Huaxin Lin

Bio

Huaxin Lin will join SIMIS in 2024 as a professor.
Prior to this, Lin has been a full professor in University of Oregon and also served for East China Normal University.He received his Ph. D. in Purdue University in 1986.
His main research field is operator algebras and its applications.Lin became an inaugurate class Fellow of American Mathematical Society in 2013.
He was awarded the First Prize of Shanghai Science and Technology Progress Award in 2005, and (shared with G. Gong and Z. Niu) the Frontiers of Science Award at International Congress of Basic Science in 2023.

Education Expereince

• Purdue University 1982-1986, Ph.D. 1986, Master of Science, 1984
• East China Normal University, 1977-1980

Working Experience

• Shanghai Institute for Mathematics and Interdisciplinary Sciences (2024-current), Professor
• University of Oregon (1994-2024), Professor
• State University of Nwe York at Buffalo (1992-1994), Visiting Assistent Professor
• University of Victoria, Canada (1991-1992), Visiting Assistent Professor.
• East China Normal University (1989-1994), University of California, Santa Barbara (1986-1988), Visiting Assistent Professor

Visiting Positions

• Copenhagen University (1990.8-1991.2)
• University of Toronto (1991.2-1991.7)
• The Fields Insititue (Summer 1994, 2007.9-12)
• Mittag-Leffler Institute (2016.4)
• Math Sciences Research Institute (MSRI) (2000.9-2001.3)
• East China Normal University (2000-2024, Zhijiang/Changjiang Lecture Professor)

Editorial Work

• Science China Mathematics (Editorial board–2015-2021)
• Annals of K-Theory (Editorial board)
• Journal of Mathematical Analysis and Applications (Associated Editor)

Awards

• An inaugurate class Fellow of American Mathematical Society (2013)
• The First Prize of Shanghai Science and Technology Progress Award in 2005
• The Frontiers of Science Award at International Congress of Basic Science in 2023 (shared with G. Gong and Z. Niu)

List of Publications

A List of 10 Selected papers

1. Almost commuting selfadjoint matrices and applications, The Fields Institute Communications, Operator Algebras and their Applications, vol 13 (1997), 193–233. (FEATURED REVIEW MR 1424963).
2. Classification of simple C*-algebras and higher dimensional noncommutative tori, Ann. of Math. 157 (2003), 521–544.
3. Classification of simple C*-algebras of tracial topological rank zero. Duke Math. J. 125 (2004), 91–119.
4. Asymptotically unitary equivalence and asymptotically inner automorphisms, Amer. J. Math. 131 (2009), no. 6, 1589–1677.
5. Asymptotic unitary equivalence and classification of simple amenable C*-algebras, Invent. Math. 183 (2011), 385–450.
6. Approximately diagonalizing matrices over C(Y ), Proc. Natl. Acad. Sci. USA 109 (2012), no. 8, 2842–2847.
7. Localizing the Elliott conjecture at strongly self-absorbing C*-algebras, II, J. Reine Angew. Math. 692 (2014), 233–243.
8. Locally AH algebras, Mem. Amer. Math. Soc. 235 (2015), no.1107, vi+109 pp.
9. A classification of finite simple amenable Z -stable C*-algebras, I–II : (with Gong, Guihua; and Niu, Zhuang). C. R. Math. Acad. Sci. Soc. R. Can. 42 (2020), no. 3, 63–450.
10. Tracial oscillation zero and Z-stability, Adv. Math. 439 (2024), Paper No. 109462, 51 pp

Books and separated editions

11. An introduction to the classification of amenable C*-algebras, World Scientific Publishing Co., Inc., River Edge, NJ, (2001), xii+320 pp. ISBN: 981-02-4680-3.
12. From the Basic Homotopy Lemma to the Classification of C*-algebras, CBMS Series, no. 124, (2017), Amer. Math. Soc./NSF, ISBN 9781470434908, pp240.
(8). Local AH algebras, Mem. Amer. Math. Soc., 235 (2015), 109pp, ISBN: 978-4704-2225-7.
13. Approximate homotopy of homomorphisms from C(X) into a simple C*-algebra, Mem. Amer. Math. Soc. 205 (2010), no. 963, vi+131 pp. ISBN: 978-0-8218-5194-4.
14. (with C.N. Phillis) Classification of Direct Limits of Even Cuntz-cirlce Algebras, Mem. Amer. Math. Soc., 118 (1996), ISBN: 978-1-4704-0144-3.
15. C*-Algebra Extensions of C(X), Mem. Amer. Math. Soc., 115 (1995), ISBN: 978-1-4704-0129-0.

