NCTS Colloquium: Jordan Theory and Analysis 2010math.cts.nthu.edu.tw/Mathematics/Program and Guide0408.pdfJordan triples in analysis on bounded symmetric domains, 3/3 (page 8) tea/coffee

NCTS Colloquium: Jordan Theory and Analysis 2010

約當理論與分析學研討會 2010

Thursday

April 8/ Room A

Friday April 9/ Room A

Saturday April 10/ Room B

Sunday April 11/ Room B

Monday April 12/ Room B

9:30-10:15am W Kaup I Shestakov W Kaup I Shestakov M Neal Chair I Shestakov G Roos I Shestakov G Roos CH Chu Tea/coffee/snacks 10:30-11:15 JS Chen W Kaup G Roos W Kaup NC Wong Chair NC Wong I Shestakov CH Chu G Roos CK Ng Tea/coffee 11:30-12:15 I Shestakov G Roos I Shestakov CH Chu Chair W Kaup W Kaup W Kaup M Neal Lunch 2:00-2:45pm G Roos PH Lee PH Lee PH Lee Chair CH Chu CL Chuang TK Lee NC Wong Tea/coffee 3:00-3:45 CK Ng CL Chuang YM Chiang TK Lee Chair JS Chen TK Lee CH Chu PH Lee Tea/coffee/snacks 4:00-4:45 CH Chu CH Chu PY Wu Chair M Neal CL Chiang NC Wong

1. Venue: NCTS at National Tsing-Hua University, Hsinchu, Taiwan. 2. Registration takes place during 8:40-9:10, and Opening is at 9:10-9:30 am, Thursday,

April 8. 3. Banquet starts at 7:00 pm, Saturday, April 10, in the Feng Yun Lou Restaurant (風雲

樓) in the Tsing-Hua campus. If you would like to join us to walk to the restaurant together, please gather at 6:30pm in the lobby of the NCTS building.

4. Those joining the half-day city tour at April 12 please show up at 1pm in the lobby of the NCTS building.

NCTS Colloquium: Jordan Theory and Analysis 2010

約當理論與分析學研討會 2010

National Center for Theoretical Sciences4F, Third General Building

National Tsing Hua UniversityNo. 101, Sec 2, Kuang Fu Road

Hsinchu, Taiwan 30043, Taiwan R.O.C.April 8–12, 2010.

April 3, 2010

Thursday, April 8, 2010

08:40 – 09:10 Registration

Lecture Room A

09:10 – 09:30 OpeningWen-Ching Li 李文卿 (National Center for Theoretical Sciences, Taiwan)Cho-Ho Chu 朱礎豪 (Queen Mary College, University of London, UK)Ngai-Ching Wong 黃毅青 (National Sun Yat-sen University, Taiwan)

09:30 – 10:15 Wilhelm Kaup (Mathematisches Institut der Universitaet Tuebingen, Germany)Applications of Jordan theory in analysis and geometry, 1/4 (page 6)

tea/coffee/snacks

10:30 – 11:15 Jein-Shan Chen 陳界山 (Taiwan Normal University, Taiwan)Applications of Euclidean Jordan algebra in optimization (page 5)

tea/coffee

11:30 – 12:15 Ivan Shestakov (University of Sao Paulo, Brazil)Structure of Jordan algebras, 1/4 (page 8)

Lunch

14:00 – 14:45 Guy Roos (St Petersburg, Russia)Jordan triples in analysis on bounded symmetric domains, 1/3 (page 8)

tea/coffee

15:00 – 15:45 Chi-Keung Ng 吳志強 (Chern Institute of Mathematics, Nankai University, China)On genuine infinite tensor products (page 7)

tea/coffee/snacks

16:00 – 16:45 Cho-Ho Chu 朱礎豪 ( Queen Mary, University of London, UK)Jordan structures in Banach spaces, 1/3 (page 5)

Friday, April 9, 2010

Lecture Room A


tea/coffee/snacks


tea/coffee


Lunch

14:00 – 14:45 Pjek-Hwee Lee 李白飛 (National Taiwan University, Taiwan)The Jordan and Lie structures of simple rings revisited, 1/3 (page 6)

tea/coffee

15:00 – 15:45 Chen-Lian Chuang 莊正良 (National Taiwan University, Taiwan)Ore extensions, higher derivations, shuffle products and differential identities (page 6)

tea/coffee/snacks


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Saturday, April 10, 2010

Lecture Room B


tea/coffee/snacks


tea/coffee


Lunch


tea/coffee

15:00 – 15:45 Edmund Y. M. Chiang 蔣翼邁 (Hong Kong University of Science and Technology,Hong Kong)

Eigen-solutions of biconfluent Heun equation with respect to a complex weight (page 5)

Banquet at 7:00pm, at Feng Yun Lou Restaurant 風風風雲雲雲樓樓樓晚晚晚宴宴宴.You can join us at 6:30pm in the lobby of the NCTS building

to walk to the restaurant together, if you would like.

