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Course Information
Shuang Zhang
Professor
619B Old Chemistry Building
513-556-4040
shuang.zhang@uc.edu
http://math.uc.edu/~zhangs/
Education
PHD, Purdue University, 1988.
Research Support
National Science Foundation . (DMS - 9626592); Funded 1996 to 1999.
National Science Foundation . (DMS - 9225076); Funded 1993 to 1996.
NSF Young Investigator , Texas A& M University. Funded 1992 to 1993.
National Science Foundation. (DMS - 9002958); Funded 1990 to 1991.
National Science Foundation. (DMS - 8902371); Funded 1989
Peer Reviewed Publications
(2005). C*-algebras generated by a projection and the reduced group C*-algebras C_rZ _ Zn and C_rZm _ Zn. Int. J. Math., 16(5), 1-22.
(2004). Toeplitz algebras and C*-algebras arising from reduced reduced group C*-algebras. Illinois J. Math, 48(1), 199-218.
W. Szymanski (2001). K-theory of certain C*-algebras associated with free products of cyclic groups. Journal of Operator Theory, 45, 251-264.
(2001). On the homotopy type of the unitary group and the Grassmann space ofpurely infinite simple C*-algebras. K-Theory, 24, 203-225.
W. Szymanski (1999). Type II1 factors generated by purely infinite simple C*-algebras associated with free groups. Proc. Amer. Math. Soc., 128, 813-818.
(1998). Purely infinite simple C*-algebras arising from the reduced group C*-algebras. Contem. Math., 228, 365-389.
(1997). Rectifiable diameters of the Grassmann spaces of von Neumann algebras and certain C*-algebras. Pacific J. of Math., 177, 377-396.
W. Szymanski (1997). Infinite Simple C*-algebras and reduced cross products of abelian C*-algebras and free groups. Manu. Math., 92, 487-514.
(1997). Toeplitz algebras and infinite simple C*-algebras associated with reduced group C*-algebras. Math. Scand., 81, 86-100.
(1994). K-theory and homotopy of certain groups and infinite Grassmann spaces associated with C*-algebras. Int. J. Math., 3, 425-445.
(1993). Exponential rank and exponential length of operators on Hilbert C*-modules. Annals of Mathematics, 137, 129-144.
(1993). Factorizations of invertible operators and K-theory of C*-algebras. Bull. Amer. Math. Soc., 28, 75-83.
(1993). K-theory and a bivariable Fredholm index. Contemporary Math., Amer. Math. Soc., 148, 155-190.
(1993). Homotopy of projections and factorization in the unitary group of certain C*-algebras. Math. Scand., 73, 281-306.
(1992). Certain C_-algebras with real rank zero and their corona and multiplieralgebras, Part I. Pacific J. Math., 155, 169-197.
(1992). Certain C_-algebras with real rank zero and their corona and multiplieralgebras, Part II. K-Theory, 6, 1-27.
(1992). Certain C_-algebras with real rank zero and their corona and multiplieralgebras, Part IV. Inter. J. Math., 3, 309-330.
H. Lin (1992). Certain simple C*-algebras with nonzero real rank whose corona algebras have real rank zero. Houston J. Math., 18, 57-71.
(1992). On the exponential rank and exponential length of C*-algebras. J. Operator Theory, 28, 337-355.
(1991). Star-shaped sets and fixed point theorems of multivalued mappings. Math. Japonica, 36, 327-334.
(1991). On the ideal structure of generalized Calkin algebras. Contemporary Math., Amer. Math. Soc., 120, 193-198.
(1991). K1-groups, quasidiagonality and interpolation by multiplier projections. Trans. Amer. Math. Soc., 325, 793-818.
(1991). Five problems on the structure of multiplier algebras of real rank zero. Contemporary Math., Amer. Math. Soc., 120, 199-203.
H. Lin (1991). On infinite simple C*-algebras. J. Funct. Anal., 100, 221-231.
(1991). Matricial structure and homotopy type of simple C*-algebras of real rank zero. J. Operator Theory, 26, 283-312.
(1990). Diagonalizing projections in the multiplier algebra and matrices over a C*-algebra. Pacific J. Math., 145, 181-200.
