Analysis Group at UB
The analysis group at UB math department has interests in various branches of mathematics related to analysis, including
analytic number theory
automorphic forms
complex geometry
dynamical systems
functional analysis
harmonic analysis
operator algebras
operator theory
quantum field theory
The group runs a weekly seminar. Past activity of the seminar can be found in the analysis seminar archive.
Faculty in Analysis Group
Currently the analysis group has 10 faculty.
Ching Chou (Ph.D., Rochester)
Lewis A. Coburn (Ph.D., University of Michigan)
My research interests include operator theory, C*-algebras, and quantum mechanics from the viewpoint of deformations of C*-algebras. The operators on which I focus are usually of Toeplitz-type and act on the square-integrable holomorphic functions on phase-space. I am interested in C*-algebras of these operators with various interesting "symbols" and the relation of such algebras to algebras of pseudo-differential operators which have been studied classically.
In the past several years, I have become interested in the structure of the Berezin symbol calculus of general operators on Bergman reproducing kernel Hilbert spaces. This calculus serves as a model for "quantization" and has been the object of considerable attention since it was introduced by Berezin in the 1970's.
My recent papers include:
W. Bauer and L. A. Coburn, "Heat flow, weighted Bergman spaces, and real-analytic Lipschitz approximation," preprint.
L. A. Coburn, "Berezin transform and Weyl-type unitary operators on the Bergman space," Proceedings of the AMS, 140 (2012) pp. 3445-3451.
L. A. Coburn, J. Isralowitz, and Bo Li, "Toeplitz operators with BMO symbols on the Segal-Bargmann space," Transactions of the AMS, 363 (2011) pp. 3015-3030.
W. Bauer, L. A. Coburn, and J. Isralowitz, "Heat flow, BMO and the compactness of Toeplitz operators", Journal of Functional Analysis 259 (2010) pp. 57-78.
L. A. Coburn and Bo Li, "Directional derivative estimates for Berezin's operator calculus," Proceedings of the AMS 136 (2008) pp. 641-649.
L. A. Coburn, "Sharp Berezin Lipschitz estimates”, Proceedings of the AMS, 135 (2007) pp. 1163-1168.
Michael J. Cowen (Ph.D., MIT)
Jonathan Dimock (Ph.D., Harvard)
James Faran, V (Ph.D., Berkeley)
Jon Kraus (Ph.D., Berkeley) Functional analysis, operator algebras, operator spaces.
Selected publications:
D Blecher and J Kraus, On a generalization of W*-modules. Banach Center Publications 91, 77-86 (2010) (Available as arXiv:0910.5404).
J. Kraus, The splitting problem for subspaces of tensor products of operator algebras, Proc. Amer. Math. Soc. 132, 1125-31 (2004).
J. Kraus, Correspondences and approximation properties for von Neumann algebras, Internat. J. Math 14, 619-665 (2003).
U. Haagerup and J. Kraus, Approximation properties for group C*-algebras and group von Neumann algebras, Trans. Amer. Math. Soc. 344, 667-699 (1994).
J. Kraus, The slice map problem and approximation properties, J. Funct. Anal. 102, 116-155 (1991).
Hanfeng Li (Ph.D., Berkeley) Operator Algebras, Noncommutative Geometry and Dynamical Systems
Hanfeng Li’s main research interest is on noncommutative geometry and dynamical systems, especially connections between operator algebras and dynamical systems. His recent work concentrates on actions of countable sofic groups and algebraic actions of general countable (amenable) groups.
Selected Publications:
D. Kerr and H. Li, "Soficity, amenability, and dynamical entropy", Amer. J. Math. to appear.
H. Li, "Compact group automorphisms, addition formulas and Fuglede-Kadison determinants". Ann. of Math. (2) 176 (2012), no. 1, 303--347.
D. Kerr and H. Li, "Entropy and the variational principle for actions of sofic groups", Invent. Math. 186 (2011), no. 3, 501--558.
G. A. Elliott and H. Li, "Morita equivalence of smooth noncommutative tori", Acta Math. 199 (2007), 1--27.
D. Kerr and H. Li, "Independence in topological and C*-dynamics ", Math. Ann. 338 (2007), no. 4, 869--926.
D. Kerr and H. Li, "Dynamical entropy in Banach spaces", Invent. Math. 162 (2005), no. 3, 649--686.
H. Li, "Strong Morita equivalence of higher-dimensional noncommutative tori", J. Reine Angew. Math. 576 (2004), 167--180.
Xiaoqing Li (Ph.D., Rutgers Univ.) Analytic number theory, automorphic forms and L-functions.
Xiaoqing Li's main research area is on analytic number theory, spectral theory of automorphic forms, trace formulas, L-functions and Langlands program. In recent years, she is especially interested in the theory of automorphic forms on higher rank groups and
bounding L-functions on the critical line.
Selected publications:
Iwaniec, Henryk and Li, Xiaoqing: “The orthogonality of Hecke eigenvalues,” Compos. Math. 143 (2007), No. 3, pp. 541-565.
Li, Xiaoqing and Sarnak, Peter: “Number variance for SL(2,Z).” www.math.princeton.edu/sarnak. 35 pp.
Li, Xiaoqing: “Bounds for GL(2)xGL(3) L-functions and GL(3) L-functions.” To appear in Annals of Mathematics. 36 pp.
Mohan Ramachandran (Ph.D., University of Illinois at Chicago)
Jingbo Xia (Ph.D., SUNY at Stony Brook)
Graduate Students in Analysis Group
Currently there are 5 graduate students in the analysis group.
Yongle Jiang
Bingbing Liang
Yongxiao Lin
Adam Orenstein