The rest of publications

16. (with X. Fu) Tracial oscillation zero and stable rank one, Canad. J. Math. 2024, pp. 168, http://dx.doi.org/10.4153/S0008414X24000099
17. (with G. Gong and Z. Niu) Homomorphisms into simple Z-stable C*-algebras, II, J. Noncommut. Geom. 17 (2023), 835–898.
18. Hereditary uniform property Γ, Sci. China Math. 66 (2023), 1813–1830.
19. (with X. Fu and K. Li) Tracial approximate divisibility and stable rank one, J. Lond. Math. Soc. 106 (2022), no. 4, 3008–3042.
20. (with G. Gong) On classification of nonunital amenable simple C*-algebras, III : The range and the reduction, Ann. K-Theory 7 (2022), no. 2, 279–384 (https://doi.org/10.2140/akt.2022.7.279) 105 pages.
21. (with P. Ng) Extensions of C*-algebras by a small ideal, Inter. Math. Res. Notices, rmac115/ https://doi.org/10.1093/imrn/rnac115, May 2022 , pp. 1–89.
22. (with X. Fu) Non-amenable simple C*-algebras with tracial approximation. Forum Math. Sigma 10 (2022), Paper No. e14, 50 pp.
23. (with X. Fu) Tracial approximation in simple C*-algebras, Canad. J. Math. 74 (2022), no. 4, 942–1004. (63 pp).
24. Unitary groups and augmented Cuntz semigroups of separable simple Z-stable C*-algebras. Internat. J. Math. 33 (2022), no. 2, Paper No. 2250018, 49 pp. (89 pp)
25. (with Guihua Gong) On classification of non-unital amenable simple C*-algebras, II. J. Geom. Phys. 158 (2020), 103865, 102 pp.
26. (with G. A. Elliott, G. Gong and Z. Niu) The classification of simple separable KK-contractible C*-algebras with finite nuclear dimension. J. Geom. Phys. 158 (2020), 103861, 51 pp.
27. (with G. A. Elliott, G. Gong and Z. Niu) Simple stably projectionless C*-algebras with generalized tracial rank one, J. Noncommutative Geometry, 14 (2020), 251–347 (96 pages).
28. (with S. Hu) Convex hulls of unitary orbits of normal elements in C–algebras with tracial rank zero, J. Funct. Anal, 278 (2020), 108306, 51 pp.
29. Crossed products and minimal dynamical systems. J. Topol. Anal. 10 (2018), no. 2, 447–469.
30. (Elliott, George A.; Gong, Guihua; Niu, Zhuang) The classification of simple separable unital Z-stable locally ASH algebras. J. Funct. Anal. 272 (2017), 5307–5359.
31. (with Sun, Wei) Tensor products of classifiable C*-algebras. J. Topol. Anal. 9 (2017), no. 3, 485504.
32. Homomorphisms from AH-algebras. J. Topol. Anal. 9 (2017), no. 1, 67–125.
33. (With Ng, P.W.) The corona algebra of the stabilized Jiang-Su algebra. J. Funct. Anal. 270 (2016), 1220–1267.
34. Minimal dynamical systems on connected odd dimensional spaces. Canad. J. Math. 67 (2015), 870–892.
35. Kishimoto’s conjugacy theorems in simple C*-algebras of tracial rank one. Integral Equations Operator Theory 83 (2015), 95–150.
36. (with S. Hu) Distance between unitary orbits of normal elements in simple C*-algebras of real rank zero. J. Funct. Anal. 269 (2015) 355–437.
37. (with G. Gong and Y. Xue) Determinant rank of C*-algebras. Pacific J. Math. 274 (2015), 405–436.
38. (with Hua, Jiajie) Rotation algebras and the Exel trace formula. Canad. J. Math. 67 (2015), 404–423,
39. (with Z. Niu) Asymptotic unitary equivalence in C*-algebras. Russ. J. Math. Phys. 22 (2015), 336–360.
40. (with Z.Niu) Homomorphisms into simple Z-stable C*-algebras. J. Operator Theory 71 (2014), 517–569.
41. A short return to simple AH-algebras with real rank zero, Math. Scand. 114, (2014). 264-274.
42. Exponentials in simple Z-stable C*-algebras, J. Funct. Anal., 266 (2014), 754-791.
43. (with J. Fang, C. Jiang and F. Xu) On generalized universal irrational rotation algebras and associated strongly irreducible operators, Inter. J. Math., 24, (2013), DOI: 10.1142/S0129167X13500596.
44. Approximate unitary equivalence in simple C*-algebras of tracial rank one. Trans. Amer. Math. Soc. 364 (2012), no. 4, 2021–2086 (66 pages).
45. (With Niu, Zhuang) The range of a class of classifiable separable simple amenable C*-algebras. J. Funct. Anal. 260 (2011), no. 1, 1–29.