(1990). C*-algebras with real rank zero and the internal structure of their corona and multiplier algebras, Part III. Can. J. Math., 62, 159-190.
(1990). A property of purely infinite simple C*-algebras. Proc. Amer. Math. Soc., 109, 717-720.
(1990). TrivialK1-flow of AF and finite von Neumann algebras. J. Funct. Anal., 92, 77-91.
(1990). A Riesz decomposition property and ideal structure of multiplier algebras. J. Operator Theory, 24, 209-225.
(1989). Stable isomorphism of hereditary C*-subalgebras and stable equivalence of open projections. Proc. Amer. Math. Soc., 105, 677-682.
(1989). On the structure of projections and ideals of corona algebras. Canadian J. Math., 41, 721-742.
(1988). Derivations and (hyper)invariant subspaces of a bounded operator. Proc. Amer. Math. Soc., 102, 261-267.
(1981). Centeric sets, star-shaped sets and fixed points. Beijing Shiyuan Natural Science Monthly, 1, 102-117.
Books
L. Ge, H. Lin, Z-J. Ruan, & D. Zhang (1998). Operator Algebras and Operator Theory. Contem. Math. Book Series, No. 228.
(1995). Quasi-diagonalizing unitaries and the generalized Weyl-von Neumanntheorem.
Invited Presentations
V. Kaftal, David Larson (01-2006). Operator-Valued Frames. Operator algebras and applications,of the American Math Society Annual Meeting , Texas.
(07-2005). Simple C*-algebras and their multiplier algebras. The First International Operator Algebra and Operator Theory Symposium, Xi’an/China.
(04-2003). K-theory of C*-algebras generated by certain reduced group C*-algebras and projections. Operator algebras and free probability, of the American Math Society Meeting, Bloomington, Indiana.
(04-2003). Rectifiable diameters of the Grassmann spaces of certain C*-algebras. Operator algebras and applications, of the American Math Society Meeting, Bloomington, IN.
(01-2003). The contractibility of unitary group of certain purely infinite simple C*-algebras. C*-extensions and classification of C*-algebras, of the American Math Society Meeting, Baltimore, MD.
(11-2002). Invariants arising from C*-algebras associated with 0-1 sequences. Wabash Seminar Monthly Series On Functional Analysis
(08-2002). Satellite Conference of the International Congress of Mathematicians, Operator Algebras and Applications, Chengde, China.
(06-2002). Around a long standing problem on simple C*-algebras. Mathematical Institute of China, Beijing, China.
(06-2002). A new approach to K-theory . Morningstar Mathematical Research Center, Beijing, China.
(08-2001). Operator Algebras, of the 2001 Canada-China Initiative In Mathematical Sciences, Vancouver, Canada.
(07-2001). Simple C*-algebras and their invariants. Workshop on Operator Algebras , Shanghai, China.
(03-1999). K-theory of certain simple C*-algebras associated with cross products of cyclic groups. Operator spaces and applications, of the American Math Society Meeting (941) , University of Illinois.
(03-1999). An overview on invariants of C*-algebras. Annual Conference of the Math Institute of the University of Illinois, Urbana, Illinois.
(01-1998). Purely infinite simple C*-algebras generated by a weighted shift and an isometry. Recent progress in the theory of operator algebras and their applications, of the American Math Society Joint Annual Meeting, Baltimore, Maryland.
(12-1997). On structure of certain purely infinite simple C*-algebras. The structure and classification of amenable C*-algebras, of the Canadian Math Society Annual Meeting, Victoria, B. C..
(07-1997). K-theory of C*-algebras and its applications. Nanjing University, China.
(07-1997). On C*-algebras and their invariants. Operator Algebras and Operator Theory, East China Normal University, China.
(07-1997). C*-algebras and von Neumann algebras, Nanjing University, China .
(06-1997). K-theory of C*-algebras . Beijing Normal University, China.
(05-1997). Regional Meeting of the American Mathematical Society , Detroit, Michigan.
(10-1996). About the K-theory of certain purely infinite C*-algebras. Annual Wabash Mini conference, IUPUI.
(08-1996). Generalized Fredholm index. University of Newcastle, Australia.
(05-1996). Structure on infinite simple C*-algebras. 24th Annual Canadian Symposium on Operator Algebras and Operator Theory, University of Saskatchewan.
