Date: | April 18 (Tue), 2006 |
Speaker: | Katsuma Ban (�� ���n) (University of Tokyo) |
Title: | Rankin-Cohen-�ɐ��R�^�̔�����p�f�ɂ��� |
Abstract: |
�����ی^�`���̐��������͈�ʂɕی^�`���ł͂Ȃ��Ȃ邪�A������g�ݍ��킹�邱�ƂŐV���Ȑ����ی^�`����^���邱�Ƃ��ł���B
�ȉ~���W�����[�`���ɑ��� Rankin-Cohen ������p�f�͂��̍ł��ȒP�ȗ�ł���B�ɐ��R�� Siegel ���W�����[�`���ɑ��邱�̂悤�ȃ^�C�v�̔�����p�f���ǂ̂悤�Ȍ`�����Ă��邩�ɂ��āA��ʓI�ȋL�q��^�����B ����̃Z�~�i�[�ł́A�ɐ��R�ɂ�錋�ʂ�\���_�I�Ȗ���Ƃ��đ��������A���̖��肪���R�� SU(p,q) �� O*(2p) ��̐����ی^�`���ɂ��g������邱�Ƃ��������B |
Date: | May 16 (Tue), 2006 |
Speaker: | Toshio Oshima (�哇���Y) (University of Tokyo) |
Title: | �m����ٓ_�^�̉��Ȕ�����p�f�n�ɂ��� |
Abstract: |
���Ȗ�Lie�Q�₻�̑Ώ̋�Ԃ��R���p�N�g���l�̂Ɏ�������ƁC�s�ϔ�����p�f�n�͂��̋��E�ɉ����Ċm����ٓ_������������p�f�n�ƂȂ�D ��������p�f�n��������̍�p�f��������Â����邱�Ƃ���ɁC ���E�̋ߖT�ő�����͓I�ȓ����ŗL���̈�ʓI�\�����l�@���C�\���_�C���� Whittaker �͌^�Ȃǂւ̉��p��_����iHarish-Chandra ���^�� Goodman-Wallach ��p�f�̔����������_�̗��ꂩ��̉��߂Ȃǂ��܂ށj�D |
Date: | June 13 (Tue), 2006 |
Speaker: | Hiroshi Oda (�D�c��) (Takushoku University) |
Title: | �ÓT�^���fLie�̈�� Verma ���Q�ɑ���ŏ������� |
Abstract: |
�ÓT�^���f Lie �� g �̎��R�\�����玩�R�ɒ�܂� U(g) �W���̐����s��
�� F �Ƃ���Dg �̃X�J���[���Verma���Q MΘ(λ) �ɑ��āC���f���j�b�N������ q(x) �� q(F) �̊e�������S�� Ann MΘ(λ) �ɑ������
���ȍŏ������̂��̂� "MΘ(λ) �̍ŏ�������" �Ƃ�ԁDM(λ) ��
MΘ(λ) �������Q�Ƃ��� Verma ���Q�Ƃ��Cq(F) �̊e������ Ann M(λ)
���������� U(g) �̗����C�f�A���� IΘ(λ) �Ƃ���ƁC�ŋ�
(1) �e λ �ɑ��� MΘ(λ) �̍ŏ��������̖�������������ꂽ�i�����͑哇�ɂ�� g = gln �̏ꍇ�ɂ͊��ɓ����Ă���j�D �Z�~�i�[�ł� (2) ���������߂� q(F) �̊e������ Harish-Chandra �����^ ���̌v�Z�@����ɐ�������D |
Date: | July 11 (Tue), 2006 |
Speaker: | Koji Nuida (�D�c���i) (National Institute of Advanced Industrial Science and Technology) |
Title: | On the isomorphism problem of Coxeter groups and related topics |
Abstract: | �R�N�Z�^�[�Q�ɂ��āA���̃R�N�Z�^�[�n�Ƃ��Ă̓��^�ނ� �R�N�Z�^�[�O���t�ƈ�Έ�Ή����邱�Ƃ͎��m�̎����ł��邪�A ����Œ��یQ�Ƃ��Ă̓��^�ނ́i���C���Q�̏ꍇ�Ɍ����Ă��j ���̂悤�ȑΉ������Ă��Ȃ��B����́A���̓��^�ނ̌�����ɂ��āA ���̗��j�̂���܂��i���ɁA�����Q���܂߂���ʂ̏ꍇ�ɂ��āA �P�O�N�قǑO�܂Ŗw�lj��̌��ʂ������Ă��Ȃ��������Ƃ͓��M�ɉ�����j�ƁA �ߔN�̌����̐i�W���A��̗��֘A���錋�ʂ������Љ��B |
Date: | July 20 (Thu), 2006, 16:30-18:00 |
Place: | Room 126, Graduate School of Mathematical Sciences |
Speaker: | Guster Ólafsson (Louisiana State University) |
Title: | The Heat equation, the Segal-Bargmann transform and generalizations — I |
Abstract: [pdf] |
|
Date: | July 25 (Tue), 2006, 16:30-18:00 |
Place: | Room 126, Graduate School of Mathematical Sciences |
