**Mini-workshop on Differential Geometry**

**March. 19. 2015**

**Kawai
hall, Graduate school of Sciences, Tohoku University,
Sendai, Japan**

Kawai hall, Graduate school of Sciences,
Tohoku University

6-3,
Aoba, Aramaki, Aoba-ku,
SENDAI 980-8578, Japan

**Program: **

10:00-10:50
Toru Kajigaya "Complex flag manifolds and Lagrangian submanifolds"

11:00-11:50 Tomohiro Fukaya "Coronae and the coarse Baum-Connes conjecture"

Lunch

13:30-14:20 Takashi Shioya "Concentration, convergence, and
dissipation of space "

14:30-15:20 Kotaro Kawai gCohomogeneity one coassociative submanifodsh

Tea break

15:40-16:30 Jason D. Lotay "Hyperkaehler
4-manifolds with boundary"

16:40-17:30 Tommaso Pacini "Coupled geometric flows: which
& why"

18:00- Party

**Abstract:**

**Toru Kajigaya (Tohoku Univ./ OCAMI)**

Title: Complex flag manifolds and Lagrangian
submanifolds

Abstract: A complex flag manifold is an orbit of the adjoint representation of a compact semi-simple Lie group. These
orbits play an important role in several contexts. In this talk we consider
some relations between Complex flag manifolds and Lagrangian
submanifolds in the following viewpoints: (i) Complex flag manifold as a submanifold
in the Euclidean space. (ii) Complex flag manifold as a homogeneous Kahler manifold.

**Tomohiro Fukaya (Tohoku Univ.)**

Title: Coronae and the coarse Baum-Connes
conjecture

Abstract: TBA

**Takashi Shioya (Tohoku Univ.)**

TitleFConcentration, convergence, and dissipation of spaces

AbstractF Gromov introduced a new topology on the set of
isomorphism classes of metric measure spaces, based on the idea of
concentration of measure phenomenon due to Levy and Milman. This is a generalization of measured Gromov-Hausdorff topology. Different from the measured Gromov-Hausdorff topology, Gromovfs
topology is suitable to study a non-GH-precompact
family of spaces. In this talk, I
show the study of convergence of spaces with unbounded dimension.

**Kotaro Kawai (University
of Tokyo)**

Title: Cohomogeneity one coassociative submanifolds

Abstract; Coassociative
submanifolds are calibrated 4-submanifolds in
G2-manifolds.

We construct explicit examples in the bundle of anti-self-dual
2-forms over the 4-sphere.

Classifying the Lie groups which have 3 or 4 dimensional
orbits,

we show that only homogeneous coassociative
submanifold is

the zero-section up to the automorphism

and construct many cohomogeneity
one examples explicitly.

**Jason D. Lotay (University College
London)**

Title: Hyperkaehler
4-manifolds with boundary

Abstract: Hyperkaehler
geometry, which arises in the study of special holonomy
and Ricci-flat metrics, is also important for theoretical physics and moduli
space problems in gauge theory. In
dimension 4, hyperkaehler geometry takes on a special
character, and a natural question arises: given a compact 3-dimensional
manifold N which can be a hypersurface in a hyperkaehler 4-manifold, when can it actually be
"filled in" to a compact hyperkaehler
4-manifold with N as its boundary?
In particular, starting from a compact hyperkaehler
4-manifold with boundary, which deformations of the boundary structure can be
extended to a hyperkaehler deformation of the
interior? I will discuss recent
progress on this problem, which is joint work with Joel Fine and Michael Singer.

**Tomasso**** Pacini (****Scuola**** Normale Superiore****)**

Title:
"Coupled geometric flows: which & why."

Abstract:
I will present an overview of recent work with J. Lotay
(UCL) concerning coupled flows in various contexts: Kahler,
almost Kahler and G2 geometry.

**Organizers**

Toru Kajigaya
(Tohoku University/ OCAMI)

Reiko Miyaoka
(Tohoku University)

**This workshop is supported by**

**JSPS g****Strategic Young Researcher Overseas Visits Program for Accelerating Brain
Circulationh **