Text only print
Full screen print
Seminar information archive
Seminar information archive ～04/25｜Today's seminar 04/26 | Future seminars 04/27～
Discrete mathematical modelling seminar
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Anton Dzhamay (University of Northern Colorado)
Gap Probabilities and discrete Painlevé equations
Anton Dzhamay (University of Northern Colorado)
Gap Probabilities and discrete Painlevé equations
[ Abstract ]
It is well-known that important statistical quantities, such as gap probabilities, in various discrete probabilistic models of random matrix type satisfy the so-called discrete Painlevé equations, which provides an effective way to computing them. In this talk we discuss this correspondence for a particular class of models, known as boxed plane partitions (equivalently, lozenge tilings of a hexagon). For uniform probability distribution, this is one of the most studied models of random surfaces. Borodin, Gorin, and Rains showed that it is possible to assign a very general elliptic weight to the distribution, with various degenerations of this weight corresponding to the degeneration cascade of discrete polynomial ensembles, such as Racah and Hahn ensembles and their q-analogues. This also correspond to the degeneration scheme of discrete Painlevé equations, due to Sakai. In this talk we consider the q-Hahn and q-Racah ensembles and corresponding discrete Painlevé equations of types q-P(A_{2}^{(1)}) and q-P(A_{1}^{(1)}).
This is joint work with Alisa Knizel (Columbia University)
It is well-known that important statistical quantities, such as gap probabilities, in various discrete probabilistic models of random matrix type satisfy the so-called discrete Painlevé equations, which provides an effective way to computing them. In this talk we discuss this correspondence for a particular class of models, known as boxed plane partitions (equivalently, lozenge tilings of a hexagon). For uniform probability distribution, this is one of the most studied models of random surfaces. Borodin, Gorin, and Rains showed that it is possible to assign a very general elliptic weight to the distribution, with various degenerations of this weight corresponding to the degeneration cascade of discrete polynomial ensembles, such as Racah and Hahn ensembles and their q-analogues. This also correspond to the degeneration scheme of discrete Painlevé equations, due to Sakai. In this talk we consider the q-Hahn and q-Racah ensembles and corresponding discrete Painlevé equations of types q-P(A_{2}^{(1)}) and q-P(A_{1}^{(1)}).
This is joint work with Alisa Knizel (Columbia University)
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Stephen McKeown (Princeton University)
Cornered Asymptotically Hyperbolic Spaces
Stephen McKeown (Princeton University)
Cornered Asymptotically Hyperbolic Spaces
[ Abstract ]
This talk will concern cornered asymptotically hyperbolic spaces, which have a finite boundary in addition to the usual infinite boundary. I will first describe the construction a normal form near the corner for these spaces. Then I will discuss formal existence and uniqueness, near the corner, of asymptotically hyperbolic Einstein metrics, with a CMC-umbilic condition imposed on the finite boundary. This is analogous to the Fefferman-Graham construction for the ordinary, non-cornered setting. Finally, I will present work in progress regarding scattering on such spaces.
This talk will concern cornered asymptotically hyperbolic spaces, which have a finite boundary in addition to the usual infinite boundary. I will first describe the construction a normal form near the corner for these spaces. Then I will discuss formal existence and uniqueness, near the corner, of asymptotically hyperbolic Einstein metrics, with a CMC-umbilic condition imposed on the finite boundary. This is analogous to the Fefferman-Graham construction for the ordinary, non-cornered setting. Finally, I will present work in progress regarding scattering on such spaces.
2018/06/22
Lectures
16:00-17:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Michael Harrison (Lehigh University)
Fibrations of R^3 by oriented lines
Michael Harrison (Lehigh University)
Fibrations of R^3 by oriented lines
[ Abstract ]
Is it possible to cover 3-dimensional space by a collection of lines, such that no two lines intersect and no two lines are parallel? More precisely, does there exist a fibration of R^3 by pairwise skew lines? We give some examples and provide a complete topological classification of such objects, by exhibiting a deformation retract from the space of skew fibrations of R^3 to its subspace of Hopf fibrations. As a corollary of the proof we obtain Gluck and Warner's classification of great circle fibrations of S^3. We continue with some recent results regarding contact structures on R^3 which are naturally induced by skew fibrations. Finally, we discuss fibrations of R^3 which may contain parallel fibers, and discuss when such objects induce contact structures.