Sunday, April 11, 2010

Lecture Room B


tea/coffee/snacks

3


tea/coffee


Lunch


tea/coffee

15:00 – 15:45 Tsiu-Kwen Lee 李秋坤 (National Taiwan University, Taiwan)Certain maps preserving zero products (page 7)

tea/coffee/snacks

16:00 – 16:45 Pei-Yuan Wu 吳培元 (National Chiao-Tung University, Taiwan)A journey through numerical ranges (page 9)

Monday, April 12, 2010

Lecture Room B

09:30 – 10:15 Matthew Neal (Denison Universityo, USA)Jordan structures in Banach space and operator space theory (page 7)

tea/coffee/snacks

10:30 – 11:15 Ngai-Ching Wong 黃毅青 (National Sun Yat-sen University, Taiwan)Linear disjointness preservers of W*-algebras (page 9)

A half-day city tour for Taipei attractions.Those joining please show up at 1pm in the lobby of the NCTS building.

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Abstracts

Eigen-solutions of biconfluent Heun equation with respectto a complex weight

Edmund Y. M. Chiang 蔣翼邁

Hong Kong University of Science and Technology, Hong Kong.

Email: [email protected]

Abstract

The Heun equation is a canonical second order linear differential equation with four regular singularpoints on the Riemann sphere. It has one more regular singular point than the Gauss hypergeometricequation. We will look at one of its confluence cases and to show that there exists eigensolutionswith respect to a complex weight. We shall make an effort to explain why these equations areimportant before going into the more technical issues.

Applications of Euclidean Jordan algebra in optimization

Jein-Shan Chen 陳界山

National Taiwan Normal University, Taiwan


Abstract

In this talk, we focus on applications of Euclidean Jordan algebra in optimization. We will introducesome optimization problems which involve Euclidean Jordan algebra. More specifically, severaltopics in symmetric cone optimization will be discussed.

Jordan structures in Banach spaces

Cho-Ho Chu

Queen Mary, University of London, UK.


Abstract

We explain how Jordan algebraic structures arose in Banach spaces and discuss applications ofJordan theory to diverse areas in analysis as well as some research problems.

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Ore extensions, higher derivations, shuffle products anddifferential identities

Chen-Lian Chuang 莊正良

National Taiwan University, Taiwan


Abstract

Ore extensions, since their discovery by Ore, have been one of the most useful constructions inalgebra. In a classical paper, Amistur used Ore extensions to investigated differential identities(identities with derivations). We found that the tricky formula in a crucial computation of Amitsur’spaper actually came from Hasse-Schmidt higher derivations. We then found that a family of higherderivations, analogous to Hasse-Schmidt higher derivations but more general, can be naturallydefined in Burkov’s Ore extensions with many indeterminates. The referee of this work pointed outthat the composition product of our higher derivations is merely the shuffle product of correspondingwords. The shuffle product comes naturally from the graded dual of the free algebra, which formsa Hopf algebra when considered as the enveloping algebra of the free Lie algebra. The refereeof another paper of ours pointed out that Burkov’s Ore extensions with many indeterminates aremerely smash products, in which the free algebra is again considered as a Hopf algebra as above.So some interesting connections waiting to be explored must exist between all these notions. Wewill talk about what we have known and what we expect to know in this direction.

Applications of Jordan theory in analysis and geometry

Wilhelm Kaup

Mathematisches Institut der Universitaet Tuebingen, Germany


Abstract

We start with the interplay between formally real Jordan algebras, self-dual homogeneous cones andbounded symmetric domains of tube type. Next the infinite dimensional analogs in Banach spacesare discussed. The interplay between Jordan triple systems and ayrbitrary bounded symmetricdomains (separately in finite and infinite dimensions) is a further topic. Finally, an interesting classof homogeneous Cauchy-Riemann manifolds is described in terms of Jordan algebras.

The Jordan and Lie structures of simple rings revisited

Pjek-Hwee Lee 李白飛



Abstract

6

In 1961 I. N. Herstein gave a one hour talk in AMS meeting concerning the Jordan and Lie structuresof simple ring rings. In this sries of talks we shall review the old results and introduce some newresults since then.