Speaker: | Boris Rubin (Louisiana State University) |
Title: | Radon transforms: Basic Concepts |
Abstract:[pdf] |
How can we reconstruct a function on a manifold
from integrals of this function over certain submanifolds? This is
one of the central problems in integral geometry and tomography,
which leads to the notion of the Radon transform.
The first talk is of introductory character. We discuss basic ideas of the original Radon's paper (1917), then proceed to the Minkowski-Funk transform and more general totally geodesic Radon transforms on the n-dimensional unit sphere. The main emphasis is an intimate connection of these transforms with the relevant harmonic analysis. We will see that Radon transforms of this type and their inverses can be regarded as members of analytic families of suitable convolution operators and successfully studied in the framework of these families. |
Date: | July 31 (Mon), 2006, 15:00-16:00 |
Place: | Room 126, Graduate School of Mathematical Sciences |
Speaker: | Guster Ólafsson (Louisiana State University) |
Title: | The Heat equation, the Segal-Bargmann transform and generalizations — II |
Abstract: [pdf] |
|
Date: | July 31 (Mon), 2006, 16:30-17:30 |
Place: | Room 126, Graduate School of Mathematical Sciences |
Speaker: | Boris Rubin (Louisiana State University) |
Title: | Radon transforms on Grassmannians and Matrix Spaces |
Abstract: [pdf] |
Diverse geometric problems in RN get a new flavor if a generic point x = (x1, ..., xN) is regarded as a matrix with appropriately organized entries (set, e.g., x = (xi,j)n x m for N = nm). This well known observation has led to a series of breakthrough achievements in mathematics. In integral geometry it suggests a number of the so-called "higher-rank" problems when such traditional scalar notions as "distance", "angle", and "scaling" become matrix-valued. I will be speaking about Radon transforms on Grassmann manifolds and matrix spaces and some related problems of harmonic analysis where these phenomena come into play. |
Date: | October 31 (Tue), 2006 |
Speaker: | Toshio Oshima (�哇���Y) (University of Tokyo) |
Title: | ���[�g�n�̕����n�̕��� |
Abstract: | ���[�g�n Ξ ���烋�[�g�n Σ �ւ� Cartan ������ۂʑ��̕��ނ��l����i���� Σ �̕����n�ƌ��Ȃ���j�DΣ �� Weyl �Q�iΣ �̓������^�j�ňڂ肠�����̂l�Ƃ݂��Ƃ��̕��ނ��܂��s���C���l�̏���������� Ξ �̎��ȓ��^�i�����n�̕��ނɑΉ��j�CΞ �̊����̎��ȓ��^�̒��ρCΣ �̎��ȓ��^�Ȃǂ��������̂ɍL�����ꍇ�̕��ނ�������^���ǂ����̔�����^����D���[�g�n�� dual pair �̊T�O���`���C���l�ނւ� Ξ �̎��ȓ��^�̍�p�̍l�@�ɗp����D |
© Toshiyuki Kobayashi