Is it possible to cover 3-dimensional space by a collection of lines, such that no two lines intersect and no two lines are parallel? More precisely, does there exist a fibration of R^3 by pairwise skew lines? We give some examples and provide a complete topological classification of such objects, by exhibiting a deformation retract from the space of skew fibrations of R^3 to its subspace of Hopf fibrations. As a corollary of the proof we obtain Gluck and Warner's classification of great circle fibrations of S^3. We continue with some recent results regarding contact structures on R^3 which are naturally induced by skew fibrations. Finally, we discuss fibrations of R^3 which may contain parallel fibers, and discuss when such objects induce contact structures.
2018/06/20
Number Theory Seminar
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Ippei Nagamachi (University of Tokyo)
Criteria for good reduction of hyperbolic polycurves (JAPANESE)
Ippei Nagamachi (University of Tokyo)
Criteria for good reduction of hyperbolic polycurves (JAPANESE)
[ Abstract ]
We give good reduction criteria for hyperbolic polycurves, i.e., successive extensions of families of curves, under mild assumption. These criteria are higher dimensional versions of the good reduction criterion for hyperbolic curves given by Oda and Tamagawa. In this talk, we construct homotopy exact sequences by using intermediate quotient groups of geometric etale fundamental groups of hyperbolic polycurves.
We give good reduction criteria for hyperbolic polycurves, i.e., successive extensions of families of curves, under mild assumption. These criteria are higher dimensional versions of the good reduction criterion for hyperbolic curves given by Oda and Tamagawa. In this talk, we construct homotopy exact sequences by using intermediate quotient groups of geometric etale fundamental groups of hyperbolic polycurves.
2018/06/19
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Yasuhiro Wakabayashi (TIT)
Dormant Miura opers and Tango structures (Japanese (writing in English))
Yasuhiro Wakabayashi (TIT)
Dormant Miura opers and Tango structures (Japanese (writing in English))
[ Abstract ]
Only Japanese abstract is available.
Only Japanese abstract is available.
Tuesday Seminar of Analysis
16:50-18:20 Room #128 (Graduate School of Math. Sci. Bldg.)
Rowan Killip (UCLA)
KdV is wellposed in $H^{-1}$ (English)
Rowan Killip (UCLA)
KdV is wellposed in $H^{-1}$ (English)
Numerical Analysis Seminar
16:50-18:20 Room #002 (Graduate School of Math. Sci. Bldg.)
Shuji Yoshikawa (Oita University)
Small data global existence for the semi-discrete scheme of a model system of hyperbolic balance laws (Japanese)
Shuji Yoshikawa (Oita University)
Small data global existence for the semi-discrete scheme of a model system of hyperbolic balance laws (Japanese)
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Hokuto Konno (The University of Tokyo)
Characteristic classes via 4-dimensional gauge theory (JAPANESE)
Hokuto Konno (The University of Tokyo)
Characteristic classes via 4-dimensional gauge theory (JAPANESE)
[ Abstract ]
Using gauge theory, more precisely SO(3)-Yang-Mills theory and Seiberg-Witten theory, I will construct characteristic classes of 4-manifold bundles. These characteristic classes are extensions of the SO(3)-Donaldson invariant and the Seiberg-Witten invariant to families of 4-manifolds, and can detect non-triviality of smooth 4-manifold bundles. The basic idea of the construction of these characteristic classes is to consider an infinite dimensional analogue of classical characteristic classes of manifold bundles, typified by the Mumford-Morita-Miller classes for surface bundles.
Using gauge theory, more precisely SO(3)-Yang-Mills theory and Seiberg-Witten theory, I will construct characteristic classes of 4-manifold bundles. These characteristic classes are extensions of the SO(3)-Donaldson invariant and the Seiberg-Witten invariant to families of 4-manifolds, and can detect non-triviality of smooth 4-manifold bundles. The basic idea of the construction of these characteristic classes is to consider an infinite dimensional analogue of classical characteristic classes of manifold bundles, typified by the Mumford-Morita-Miller classes for surface bundles.