Certain maps preserving zero products

Tsiu Kwen Lee 李秋坤



Abstract

We characterize certain maps which preserves zero products. These maps are solved completely interms of derivations and elementary operators.

Jordan structures in Banach space and operator spacetheory

Matthew Neal

Denison University, USA.


Abstract

In this talk we will give recent results concerning classical problems in Banach space theory inthe setting of normed Jordan triple systems. In particular we will give an exhaustive treatment ofautomatic contractive complimentation for preduals of JBW*-triples. In other words, if a subspaceof the pre-dual of a JBW*-triple A is linearly isometric to the pre-dual of a JBW*-triple B, whenis there automatically a contractive projection of A onto B? We will also give a short history ofthese kinds of results in Banach space theory. If time permits, we will also discuss recent automaticcontinuity results on normed Jordan triples. After this we will give new results on the interplay ofternary *-structures and complete holomorphic vector fields in operator space theory. In particular,we will use these tools to give new operator space norm criteria for (1) when an operator space isunital and (2) when certain classes of operator spaces are completely isometric to operator algebras.These are two long open and important problems in operator space theory.

On genuine infinite tensor products

Chi-Keung Ng 吳志強

Chern Institute of Mathematics, Nankai University, China.


Abstract

7

We will study genuine infinite tensor products of vector spaces, unital algebras, inner-product spacesas well as ∗-representations of unital ∗-algebras. By a genuine infinite tensor product, we meansone that defined as the object whose linear maps coincide with multilinear maps on the product ofa family of infinite numbers of objects (instead of as a direct limit of finite tensor products).

Jordan triples in analysis on bounded symmetric domains

Guy Roos

St Petersburg, Russia


Abstract

The lectures will be in three parts :

1. An introduction to bounded symmetric domains in Cn as the natural generalization of theunit disc in C, with examples of the associated Jordan structures and their role in geometryand analysis on the domain.

2. Hermitian positive Jordan triples and bounded symmetric domains: an outline of the generaltheory of Hermitian positive Jordan triples, equivalence of category with bounded symmetricdomains, application of Jordan theory (idempotents, minimal polynomial, spectral decom-position, Peirce decomposition) to geometry and analysis on the domain (geometry of theboundary, automorphisms, reproducing kernels of weighted Bergman spaces).

3. Special chapters: volume of bounded symmetric domains, compactification, symplectic dual-ity, extension of Bohr’s theorem to bounded symmetric domains , polynomial morphisms ofJordan triples.

Structure of Jordan algebras

Ivan Shestakov

University of Sao Paulo, Brazil


Abstract

I plan to give an introductory mini-course on Jordan Structure Theory. The following themes willbe considered in my lectures:

1. Finite dimensional Jordan algebras.

2. Special and exceptional Jordan algebras, s-identities and tetrad-eaters.

3. Structure Theory of Jordan algebras. Non-degenerate Jordan algebras and pairs.

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4. Jordan Superalgebras.

Linear disjointness preservers of W*-algebras

Ngai-Ching Wong

National Sun Yat-sen University, Taiwan


Abstract

In this talk, we shall give a complete description of the structure of zero product and orthogonalitypreserving linear maps between W*-algebras. In particular, two W*-algebras are ∗-isomorphic if andonly if there is a bijective linear map between them observing their zero product or orthogonalitystructure. It is also the case when they have identical linear and left (right) ideal structures.

A journey through numerical ranges

Pei-Yuan Wu 吳培元

National Chiao-Tung University, Taiwan


Abstract

The numerical range W (A) of a bounded linear operator A on a complex Hilbert space H is thesubset of the complex plane consisting of the inner products of the vectors Ax and x for all unitvectors x in H, and the numerical radius of A is the maximum distance from the origin to themembers of W (A).In this talk, we briefly discuss three topics in the study of numerical ranges which we have con-tributed, together with Hwa-Long Gau, over the past ten years: (1) Anderson’s theorem on thecondition for the numerical range of a finite matrix to be equal to a circular disc, (2) Holbrook’sresult on the numerical radius of the product of two commuting operators, and (3) Williams andCrimmins’s result on the condition for the equality of the numerical radius to half of the norm ofan operator.

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Documents

NCTS Colloquium: Jordan Theory and Analysis 2010math.cts.nthu.edu.tw/Mathematics/Program and Guide0408.pdfJordan triples in analysis on bounded symmetric domains, 3/3 (page 8) tea/coffee