46. Unitaries in a simple C*-algebra of tracial rank one. Internat. J. Math. 21 (2010), no. 10, 1267-1281.
47. (with N. C. Phillips) Crossed products by minimal homeomorphisms. J. Reine Angew. Math. 641 (2010), 95–122.
48. Inductive limits of subhomogeneous C*-algebras with Hausdorff spectrum. J. Funct. Anal. 258 (2010), 1909–1932.
49. Homotopy of unitaries in simple C*-algebras with tracial rank one. J. Funct. Anal. 258 (2010), 1822–1882 (63 pages).
50. The range of approximate unitary equivalence classes of homomorphisms from AH-algebras. Math. Z. 263 (2009), 903–922.
51. Unitary equivalences for essential extensions of C*-algebras. Proc. Amer. Math. Soc. 137 (2009), no. 10, 3407–3420. (With Niu, Zhuang)
52. Lifting KK-elements, asymptotic unitary equivalence and classification of simple C*-algebras. Adv. Math. 219 (2008), no. 5, 1729–1769.
53. AF-embeddings of the crossed products of AH-algebras by finitely generated abelian groups. Int. Math. Res. Pap. IMRP 2008, no. 3, Art. ID rpn007, (67 pages).
54. (With Osaka, Hiroyuki) Tracial Rokhlin property for automorphisms on simple AT-algebras. Ergodic Theory Dynam. Systems 28 (2008), no. 4, 1215–1241.
55. AF-embedding of crossed products of AH-algebras by Z and asymptotic AF-embedding. Indiana Univ. Math. J. 57 (2008), 891–944.
56. Tracial Rokhlin property for automorphisms on simple AT-algebras, Ergod. Th. & Sys. 28, (2008), 1215-1241.
57. Furstenberg transformations and approximate conjugacy. Canad. J. Math. 60 (2008), 189–207.
58. Minimal homeomorphisms and approximate conjugacy in measure, Illinois J. Math., 51 (2007), 1159-1188.
59. Simple nuclear C*-algebras of tracial topological rank one. J. Funct. Anal. 251 (2007), 601–679.
60. Weak semiprojectivity in purely infinite simple C*-algebras. Canad. J. Math. 59 (2007), 343–371.
61. Full extensions and approximate unitary equivalence. Pacific J. Math. 229 (2007), 389–428.
62. Classification of homomorphisms and dynamical systems, Trans. Amer. Math. Soc. 359 (2007), 859-895.
63. (with H. Hiroki) Minimal dynamical systems on the product of the Cantor set and the circle II, Selecta Math. 12 (2006), 199-239.
64. The Rokhlin property for automorphisms on simple C*-algebras, Contemp. Math. 414 ( 2006), 189-215.
65. An approximate universal coefficient theorem. Trans. Amer. Math. Soc. 357 (2005), 3375–3405.
66. (with Hiroki Matui) Minimal dynamical systems on the product of the Cantor set and the circle, Comm. Math. Physics, 257 (2005), 425-471.
67. Extensions by simple C*-algebras: quasidiagonal extensions. Canad. J. Math. 57 (2005), 351–399.
68. (with H. Matui) Minimal dynamical systems and approximate conjugacy. Math. Ann. 332 (2005), 795–822.
69. Tracial equivalence for C*-algebras and orbit equivalence for minimal dynamical systems. Proc. Edinb. Math. Soc. 48 (2005), 673–690.
70. (with S. Hu and Y. Xue) Limits of homomorphisms with finite-dimensional range. Internat. J. Math. 16 (2005), 807–821.
71. (with H. Osaka) The Rokhlin property and the tracial topological rank. J. Funct. Anal. 218 (2005), 475–494.
72. Traces and simple C*-algebras of tracial topological rank zero, J. Reine Angew. Math. (2004), 568 (2004), 99–137.
73. A separable Brown-Douglas-Fillmore theorem and weak stability, Trans. Amer. Math. Soc. 356 (2004), 2889–2925.
74. (with S. Hu and Y. Xue) The tracial topological rank of C*-algebras. II. Indiana Univ. Math. J. 53 (2004), 1578–1603.
75. Simple corona C*-algebras, Proc. Amer. Math. Soc. 132 (2004), 3215–3224.
76. (with Hu, Shanwen and Xue, Yifeng) The tracial topological rank of extensions of C*-algebras, Math. Scand. 94 (2004), no. 1, 125–147.
77. Simple AH-algebras with real rank zero, Proc. Amer. Math. Soc., 131 (2003), 3813-3819.
78. (with Osaka, H.) Tracially quasidiagonal extensions and topological stable rank. Illinois J. Math. 47 (2003), no. 3, 921–937.