Tuesday Seminar on Topology
14:30-16:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Kenji Fukaya (Simons center, SUNY)
Relative and equivariant Lagrangian Floer homology and Atiyah-Floer conjecture (JAPANESE)
Kenji Fukaya (Simons center, SUNY)
Relative and equivariant Lagrangian Floer homology and Atiyah-Floer conjecture (JAPANESE)
[ Abstract ]
Atiyah-Floer conjecture concerns a relationship between Floer homology in Gauge theory and Lagrangian Floer homology. One of its difficulty is that the symplectic manifold on wich we consider Lagrangian Floer homology is in general singular. In this talk I will explain that, by using relative and equivariant version of Lagrangian Floer homology, we can resolve this problem and can at least state the conjecture as rigorous mathematical conjecture.
Atiyah-Floer conjecture concerns a relationship between Floer homology in Gauge theory and Lagrangian Floer homology. One of its difficulty is that the symplectic manifold on wich we consider Lagrangian Floer homology is in general singular. In this talk I will explain that, by using relative and equivariant version of Lagrangian Floer homology, we can resolve this problem and can at least state the conjecture as rigorous mathematical conjecture.
2018/06/18
Tokyo Probability Seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Hideki TANEMURA (Department of Mathematics, Keio University)
(JAPANESE)
Hideki TANEMURA (Department of Mathematics, Keio University)
(JAPANESE)
Operator Algebra Seminars
16:45-18:15 Room #122 (Graduate School of Math. Sci. Bldg.)
Ryszard Nest (Copenhagen Univ.)
Equivariant index theorem (English)
Ryszard Nest (Copenhagen Univ.)
Equivariant index theorem (English)
2018/06/13
Operator Algebra Seminars
16:45-18:15 Room #126 (Graduate School of Math. Sci. Bldg.)
Ryokichi Tanaka (Tohoku Univ.)
Poisson boundary for the discrete affine group (English)
Ryokichi Tanaka (Tohoku Univ.)
Poisson boundary for the discrete affine group (English)
2018/06/12
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Takahiro Shibata (Kyoto)
Ample canonical heights for endomorphisms on projective varieties (English or Japanese)
Takahiro Shibata (Kyoto)
Ample canonical heights for endomorphisms on projective varieties (English or Japanese)
[ Abstract ]
Given a smooth projective variety on a number field and an
endomorphism on it, we would like to know how the height of a point
grows by iteration of the action of the endomorphism. When the
endomorphism is polarized, Call and Silverman construct the canonical
height, which is an important tool for the calculation of growth of
heights. In this talk, we will give a generalization of the Call-
Silverman canonical heights for not necessarily polarized endomorphisms,
ample canonical heights, and propose an analogue of the Northcott
finiteness theorem as a conjecture. We will see that the conjecture
holds when the variety is an abelian variety or a surface.
Given a smooth projective variety on a number field and an
endomorphism on it, we would like to know how the height of a point
grows by iteration of the action of the endomorphism. When the
endomorphism is polarized, Call and Silverman construct the canonical
height, which is an important tool for the calculation of growth of
heights. In this talk, we will give a generalization of the Call-
Silverman canonical heights for not necessarily polarized endomorphisms,
ample canonical heights, and propose an analogue of the Northcott
finiteness theorem as a conjecture. We will see that the conjecture
holds when the variety is an abelian variety or a surface.
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Yoshihiko Mitsumatsu (Chuo University)
Turbulization of 2-dimensional foliations on 4-manifolds (JAPANESE)
Yoshihiko Mitsumatsu (Chuo University)
Turbulization of 2-dimensional foliations on 4-manifolds (JAPANESE)
[ Abstract ]
This is a report on a joint work with Elmar VOGT(Freie Universität Berlin). For codimension 1 foliations, the process of turbulization, i.e., inserting a Reeb component along a closed transversal, is well-known, while for higher codimensional foliation, similar processes were not understood until around 2006.
In this talk, first we formulate the turbulization along a closed transversal. Then in our dimension setting, namely 2-dimensional foliations on 4-manifolds ((4,2)-foliations), a cohomological criterion is given for a given transversal to a foliation, which tells the turbulization is possible or not, relying on the Thurston's h-principle. Also we give cocrete geometric constructions of turbulizations.
The cohomological criterion for turbulization is deduced from a more general criterion for a given embedded surface to be a compact leaf or a closed transversal of some foliation, which is stated in terms of the euler classes of tangent and normal bndle of the foliation to look for. The anormalous cohomological solutions for certain cases suggested the geometric realization of turbulization, while the cohomological criterion is obtained by the h-principle.
