reductions often have insufficient number of parameters. How do we obtain the general case with all essential parameters?
To solve these problems, we investigated the periodic reductions from the viewpoint of Painlevé systems.
In this talk, we show how to construct a lattice where ABS equations arise from relationships between $\\tau$ functions of Painlevé systems and explain how this lattice relates to a hyper cube associated with an ABS equation on each face.
In particular, we consider the $q$-Painlevé equations, which have the affine Weyl group symmetry of type $(A_2+A_1)^{(1)}$.
2014/07/07
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Sho Tanimoto (Rice University)
Balanced line bundles (JAPANESE)
Sho Tanimoto (Rice University)
Balanced line bundles (JAPANESE)
[ Abstract ]
A conjecture of Batyrev and Manin relates arithmetic properties of
varieties with big anticanonical class to geometric invariants; in
particular, counting functions defined by metrized ample line bundles
and the corresponding asymptotics of rational points of bounded height
are interpreted in terms of cones of effective divisors and certain
thresholds with respect to these cones. This framework leads to the
notion of balanced line bundles, whose counting functions, conjecturally,
capture generic distributions of rational points. We investigate
balanced line bundles in the context of the Minimal Model Program, with
special regard to the classification of Fano threefolds and Mori fiber
spaces.
This is joint work with Brian Lehmann and Yuri Tschinkel.
A conjecture of Batyrev and Manin relates arithmetic properties of
varieties with big anticanonical class to geometric invariants; in
particular, counting functions defined by metrized ample line bundles
and the corresponding asymptotics of rational points of bounded height
are interpreted in terms of cones of effective divisors and certain
thresholds with respect to these cones. This framework leads to the
notion of balanced line bundles, whose counting functions, conjecturally,
capture generic distributions of rational points. We investigate
balanced line bundles in the context of the Minimal Model Program, with
special regard to the classification of Fano threefolds and Mori fiber
spaces.
This is joint work with Brian Lehmann and Yuri Tschinkel.
2014/07/03
Applied Analysis
16:00-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Kazuhiro Ishige (Tohoku University)
Parabolic power concavity and parabolic boundary value problems (JAPANESE)
Kazuhiro Ishige (Tohoku University)
Parabolic power concavity and parabolic boundary value problems (JAPANESE)
FMSP Lectures
16:00-18:00 Room #470 (Graduate School of Math. Sci. Bldg.)
Gordan Savin (Univ. of Utah)
Structure of rational orbits in prehomogeneous spaces. (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Savin.pdf
Gordan Savin (Univ. of Utah)
Structure of rational orbits in prehomogeneous spaces. (ENGLISH)
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Savin.pdf
2014/07/01
Tuesday Seminar on Topology
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Yohsuke Imagi (Kavli IPMU)
Singularities of special Lagrangian submanifolds (JAPANESE)
Yohsuke Imagi (Kavli IPMU)
Singularities of special Lagrangian submanifolds (JAPANESE)
[ Abstract ]
There are interesting invariants defined by "counting" geometric
objects, such as instantons in dimension 4 and pseudo-holomorphic curves
in symplectic manifolds. To do the counting in a sensible way, however,
we have to care about singularities of the geometric objects. Special
Lagrangian submanifolds seem very difficult to "count" as their
singularities may be very complicated. I'll talk about simple
singularities for which we can make an analogy with instantons in
dimension 4 and pseudo-holomorphic curves in symplectic manifolds. To do
it I'll use some techniques from geometric measure theory and Lagrangian
Floer theory, and the Floer-theoretic part is a joint work with Dominic
Joyce and Oliveira dos Santos.
There are interesting invariants defined by "counting" geometric
objects, such as instantons in dimension 4 and pseudo-holomorphic curves
in symplectic manifolds. To do the counting in a sensible way, however,
we have to care about singularities of the geometric objects. Special
Lagrangian submanifolds seem very difficult to "count" as their
singularities may be very complicated. I'll talk about simple
singularities for which we can make an analogy with instantons in
dimension 4 and pseudo-holomorphic curves in symplectic manifolds. To do
it I'll use some techniques from geometric measure theory and Lagrangian
Floer theory, and the Floer-theoretic part is a joint work with Dominic
Joyce and Oliveira dos Santos.
Lie Groups and Representation Theory
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Pablo Ramacher
(Marburg University)
WONDERFUL VARIETIES. REGULARIZED TRACES AND CHARACTERS (ENGLISH)
Pablo Ramacher
(Marburg University)
WONDERFUL VARIETIES. REGULARIZED TRACES AND CHARACTERS (ENGLISH)
[ Abstract ]
Let G be a connected reductive complex algebraic group with split real form $G^\\sigma$.
In this talk, we introduce a distribution character for the regular representation of $G^\\sigma$ on the real locus of a strict wonderful G-variety X, showing that on a certain open subset of $G^\\sigma$ of transversal elements it is locally integrable, and given by a sum over fixed points.
Let G be a connected reductive complex algebraic group with split real form $G^\\sigma$.
In this talk, we introduce a distribution character for the regular representation of $G^\\sigma$ on the real locus of a strict wonderful G-variety X, showing that on a certain open subset of $G^\\sigma$ of transversal elements it is locally integrable, and given by a sum over fixed points.
2014/06/30
Seminar on Geometric Complex Analysis
10:30-12:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Keiji Oguiso (Osaka University)
Primitive automorphisms of positive entropy of rational and Calabi-Yau threefolds (JAPANESE)
Keiji Oguiso (Osaka University)
Primitive automorphisms of positive entropy of rational and Calabi-Yau threefolds (JAPANESE)
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Akiyoshi Sannai (University of Tokyo)
Invariant subrings of the Cox rings of K3surfaces by automorphism groups (JAPANESE)
Akiyoshi Sannai (University of Tokyo)
Invariant subrings of the Cox rings of K3surfaces by automorphism groups (JAPANESE)
[ Abstract ]
Cox rings were introduced by D.Cox and are important rings which appeared in algebraic geometry. One of the main topic related with Cox rings is the finite generation of them. In this talk, we consider the Cox rings of K3 surfaces and answer the following question asked by D. Huybrechts; Are the invariant subrings of the Cox rings of K3 surfaces by automorphism groups finitely generated in general?
Cox rings were introduced by D.Cox and are important rings which appeared in algebraic geometry. One of the main topic related with Cox rings is the finite generation of them. In this talk, we consider the Cox rings of K3 surfaces and answer the following question asked by D. Huybrechts; Are the invariant subrings of the Cox rings of K3 surfaces by automorphism groups finitely generated in general?
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