Mini-workshop on Differential Geometry

March. 19. 2015

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

Directions

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 “Cohomogeneity one coassociative submanifods”
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.)

Title：Concentration, convergence, and dissipation of spaces

Abstract： 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, Gromov’s 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 “Strategic Young Researcher Overseas Visits Program for Accelerating Brain Circulation”