Some other modifications are also formulated for (4,2)-foliations and their possibility are assured by the anormalous solutions mentioned above. For some of them, good geometric realizations are not yet known. So far the difficulty lies on the problem of the connected components of the space of representations of the surface groups to Diff S^1.
If the time permits, some special features on the h-principle for 2-dimensional foliations are also explained.
This is a report on a joint work with Elmar VOGT(Freie Universität Berlin). For codimension 1 foliations, the process of turbulization, i.e., inserting a Reeb component along a closed transversal, is well-known, while for higher codimensional foliation, similar processes were not understood until around 2006.
In this talk, first we formulate the turbulization along a closed transversal. Then in our dimension setting, namely 2-dimensional foliations on 4-manifolds ((4,2)-foliations), a cohomological criterion is given for a given transversal to a foliation, which tells the turbulization is possible or not, relying on the Thurston's h-principle. Also we give cocrete geometric constructions of turbulizations.
The cohomological criterion for turbulization is deduced from a more general criterion for a given embedded surface to be a compact leaf or a closed transversal of some foliation, which is stated in terms of the euler classes of tangent and normal bndle of the foliation to look for. The anormalous cohomological solutions for certain cases suggested the geometric realization of turbulization, while the cohomological criterion is obtained by the h-principle.
Some other modifications are also formulated for (4,2)-foliations and their possibility are assured by the anormalous solutions mentioned above. For some of them, good geometric realizations are not yet known. So far the difficulty lies on the problem of the connected components of the space of representations of the surface groups to Diff S^1.
If the time permits, some special features on the h-principle for 2-dimensional foliations are also explained.
Lectures
15:00-16:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Alexander Kupers (Harvard University)
Cellular E_2-algebras and the unstable homology of mapping class groups
Alexander Kupers (Harvard University)
Cellular E_2-algebras and the unstable homology of mapping class groups
[ Abstract ]
We discuss joint work with Soren Galatius and Oscar Randal-Williams on the application of higher-algebraic techniques to classical questions about the homology of mapping class groups. This uses a new "multiplicative" approach to homological stability -- in contrast to the "additive" one due to Quillen -- which has the advantage of providing information outside of the stable range.
We discuss joint work with Soren Galatius and Oscar Randal-Williams on the application of higher-algebraic techniques to classical questions about the homology of mapping class groups. This uses a new "multiplicative" approach to homological stability -- in contrast to the "additive" one due to Quillen -- which has the advantage of providing information outside of the stable range.
2018/06/11
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yusaku Tiba (Ochanomizu University)
Cohomology of non-pluriharmonic loci (JAPANESE)
Yusaku Tiba (Ochanomizu University)
Cohomology of non-pluriharmonic loci (JAPANESE)
[ Abstract ]
In this talk, we study a pseudoconvex counterpart of the Lefschetz hyperplane theorem.
We show a relation between the cohomology of a pseudoconvex domain and the cohomology of the non-pluriharmonic locus of an exhaustive plurisubharmonic function.
In this talk, we study a pseudoconvex counterpart of the Lefschetz hyperplane theorem.
We show a relation between the cohomology of a pseudoconvex domain and the cohomology of the non-pluriharmonic locus of an exhaustive plurisubharmonic function.
2018/06/06
Number Theory Seminar
17:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Nicolas Templier (Cornell University)
On the Ramanujan conjecture for automorphic forms over function fields
Nicolas Templier (Cornell University)
On the Ramanujan conjecture for automorphic forms over function fields
[ Abstract ]
Let G be a reductive group over a function field of large enough characteristic. We prove the temperedness at unramified places of automorphic representations of G, subject to a local assumption at one place, stronger than supercuspidality. Such an assumption is necessary, as was first shown by Saito-Kurokawa and Howe-Piatetskii-Shapiro in the 70's. Our method relies on the l-adic geometry of Bun_G, and on trace formulas. Work with Will Sawin.
Let G be a reductive group over a function field of large enough characteristic. We prove the temperedness at unramified places of automorphic representations of G, subject to a local assumption at one place, stronger than supercuspidality. Such an assumption is necessary, as was first shown by Saito-Kurokawa and Howe-Piatetskii-Shapiro in the 70's. Our method relies on the l-adic geometry of Bun_G, and on trace formulas. Work with Will Sawin.
