@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@To English version
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F 518(y)@15F0017F15
@ꏊ F ȑw_yLpX331
@@@15:0016:00
@@@@u F |@i (ȑw)
@@@@u^Cg F Recursion operatorSymplectic-Haantjesl
@@@@@@@@@@@@@@@̍\ɂ

@@@@AuXgNg F For a completely integrable system, the way of
@@@finding the first integrals is not formulated in general.
In classical
@@@mechanics, a completely integrable systems in the sense of Liouville
@@@are called simply an integrable system.
It is well known there are
@@@several approaches to find the first integrals such as the method of
@@@Lax, the Lie algebra adject from the soliton theory, etc.
Also, certain
@@@ways of characterizing integrable systems with (1, 1)-tensors is
@@@investigated, recently.
Known examples of integrable systems with
@@@(1, 1)-tensors are recursion operators and symplectic-Haantjes manifolds.

@@@For a dynamical system, the system is proved to be integrable if there
@@@exists a (1, 1)-tensor which satisfies certain conditions.
In this talk,
@@@using their method we construct recursion operators and
@@@symplectic-Haantjes manifolds for several Hamiltonian systems of two
@@@degrees of freedom.

@@@This talk is based on a joint work with Akira Yoshioka and Kiyonori Hosokawa.

@@@16:1517:15
@@@@u F @F (cw)
@@@@u^Cg F Hom-Lie㐔ɑ΂Lie
@@@@@@@@@@@@sȗ_̐iWɂ

@@@@AuXgNg FHom-Lie㐔́ALie㐔ؒf
@@@@ʑłЂ˂悤ȍ\xNgohłB
@@@@̊TǑƂȂHom-Lie㐔͌㐔$\sigma$-
@@@@œAVirasoro㐔ȂǂƂ̊֘AmĂB
@@@@Hom-Lie
㐔́uLie㐔ɑ΂Lie㐔vƓlAHom-Lie
@@@@̊􉽊wIȈʉƂĒALie㐔ɑ΂Đ藧
@@@@ʂsĐ藧ƂmĂB
@@@@{uł͊ɒmĂ邢̌ʂЉƂƂɁAu҂
@@@@Hom-Lie㐔Hom-Nijenhuis\Hom-Dirac\Ȃǂ
@@@@΂錋ʂȂǂЉB

@@@@@@@@@@2019Nx̋L^

@@ F@32(y)@16F0017F00
@@ꏊ F ȑw_yLpX341i34Kj
@@u F Alexander Hock (~X^[w)
@@u^Cg F Exact solution of matricial \phi^3_2 model to
@@@@@@@@@@@all genus by topological recursion
@@ @AuXgNg F
Developed methods will be extended to find exact solution
@@@@@@@@
for the \phi_2^3 matrix model with an external matrix E in the large N limit.
@@@@@@@@This model can be understood as regularized Kontsevich model, where the
@@@@@@@@regularization ensures UV finiteness in 2 dimensions in case of linear eigen
@@@@@@@@values. The universal structure of topological recursion is used and slightly
@@@@@@@@affected by the regularization for the one boundary (puncture) sector.
@@@@@@@@All correlation functions of genus g with B boundary components are achieved
@@@@@@@@by a differential operator A_X acting on the one boundary solution. The results
@@@@@@@@are exact and describes the summation of all weighted 3 valent graphs on
@@@@@@@@a B-punctured Riemann surface of genus g. Even though a \phi^3 model is
@@@@@@@@unstable, it arises as a exactly solvable noncommutative qunatum field theory

@@@@@@@@on a highly deformed Moyal space.

