# Bộ môn Giải tích

### Faculty of Mathematics, Mechanics and Informatics (SeMAn – MIM)

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+ 09h00 – 11h00, 31/10/2008: Dr. Dang Anh Tuan (Sect. of Math. Analysis, MIM, Ha Noi University of Science):

Title: Introduction to Morse Theory (part 2).

Venue: 422 T1, Ha Noi University of Science.

Abstract: NA

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09h00 – 11h00, 21/11/2008: Nguyen Huy Hoang (Institution:…):

Title: Điều kiện nghiệm suy rộng trên nghiệm dạng Grammian của phương trình Kadoutsev-Peviashvili.

Venue: 422 T1, Ha Noi University of Science.

Abstract: NA

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+ 14h00 – 16h00, 21/11/2008: Nguyen Dang Manh (Institution: Section of Analysis, Faculty of Mathematics-Mechanics-Informatics)

Title: Duality in Equivariant KK-theory and the structures of $C^*$-algebras of homogeneous spaces.

Venue: 422 T1, Ha Noi University of Science.

Abstract:

In this text, I will give a brief description of  my thesis including the main themes and results.

The first framework in my thesis is the study of a stabilization in the equivalent $KK$-theory. In 1980, Kasparov built equivariant $KK$-theory from the inequivariant one in order to solve a special case of the Novikov conjecture. This theory was developed rapidly by many mathematicians such as Cunzt, Higson, Skandalis, Meyer, Thomsen, etc. In 2000, Meyer constructed characteristics of elements of a $KK$-group by  elementary-essential Kasparov triples when he managed to build the equivariant version of Cuntz picture for equivariant $KK$-theory. The first part of my thesis is to study the Thomsen stabilization of them under the perturbation of degenerate ones.

The second part of my thesis is to study Thomsen duality in $KK$-theory and do our problem of finding its application. In 1981, Paschke obtained the isomorphism between $K_0(B^c)$ and the BDF-extension group $Ext^{-1}(A)$ where $A$ is a separable unital $C^*$-algebra and $B^c$ is the commutant  in the Calkin algebra of the image $B$ of $A$ under a trivial extension. In later years, this results were generalized by Vallette, Skandalis, Higson and Thomsen. In 2005, Thomsen showed that under minor assumptions (algebras are not necessary nuclear)  equivariant $KK$-groups of couples of algebras are isomorphic to $K$-group of a $C^*$-algebra. In my thesis, I will study this duality and apply this duality to investigate the relative $KK$-theory, a generalization of the relative $K$-homology; in some certain cases, we have obtained the same results for the relative $KK$-theory as the relative $K$-homology.

The last part of my thesis is to propose the concepts of noncommutative homogeneous spaces, discuss when we acquire actual homogeneous spaces, and research their structures. It is well-known that the noncommutative geometry programme proposed by Alain Connes is a very big open problem. In known cases, we have already built noncommutative versions of corresponding commutative objects, such as locally Hausdorff compact spaces-$C^*$-algebras, vector bundles-finite projective modules, groups-quantum groups, classical analysis-quantum analysis, $BDF$-theory-$KK$-theory, etc. Recently, Do Ngoc Diep has constructed many noncommutative objects successfully such as the noncommutative Chern characters for some certain groups, Riemann-Roch theorem and index theorem in NCG, Graded C$\check{e}$ch cohomology in NCG, etc (cf. His publications in MathSciNet of AMS). Our problem of investigating the structures of noncommutative homogeneous spaces is a continuing project of the series. We have obtained descriptions in $K$-theory level of these spaces.

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## 4 phản hồi »

1. Hy vọng mọi người tích cực cập nhật vào mục này cho thêm phần phong phú.

Bình luận bởi doanchi — 31/10/2008 @ 20:33

2. Cho hoi nghia cua cum tu hsiao-g-wendland-w-boundary-integral-equations

Bình luận bởi Truong — 05/07/2011 @ 15:10

3. boundary-integral-equations

Bình luận bởi Truong — 05/07/2011 @ 15:11

• Phương trình tích phân bờ (biên) ???

Bình luận bởi doanchi — 10/07/2011 @ 21:05