2018/06/05
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Hiroki Matui (Chiba University)
Topological full groups and generalizations of the Higman-Thompson groups (JAPANESE)
Hiroki Matui (Chiba University)
Topological full groups and generalizations of the Higman-Thompson groups (JAPANESE)
[ Abstract ]
For a topological dynamical system on the Cantor set, one can introduce its topological full group, which is a countable subgroup of the homeomorphism group of the Cantor set. The Higman-Thompson group V_n is regarded as the topological full group of the one-sided full shift over n symbols. Replacing the one-sided full shift with other dynamical systems, we obtain variants of the Higman-Thompson group. It is then natural to ask whether those generalized Higman-Thompson groups possess similar (or different) features. I would like to discuss isomorphism classes of these groups, finiteness properties, abelianizations, connections to C*-algebras and their K-theory, and so on.
For a topological dynamical system on the Cantor set, one can introduce its topological full group, which is a countable subgroup of the homeomorphism group of the Cantor set. The Higman-Thompson group V_n is regarded as the topological full group of the one-sided full shift over n symbols. Replacing the one-sided full shift with other dynamical systems, we obtain variants of the Higman-Thompson group. It is then natural to ask whether those generalized Higman-Thompson groups possess similar (or different) features. I would like to discuss isomorphism classes of these groups, finiteness properties, abelianizations, connections to C*-algebras and their K-theory, and so on.
2018/06/04
Tokyo Probability Seminar
16:00-17:30 Room #126 (Graduate School of Math. Sci. Bldg.)
Hiroyoshi MITAKE (Graduate School of Mathematical Sciences, The University of Tokyo)
Uniqueness set for degenerate Hamilton-Jacobi equations (JAPANESE)
Hiroyoshi MITAKE (Graduate School of Mathematical Sciences, The University of Tokyo)
Uniqueness set for degenerate Hamilton-Jacobi equations (JAPANESE)
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Junjiro Noguchi (The University of Tokyo)
(JAPANESE)
Junjiro Noguchi (The University of Tokyo)
(JAPANESE)
2018/05/31
Numerical Analysis Seminar
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Olivier Pironneau (Sorbonne University and Academy of Sciences)
Parallel Computing Methods for Quantitative Finance: the Parareal Algorithm for American Options (English)
Olivier Pironneau (Sorbonne University and Academy of Sciences)
Parallel Computing Methods for Quantitative Finance: the Parareal Algorithm for American Options (English)
[ Abstract ]
With parallelism in mind we investigate the parareal method for American contracts both theoretically and numerically. Least-Square Monte-Carlo (LSMC) and parareal time decomposition with two or more levels are used, leading to an efficient parallel implementation which scales linearly with the number of processors and is appropriate to any multiprocessor-memory architecture in its multilevel version. We prove $L^2$ superlinear convergence for an LSMC backward in time computation of American contracts, when the conditional expectations are known, i.e. before Monte-Carlo discretization. In all cases the computing time is increased only by a constant factor, compared to the sequential algorithm on the finest grid, and speed-up is guaranteed when the number of processors is larger than that constant. A numerical implementation will be shown to confirm the theoretical error estimates.
With parallelism in mind we investigate the parareal method for American contracts both theoretically and numerically. Least-Square Monte-Carlo (LSMC) and parareal time decomposition with two or more levels are used, leading to an efficient parallel implementation which scales linearly with the number of processors and is appropriate to any multiprocessor-memory architecture in its multilevel version. We prove $L^2$ superlinear convergence for an LSMC backward in time computation of American contracts, when the conditional expectations are known, i.e. before Monte-Carlo discretization. In all cases the computing time is increased only by a constant factor, compared to the sequential algorithm on the finest grid, and speed-up is guaranteed when the number of processors is larger than that constant. A numerical implementation will be shown to confirm the theoretical error estimates.
