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　　　　　　　　　　　　　　Record of 2019

　
　　Date ： 2 March
　　Place ： Tokyo University of Science (Kagurazaka Campus)
　　16:00-17:00
　　　　Speaker ： Alexander Hock
　　　　　　（Mathematisches Institut der Westfälischen Wilhelms-Universität, Germany）
　　　　Title ： Exact solution of matricial \phi^3_2 model to all genus by
　　　　　　　　 topological recursion
　　 　 Abstract ：
　　　　　　　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 eigenvalues.
　　　　　　　　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.

　　　Date ： 27 April
　　　Place ： Tokyo University of Science (Kagurazaka Campus)
　　　15:00-16:00
　　　　Speaker ： Honoka Kobayashi （Tokyo University of Science）
　　　　Title : Pseudo-hyperbolic Gauss maps of submanifolds with
　　　　　　　　constant mean curvature in pseudo-hyperbolic space
　　　　Abstract ： 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 the jointwork with Naoyuki Koike.

　　　　16::15-17:15
　　　　Speaker ： Atsufumi Honda （Yokohama National University）
　　　　Title : Mixed type surfaces with bounded Gaussian curvature
　　　　　　　　in three-dimensional Lorentzian manifolds
　　　Abstract : 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).

Date ： 18 May
　　Place ： Tokyo University of Science (Kagurazaka Campus)
　　15:00-16:00
　　　　Speaker ： Tsukasa Takeuchi （Tokyo University of Science）
　　　　Title : On the construction of recursion operators and
　　　　　　　　of symplectic-Haantjes manifolds
　　　　Abstract ： 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.
　　
　　16:15-17:15
　　　　Speaker ： Tomoya Nakamura （Waseda University）
　　　　Title :On the development of a theories parallel to
　　　　　　　　Lie algebroids for Hom-Lie algebroids
　　　　Abstract ： 　


　　　　　　　　　　　　　Record of 2018

　　Date ： 22 December
　　Place ： Tokyo University of Science (Kagurazaka Campus)
　　15:30-16:30
　　　　Speaker ： Keita Kunikawa （Tohoku University）
　　　　Title : Convergence of mean curvature flow in hyperkähler manifolds
　　　　Abstarct ：

　　　 　Inspired by the work of Leung-Wan, we study the mean curvature flow in
　　　　　　hyperkahler manifolds starting from hyper-Lagrangian submanifolds,
　　　　　　a class of middle dimensional submanifolds, which contains the class of
　　　　　　complex Lagrangian submanifolds. For each hyper-Lagrangian submanifold,
　　　　　　we define a new energy concept called the "twistor energy" by means of
　　　　　　the associated twistor family. In this talk, we will show that the mean curvature
　　　　　　flow starting at any hyper-Lagrangian submanifold with sufficiently small
　　　　　　twistor energy will exist for all time and converge to a complex Lagrangian
　　　　　　submanifold for one of the hyperkähler complex structure. In particular, our result
　　　　　　implies some kind of energy gap theorem for hyperkähler manifolds which have
　　　　　　no complex Lagrangian submanifolds.
　　　　　　This talk is based on a joint work with Ryosuke Takahashi. 
　　16:45-17:45
　　　　Speaker ： Yasufumi Nitta （Tokyo University of Science）
　　　　Title ： Uniform relative stability and coercivity
　　　　　　　　 for polarized toric manifolds
　　　　Abstract :
　　　　　 We study a relation between algebro-geometric stability and the growth of
　　　　　　the modified K-energy which characterizes the extremal Kahler 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.

Organizers : Naoyuki Koike, Makiko Tanaka, Akifumi Sako,
　　　　　　　　　Yasufumi Nitta, Kurando Baba, Homare Tadano,
　　　　　　　　　Hikaru Yamamoto

Please click here about records of Kagurazaka Geometry Seminar (2002-2017).