Lizhen Ji, Hideko Sekiguchi, Reiko Miyaoka #1, Reiko Miyaoka #2,
| Date: | March 10 (Fri), 2017, 17:00-18:30 |
| Place: | Room 056, Graduate School of Mathematical Sciences, the University of Tokyo |
| Speaker: | Lizhen Ji (University of Michigan, USA) |
| Title: | Satake compactifications and metric Schottky problems |
| Abstract: [ pdf ] |
The quotient of the Poincare upper half plane by the modular group SL(2,
Z) is a basic locally symmetric space and also the moduli space of
compact Riemann surfaces
of genus 1, and it admits two important classes of generalization:
J: M_g --> A_g. In this talk, I will discuss some results along these lines related to the Stake compactifications and the Schottky problems on understanding the image J(M_g) in A_g from the metric perspective. (joint with topology seminar) |
| Date: | September 26 (Tue), 2017, 17:00-18:30 |
| Place: | Room 056, Graduate School of Mathematical Sciences, the University of Tokyo |
| Speaker: | Hideko Sekiguchi (The University of Tokyo, Japan) |
| Title: | Representations of Semisimple Lie Groups and Penrose Transform |
| Abstract: [ pdf ] |
The classical Penrose transform is generalized to an intertwining
operator on Dolbeault cohomologies of complex homogeneous spaces $X$ of
(real) semisimple Lie groups. I plan to discuss a detailed analysis when $X$ is an indefinite Grassmann manifold. To be more precise, we determine the image of the Penrose transform, from the Dolbeault cohomology group on the indefinite Grassmann manifold consisting of maximally positive $k$-planes in ${\mathbb{C}}^{p,q}$ ($1 \le k \le \min(p,q)$) to the space of holomorphic functions over the bounded symmetric domain. Furthermore, we prove that there is a duality between Dolbeault cohomology groups in two indefinite Grassmann manifolds, namely, that of positive $k$-planes and that of negative $k$-planes. (joint with topology seminar) |
| Date: | October 24 (Tue), 2017, 17:30-18:30 |
| Place: | Room 056, Graduate School of Mathematical Sciences, the University of Tokyo |
| Speaker: | Reiko Miyaoka (Tohoku University, Japan) |
| Title: | Approach from the submanifold theory to the Floer homology of
Lagrangian intersections ���O�����W�������̃t���A�z�����W�[�ɑ��镔�����l�̘_����̃A�v���[�` |
| Abstract: [ pdf ] |
The Gauss map images of isoparametric hypersurfaces in the spheres
supply a rich family of minimal Lagrangian submanifolds of the complex
hyperquadric Q_n(C). In simple cases, these are real forms of Q_n(C),
and their Floer homology is known. In this talk, we consider the case
when the number of distinct principal curvatures is 3,4,6, and report
our results. This is a
joint work with Hiroshi Iriyeh (Ibaraki U.), Hui Ma (Tsinghua U.) and
Yoshihiro Ohnita (Osaka City U.). ���ʂ̓��a���Ȗʂ̃K�E�X�ʑ��ɂ�鑜�́C���f�Q�����Ȗ�Q_n(C)�̋ɏ����O�� ���W���������l�̖̂L�x�ȗ��^����D�ȒP�ȏꍇ�C�����Q_n(C)�̎��`�Ƃ� ��C���̃t���A�z�����W�[�͊��m�ł���D�����ł͑��قȂ��ȗ��̌��� 3,4,6�̏ꍇ�ɓ���ꂽ���ʂ���邱�Ƃ��q�ׂ�D�������́C���]���i��� ��j�CHui Ma�i���ؑ�w�j�C��m�c�`�T�i���s��j�Ƃ̋��������ł���D (joint with topology seminar) �W���u�`�����j������s���܂��B �Z�~�i�[�̊J�n�����͂����ƈقȂ�܂��B |
| �W���u�` | |
| Date: | October 23 (Mon)-27 (Fri), 2017 |
| Place: | ������w��w�@�����Ȋw������ �����Ȋw���ʍu�`II�C�����Ȋw���_B |
| Speaker: | �{����q (���k��w��w�@���w������) |
| Title: | ���a���Ȗʘ_����Ƃ��̉��p |
| Abstract: [ pdf ] |
�L�x�ȗ�������a���Ȗʂ��w�Ԃ��Ƃɂ��C�������l�̘_��
��{��g�ɂ���D���̃K�E�X�ʑ��̑�����Ȃ郉�O�����W���������l�̂�
�������_���l���C�t���A�z�����W�[��_����D ���a���Ȗʑ��Ƃ́C20 ���I�����̃C�^���A�ɂ�������w�ɒ[�� ��C�i�s�g�ʂ̂��钴�Ȗʑ��̂��Ƃł���D�Â������͓I�ɂ��M�`���� ���ꂩ��_�����Ă���D���[�N���b�h��ԂƑo�ȋ�Ԃł͊ȒP�Ȃ��̂��� ����Ȃ����C���ʂł͑����̔��ȗႪ���݂��C����Clifford �̕\���� ��\���������̂͏d�v�ł���D ��ʃ��[�}�����l�̂̒��ł��l�����邪�C�{�u�`�ł͋��ʂ̓��a���Ȗ� ���ɓI�����ڂ�C���̊�{�����C���m�̕��ނ��q�ׂ�D ���p�Ƃ��āC���a���Ȗʂ̃K�E�X�ʑ��̑��Ƃ��ē����镡�f�Q�����Ȗ� Qn(C) �̃��O�����W���������l�̂ɂ��āC���O�����W�������̃t���A�z�� ���W�[�Ɋւ���ŋ߂̌��ʂ��Љ��i���̕����͉Ηj�̃g�|���W�[�E���[ �Q�_�E�\���_�����Z�~�i�[�ł��b���܂��j�D
�u�`�T�v�F |
© Toshiyuki Kobayashi