2018/05/30
Number Theory Seminar
17:00-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Daichi Takeuchi (University of Tokyo)
Blow-ups and the class field theory for curves (JAPANESE)
Daichi Takeuchi (University of Tokyo)
Blow-ups and the class field theory for curves (JAPANESE)
2018/05/29
Tuesday Seminar on Topology
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Kouki Sato (The university of Tokyo)
A partial order on nu+ equivalence classes (JAPANESE)
Kouki Sato (The university of Tokyo)
A partial order on nu+ equivalence classes (JAPANESE)
[ Abstract ]
The nu+ equivalence is an equivalence relation on the knot concordance group. Hom proves that many concordance invariants derived from Heegaard Floer homology are invariant under nu+ equivalence. In this work, we introduce a partial order on nu+ equivalence classes, and study its algebraic and geometrical properties. As an application, we prove that any genus one knot is nu+ equivalent to one of the unknot, the trefoil and its mirror.
The nu+ equivalence is an equivalence relation on the knot concordance group. Hom proves that many concordance invariants derived from Heegaard Floer homology are invariant under nu+ equivalence. In this work, we introduce a partial order on nu+ equivalence classes, and study its algebraic and geometrical properties. As an application, we prove that any genus one knot is nu+ equivalent to one of the unknot, the trefoil and its mirror.
Algebraic Geometry Seminar
15:30-17:00 Room #122 (Graduate School of Math. Sci. Bldg.)
Alessandra Sarti (Universit\'e de Poitiers)
Nikulin configurations on Kummer surfaces (English)
Alessandra Sarti (Universit\'e de Poitiers)
Nikulin configurations on Kummer surfaces (English)
[ Abstract ]
A Nikulin configuration is the data of
16 disjoint smooth rational curves on a K3 surface.
According to results of Nikulin this means that the K3 surface
is a Kummer surface and the abelian surface in the Kummer structure
is determined by the 16 curves. An old question of Shioda is about the
existence of non isomorphic Kummer structures on the same Kummer K3
surface.
The question was positively answered and studied by several authors, and
it was shown that the number of non-isomorphic Kummer structures is
finite,
but no explicit geometric construction of such structures was given.
In the talk I will show how to construct explicitely non isomorphic
Kummer structures on generic Kummer K3 surfaces.
This is a joint work with X. Roulleau.
A Nikulin configuration is the data of
16 disjoint smooth rational curves on a K3 surface.
According to results of Nikulin this means that the K3 surface
is a Kummer surface and the abelian surface in the Kummer structure
is determined by the 16 curves. An old question of Shioda is about the
existence of non isomorphic Kummer structures on the same Kummer K3
surface.
The question was positively answered and studied by several authors, and
it was shown that the number of non-isomorphic Kummer structures is
finite,
but no explicit geometric construction of such structures was given.
In the talk I will show how to construct explicitely non isomorphic
Kummer structures on generic Kummer K3 surfaces.
This is a joint work with X. Roulleau.
2018/05/28
Seminar on Geometric Complex Analysis
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Satoshi Nakamura (Tohoku University)
A generalization of Kähler Einstein metrics for Fano manifolds with non-vanishing Futaki invariant (JAPANESE)
Satoshi Nakamura (Tohoku University)
A generalization of Kähler Einstein metrics for Fano manifolds with non-vanishing Futaki invariant (JAPANESE)
[ Abstract ]
The existence problem of Kähler Einstein metrics for Fano manifolds was one of the central problems in Kähler Geometry. The vanishing of the Futaki invariant is known as an obstruction to the existence of Kähler Einstein metrics. Generalized Kähler Einstein metrics (GKE for short), introduced by Mabuchi in 2000, is a generalization of Kähler Einstein metrics for Fano manifolds with non-vanishing Futaki invariant. In this talk, we give the followings:
(i) The positivity for the Hessian of the Ricci Calabi functional which characterizes GKE as its critical points, and its application.
(ii) A criterion for the existence of GKE on toric Fano manifolds from view points of an algebraic stability and an analytic stability.
The existence problem of Kähler Einstein metrics for Fano manifolds was one of the central problems in Kähler Geometry. The vanishing of the Futaki invariant is known as an obstruction to the existence of Kähler Einstein metrics. Generalized Kähler Einstein metrics (GKE for short), introduced by Mabuchi in 2000, is a generalization of Kähler Einstein metrics for Fano manifolds with non-vanishing Futaki invariant. In this talk, we give the followings:
(i) The positivity for the Hessian of the Ricci Calabi functional which characterizes GKE as its critical points, and its application.
(ii) A criterion for the existence of GKE on toric Fano manifolds from view points of an algebraic stability and an analytic stability.
< Previous 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186 Next >