F 427(y)@15F0017F15
@ꏊ F ȑw_yLpX331
@@@15:0016:00
@@@@u F с@T (ȑw)
@@@@u^Cg F [oȋԓ̕ϋȗȕl
@@@@@@@@@@@@̋[oȓIKEXʑ

@@@@AuXgNg F
We investigated oriented surfaces of constant mean and

Gaussian curvatures and non-diagonalizable shape operator in pseudo-hyperbolic space.
It is known that such Lorentzian surfaces in 3-dimensional anti-de Sitter space are
either a B-scroll or a complex circle.In this talk, we first state result for the type numbers

of the pseudo-hyperbolic Gauss maps of a B-scroll and a complex circle.
Secondly, we state results for the type numbers of the pseudo-hyperbolic Gauss maps of
generalized umbilical hypersurfaces which are a natural generalizations of B-scrolls in the
general dimensional anti-de Sitter space.Also, we state constructions of consider as
surfaces can be generalized umbilical hypersurfaces in the pseudo-hyperbolic space and
pseudo-sphere of index 2 and B-scroll in 5-dimensional pseudo-hyperbolic space of index 2
.

This talk is based on a joint work with Naoyuki Koike.

@@@16:1517:15
@@@@u F {c@~j (lw)
@@@@u^Cg F 3[cl̗̓LEȃKEXȗ
@@@@@@@@@@@@^Ȗ
@@@@AuXgNg F
A mixed type surface is a connected regular surface in
a Lorentzian 3-manifold with non-empty spacelike and timelike point sets. The induced
metric of a mixed type surface is a signature-changing metric, and their lightlike points

may be regarded as singular points of such metrics. In this talk, we investigate the behavior
of Gaussian curvature at a non-degenerate lightlike point of a mixed type surface.
To characterize the boundedness of Gaussian curvature at a non-degenerate lightlike
points, we introduce several fundamental invariants along non-degenerate lightlike points,
such as the lightlike singular curvature and the lightlike normal curvature. Moreover, using
the results by Pelletier and Steller, we obtain the Gauss-Bonnet type formula for mixed
type surfaces with bounded Gaussian curvature. This talk is based on a joint work
(arXiv:1811.11392) with K. Saji (Kobe University) and K. Teramoto (Kyushu University).

@@@@@@@@@@@@
2018Nx̋L^

@@ F 1222(y)@15F3017F45
@@ꏊ F ȑw_yLpX233
@@@@15:3016:30
@@@@@u F @c (kw)
@@@@@u^Cg F nCp[P[[l̂̒̕ϋȗ
@@@@@uAuXgNg F

@@@@@@Leung-Wan̓nCp[P[[l̂̒, nCp[OWl
@@@@@@@@ƂTO𓱓,̐ϋȗɉĕۂ邱ƂD
@@@@@@@@{uł,nCp[OWl̂ɑ΂ĎRɒ
@@@@@@@@ucCX^[GlM[vƂ̂Vɍl, \cCX^[GlM[
@@@@@@@@nCp[OWl̂ϋȗɉĕfOW
@@@@@@@@l̂Ɏ邱ƂЉD
@@@@@@@@ȂC̍u͍Ǖ㎁Ƃ̋ɊÂD

@@@@@@@.

@@ @16:4517:45
@@@@@u F Vc@ו (ȑw)
@@@@@u^Cg F Uniform relative stability and coercivity
@@@@@@@@@@@@@@for polarized toric manifolds
@@@@@uAuXgNg F
@@@@@@
We study a relation between algebro-geometric stability and the growth of
@@@@@@@@the modified K-energy which characterizes the extremal K
ahler metric as
@@@@@@@@a critical point. In this talk, we introduce uniform relative K-polystability
@@@@@@@@for polarized toric manifolds and show that it implies the coercivity of the
@@@@@@@@modified K-energy modulo the maximal torus action. If time allows, we will
@@@@@@@@also discuss on the converse direction.@
@@@@@@@@This talk is based on a joint work with Shunsuke Saito and Naoto Yotsutani.

@@ANZX F NbNĂB

@@@blF@r@VCc@^IqCÁ@jCVc@וCn@lC@_CR{@

@@O_y􉽊wZ~i[̋L^(2002N`2017N)̋L^ɂ܂Ă
@@