(05-1996). Reduced group C*-algebras and associated infinite simple C*-algebras. NSF Annual Conference on Great Plains Operator Theory, Arizona State University.
(07-1995). Simple C*-algebras and reduced cross products. Invariants of Operator Algebras, Cork, Ireland.
(06-1995). Can simple C*-algebras contain both nonzero finite and infinite projections?. Operator Symposium of Canada, Fields Institute, Waterloo.
(04-1995). Toeplitz C*-algebras associated with free products of cyclic groups. University of New York at Buffalo
(03-1995). Simple C*-algebras of real rank zero. Purdue University and Indiana University at Indianapolis
(10-1994). A long standing problem on simple C*-algebras and recent progress. Extramural Modern Analysis Mini conference , Indiana University - Purdue University at Indianapolis.
(06-1994). Purely infinite simple C*-algebras generated by one projection and reduced group C*-algebras. Simple C*-algebras, of the American Math Society, University of Oregon, Eugene.
(05-1994). Structure of certain simple C*-algebras. Annual Conference on Great Plains Operator Theory , University of Nebraska.
(10-1993). C*-algebras generated by reduced group C*-algebras and one a projection. Extramural Modern Analysis Mini conference, Indiana University.
(07-1993). Mathematical Institute of the Academic Sinica of China, Beijing, China.
(1993). Department of Mathematics, Indiana University - Bloomington.
(10-1992). Rectifiable diameters of von Neumann algebras and certain C*-algebras. Operator Theory and Operator Algebras, of the American Math Society, Wright State University, Dayton.
(08-1992). K-theory and the multiplier algebras. Royal Danish Academy of Sciences and Letters, a commemorative symposium on Invariants in Operator Algebras , Copenhegan, Denmark.
(07-1992). K-theory and invertible operators on a Hilbert C*-modules. Texas A& M University
(05-1992). Essential commutant and K-theoretical invariants. NSF Annual Conference on Great Plains Operator Theory, University of Iowa.
(03-1992). Homotopy groups of the unitary groups and Grassmann spaces of certain C*-algebras. Operator Algebras, of the conference of the American Math Society, Tuscaluoosa, Alabama.
(03-1992). K-theory and homotopy of certain groups and infinite Grassmann spaces associated with C*-algebras. Operator Algebras And Algebraic Topology, of the conference of the American Math Society, Springfield, Missouri.
(02-1992). Factorizations of invertible operators and Fredholm index. NSF Wabash Functional Analysis Seminar
(08-1991). Factorizations of invertible operators on Hilbert C*- modules. NSF CBMS-Regional conference Homology and Index Theory
(05-1991). Factorization of unitary elements in C*-algebras. NSF Annual Conference on Great Plains Operator Theory, Texas A& M University.
(04-1991). A proof for the Phillips-Ringrose conjecture. Wabash Extramural Modern Analysis Mini Conference, IUPUI , Indianapolis, IN.
(01-1991). Certain C*-algebras of real rank zero and their multiplier algebras. Non-commutative Topology And C*-Algebras, of the American Math Society Joint Annual Meeting , San Francisco, CA.
(11-1990). A Riesz decomposition property and applications. Operator Theory/ Operator Algebras, of the conference of the American Math Society, University of California/Irvine.
(04-1990). The NSF Great Plains Operator Theory Conference , University of New Mexico.
(03-1990). Quasidiagonal operators on a Hilbert C*-module. Arizona State University
(03-1990). Internal structure of multiplier algebras. University of Georgia
(02-1990). C*-algebras with the FS property. University of Alabama
(10-1989). Simultaneously quasi-diagonalizing two projections and trivial K1-group. 852th American Math Society , Muncie, Indiana.
(05-1989). K1-group and structure of certain multiplier C*-algebras. The 17th Annual Canadian Symposium on Operator Algebras and Operator Theory, University of Toronto.
Colloquia
(05-1990). Ideal structure of generalized Calkin algebras. Texas Christian University.
(01-1990). Some recent results about simple C*-algebras of real rank zero. Louisville, KY.
(05-1988). Quasi-diagonality in multiplier algebras. Indiana University -Purdue University at Indianapolis.