79. Tracially quasidiagonal extensions, Canad. Math. Bull., 46, 2003, 388-399.
80. (with Shanwen Hu and Yifeng Xue) K-theory of C*-algebras with tracial topological rank k. Internat. J. Math. 14 (2003), 153–170.
81. (with Shanwen Hu and Yifeng Xue) Tracial limit of C*-algebras. Acta Math. Sin. (Engl. Ser.) 19 (2003), 535–5
82. Stable approximate unitary equivalences of homomorphisms, J. Operator Theory, 47 (2002), 343–378.
83. Simple C*-algebras with unique tracial states and quantized topological spaces. Acta Math. Sin. (Engl. Ser.) 18 (2002), 181–198.
84. Tracially AF C*-algebras, Trans. Amer. Math. Soc. 353 (2001), no. 2, 693–722.
85. The tracial topological rank of C*-algebras, Proc. London Math. Soc. (3) 83 (2001), no. 1, 199–234.
86. Classification of simple tracially AF C*-algebras, Canad. J. Math. 53 (2001), no. 1, 161–194.
87. Residually finite dimensional and AF-embeddable C*-algebras, Proc. Amer. Math. Soc. 129 (2001), no. 6, 1689–1696.
88. Simple C*-algebras with locally bounded irreducible representations, J. Funct. Anal., 187 (2001), 42-69.
89. Embedding of an AH-algebra into a simple C*-algebra with prescribed KK-data, K-theory, 24, (2001), 135-156.
90. Homomorphisms from C*-algebras with continuous trace, Math. Scand, 86 (2000), 249–272.
91. (With Guihua Gong) Almost multiplicative morphisms and K-theory, Inter. J. Math., 11 (2000), 983–1000.
92. (With Guihua Gong) Classification of homomorphisms from C(X) into simple C*-algebras of real rank zero, Acta Math. Sinica (N,S), 16 (2000), 181-206.
93. C*-algebras of trivial K-theory and semilattices, Inter. J. Math., 10 (1999), 93-128.
94. Lifting automorphisms, K-Theory, 16 (1999), 105-127.
95. When almost multiplicative morphisms are close to homomorphisms Trans. Amer. Math. Soc. 351 (1999), pp. 5027-5049.
96. A classification theorem for infinite Toeplitz algebras, Contem. Math. 228 (1998), 219-275.
97. (With Guihua Gong) Almost multiplicative morphisms and almost commuting matrices, J. Operator Theory, 40 (1998), 217-275.
98. Classification of simple C*-algebras with a unique trace, Amer. J. Math., 120 (1998), 1289-1315.
99. Extensions by C*-algebras with real rank zero III, Proc. London Math. Soc., 76 (1998), 634-666.
100. Almost commuting unitaries and classification of purely infinite simple C*-algebras, J. Func. Anal., 155 (1998), 1-24.
101. Homomorphisms of C(X) into C*-algebras, Cand. J. Math., 49 (1997), 963-1009.
102. C*-algebras with weak (FN), J. Funct. Anal., 150 (1997) 65-74.
103. Extensions of C(X) by simple C*-algebras of real rank zero, Amer. J. Math., 119 (1997), 1263-1289.
104. (With H. Osaka), Real rank of multiplier algebras of C*-algebras of real rank zero, The Fields Institute Communications, Operator Algebras and their Applications, vol 13 (1997), 235-241.
105. Almost multiplicative morphisms and applications, Journal of Operator Theory, 37 (1997), 121-154.
106. The generalized Berg theorem and BDF-theorem, Transactions Amer. Math. Soc., 349 (1997), 529-545.
107. Type I C*-algebra of real rank zero, Proceedings Amer. Math. Soc., 125 (1997), 2671-2676.
108. (With H. Su), Classification of direct limits of Toeplitz algebras, Pacific J. Math., 181 (1997), 89-140.
109. Approximation by normal elements with finite spectra in C*-algebras of real rank zero, Pacific Journal of Mathematics, 173 (1996), 443-489.
110. On the classification of C*-algebras of real rank zero with zero K1, Journal of Operator Theory, 35 (1996), 147-178.
111. (With G. A. Elliott, G. Gong and C. Pasnicu), Abelian C*-subalgebras and inductive limit C*-algebras, Duke Math. J., 85, (1996), 511-554.
112. C*-algebra extensions of C(X), Memoirs Amer. Math. Soc., 115 (1995), no.550.
113. (With M. Rφrdam) Extensions of inductive limits of circle algebras, Journal of London Math., 51 (1995), 603-613.
114. (With N. C. Phillips), Approximate Unitary equivalence of homomorphisms from O∞, Journal fur die reine und angewandte Mathematics 464 (1995), 173-186.
115. (With N. C. Phillips), Almost multiplicative morphisms and Cuntz algebra O2, International J. Math., 6 (1995) 625-643.
116. Extensions by C*-algebras with real rank zero II, Proceedings of London Math. Soc., 71 (1995), 641-674. (With N. C. Phillips),
117. Classification of direct limits of even Cuntz-circle algebras, Memoirs Amer. Math. Soc., 118, no. 565, (1995).
118. Almost commuting unitaries in purely infinite simple C*-algebras, Math. Ann., 303 (1995), 599-616.
119. Generalized Weyl-von Neumann theorems (II), Mathematica Scandinavica, 77 (1995), 129-147.
120. Approximation by normal elements with finite spectrum in simple AF-algebras, Journal of Operator Theory, 31 (1994), 83-98.
121. With G. A. Elliott, G. Gong and C. Pasnicu, Homomorphisms, homotopies and approximation by circle algebras, C. R. Math. Rep. Acad. Sci. Canada, vol. XVI (1994), no.1, 45-50.
122. Generalized Weyl-von Neumann theorem and C*-algebra extensions, Algebraic Methods in Operator Theory, edited by Raul Curto and Palle E. T. Jørgensen, Birkhauser, Boston/Basel/Berlin, 1994.
123. Almost normal elements, International J. Math. 5 (1994) 765-778.
124. Exponential rank of C*-algebras with real rank zero and the Brown-Pedersen conjectures, Journal of Functional Analysis, 114 (1993), 1-11.
125. Extension of multipliers and injective Hilbert modules, Chin. Ann. of Math. Ser B, 14 (1993), no.3, 387-396 (in English).
126. Extensions by C*-algebras with real rank zero, International. J. Math., 4 (1993) 231-252.
127. Skeleton C*-subalgebras, Canadian Journal of Mathematics, 44 (1992), 324-341.
128. Injective Hilbert modules, Pacific Journal of Mathematics, 154 (1992), 131-164.
129. Invariant subspaces and eigenvalues for elements in C*-algebras, Chin. Ann. of Math. B 13 (1992) no 4, 422-429 (in English),
130. Singly supported C*-algebras, Mathematica Scandinavica, 71 (1992), 133-144.
131. With Guihua Gong, Exponential rank of inductive limit C*-algebras, Mathematica Scandinavica, 71 (1992), 301-319.
132. With S. Zhang, Certain Simple C*-algebras with nonzero real rank whose corona algebras have real rank zero, Houston Journal of Math￾ematics, 18 (1992), 57-71.
133. Hilbert modules and their bounded module maps, Scientia Sinica (Science in China), Ser. A, 34 (1991) 1409-1421(in English).
134. Support algebras and their quasi-multipliers, Transactions Amer. Math. Soc. 325(1991) 829-854.
135. Simple C*-algebras with continuous scales and simple corona algebras, Proceedings Amer. Math. Soc. 112 (1991) 871-880
136. (With S. Zhang) On infinite simple C*-algebras, Journal of Functional Analysis, 100 (1991), 221-231.
137. Bounded module maps and completely positive maps, Journal of Operator Theory 26 (1991) 121-138.
138. Generalized Weyl-von Neumann theorems, International Journal of Mathematics, 2 (1991) 725-739.
139. Equivalent open projections and their corresponding hereditary C*-subalgebr as, Journal of London Math. Soc., 41(1990), 295-301.
140. The structure of quasimultipliers of C*-algebras, Transactions. Amer. Math. Soc., 315(1989), 147-172.
141. On σ-finite integrals on C*-algebras, Chin. Ann. of Math., 10(B) (4) (1989), 537-548 (in English).
142. Simplicity of the quotient algebra M(A)/A of a simple C*-algebra, Mathematica. Scandinavica, 65(1989), 119-128.
143. Fundamental approximate identities and quasi-multipliers of simple AF- C*-al gebras, Journal of Functional Analysis. 79(1988), 32-43.
144. Ideals of multiplier algebras of simple AF-C*-algebras, Proceedings Amer. Math. Soc., 104(1988), 239-244.
145. Small commutators and invariant subspaces, Proceedings Amer. Math. Soc., 96(1986), 443-446.
146. Invariant subspaces for operators U-commuting with compact operators, Journal of ECNU., Sci.ed. (4) (1985), 119-124.