HR job title
- Professor
- Contact Info
Yu, Guoliang Professor
Positions
- Professor, Mathematics, College of Arts and Sciences
My research focuses on noncommutative geometry, K-theory of operator algebras, index theory, topology and analysis of manifolds, and geometric group theory.
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Overview
Publications
selected publications
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academic article
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Xie, Z., & Yu, G.
(2021).
Delocalized Eta Invariants, Algebraicity, and K-Theory of Group C*-Algebras. 2021(15), 11731-11766.
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Gong, S., Wu, J., & Yu, G.
(2021).
The Novikov conjecture, the group of volume preserving diffeomorphisms and Hilbert-Hadamard spaces. GEOMETRIC AND FUNCTIONAL ANALYSIS.
31(2), 206-267.
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Weinberger, S., Xie, Z., & Yu, G.
(2021).
Additivity of Higher Rho Invariants and Nonrigidity of Topological Manifolds. Communications on Pure and Applied Mathematics.
74(1), 3-113.
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Fu, B., Wang, X., & Yu, G.
(2020).
The Equivariant Coarse Novikov Conjecture and Coarse Embedding. 380(1), 245-272.
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Chen, X., Liu, H., & Yu, G.
(2020).
Higher invariant is an obstruction to the inverse being local. Journal of Geometry and Physics.
150, 103592-103592.
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Chang, S., Weinberger, S., & Yu, G.
(2020).
Positive scalar curvature and a new index theory for noncompact manifolds. Journal of Geometry and Physics.
149, 103575-103575.
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Oyono-Oyono, H., & Yu, G.
(2019).
Quantitative K-theory and the Knneth formula for operator algebras. Journal of Functional Analysis.
277(7), 2003-2091.
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Yu, G.
(2019).
The Novikov conjecture. Russian Mathematical Surveys.
74(3(447)), 167-184.
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Ramras, D. A., Tessera, R., & Yu, G.
(2019).
Addendum to Finite decomposition complexity and the integral Novikov conjecture for higher algebraic K-theory (J. reine angew. Math. 694 (2014), 129178). Journal fuer die Reine und Angewandte Mathematik: Crelle's journal.
2019(746), 305-310.
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Douglas, R. G., Jabbari, M., Tang, X., & Yu, G.
(2018).
A new index theorem for monomial ideals by resolutions. Journal of Functional Analysis.
275(3), 735-760.
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Connes, A., Nest, R., Schick, T., & Yu, G.
(2018).
Non-commutative Geometry, Index Theory and Mathematical Physics. Oberwolfach Reports.
15(3), 1911-1981.
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Guentner, E., Willett, R., & Yu, G.
(2017).
Dynamic asymptotic dimension: relation to dynamics, topology, coarse geometry, and C-algebras. Mathematische Annalen.
367(1-2), 785-829.
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Xie, Z., & Yu, G.
(2017).
Higher rho invariants and the moduli space of positive scalar curvature metrics. Advances in Mathematics.
307(Mat. Sb.18911998), 1046-1069.
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Yu, G.
(2017).
The Novikov conjecture for algebraic K-theory of the group algebra over the ring of Schatten class operators. Advances in Mathematics.
307, 727-753.
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Douglas, R. G., Tang, X., & Yu, G.
(2016).
An analytic Grothendieck Riemann Roch theorem. Advances in Mathematics.
294, 307-331.
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Weinberger, S., & Yu, G.
(2015).
Finite part of operator K theory for groups finitely embeddable into Hilbert space and the degree of nonrigidity of manifolds. Geometry and Topology.
19(5), 2767-2799.
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Oyono-Oyono, H., & Yu, G.
(2015).
K-thorie quantitative pour les algbres doprateurs. Annales de l'Institut Fourier.
65(2), 605-674.
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Chen, X., Wang, Q., & Yu, G.
(2015).
The coarse Novikov conjecture and Banach spaces with Property (H). Journal of Functional Analysis.
268(9), 2754-2786.
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Connes, A., Cuntz, J., Vaes, S., & Yu, G.
(2015).
Noncommutative Geometry. Oberwolfach Reports.
12(2), 1631-1700.
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Ramras, D. A., Tessera, R., & Yu, G.
(2014).
Finite decomposition complexity and the integral Novikov conjecture for higher algebraic K-theory. Journal fuer die Reine und Angewandte Mathematik: Crelle's journal.
2014(694), 129-178.
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Willett, R., & Yu, G.
(2014).
Geometric property (T). Chinese Annals of Mathematics: Series B.
35(5), 761-800.
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Xie, Z., & Yu, G.
(2014).
A relative higher index theorem, diffeomorphisms and positive scalar curvature. Advances in Mathematics.
250, 35-73.
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Xie, Z., & Yu, G.
(2014).
Positive scalar curvature, higher rho invariants and localization algebras. Advances in Mathematics.
262, 823-866.
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Guentner, E., Tessera, R., & Yu, G.
(2013).
Discrete groups with finite decomposition complexity. Groups, Geometry, and Dynamics.
7(2), 377-402.
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Ramras, D., Willett, R., & Yu, G.
(2013).
A finite-dimensional approach to the strong Novikov conjecture. Algebraic and Geometric Topology.
13(4), 2283-2316.
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Chen, X., Wang, Q., & Yu, G.
(2013).
The maximal coarse Baum-Connes conjecture for spaces which admit a fibred coarse embedding into Hilbert space. Advances in Mathematics.
249, 88-130.
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Connes, A., Cuntz, J., Rieffel, M., & Yu, G.
(2013).
Noncommutative Geometry. Oberwolfach Reports.
10(3), 2553-2629.
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Kasparov, G., & Yu, G.
(2012).
The Novikov conjecture and geometry of Banach spaces. Geometry and Topology.
16(3), 1859-1880.
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Guentner, E., Tessera, R., & Yu, G.
(2012).
A notion of geometric complexity and its application to topological rigidity. Inventiones Mathematicae.
189(2), 315-357.
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Willett, R., & Yu, G.
(2012).
Higher index theory for certain expanders and Gromov monster groups, I. Advances in Mathematics.
229(3), 1380-1416.
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Willett, R., & Yu, G.
(2012).
Higher index theory for certain expanders and Gromov monster groups, II. Advances in Mathematics.
229(3), 1762-1803.
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Guentner, E., Tessera, R., & Yu, G.
(2011).
Operator norm localization for linear groups and its application to K-theory. Advances in Mathematics.
226(4), 3495-3510.
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Connes, A., Cuntz, J., Rieffel, M., & Yu, G.
(2011).
Noncommutative Geometry. Oberwolfach Reports.
2549-2622.
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Chang, S., Weinberger, S., & Yu, G.
(2010).
Taming 3-manifolds using scalar curvature. Geometriae Dedicata.
148(1), 3-14.
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Oyono-Oyono, H., & Yu, G.
(2009).
K-theory for the maximal Roe algebra of certain expanders. Journal of Functional Analysis.
257(10), 3239-3292.
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Gong, G., Wang, Q., & Yu, G.
(2008).
Geometrization of the Strong Novikov Conjecture for residually finite groups. Journal fuer die Reine und Angewandte Mathematik: Crelle's journal.
2008(621), 159-189.
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Chang, S. S., Ferry, S., & Yu, G.
(2008).
Bounded rigidity of manifolds and asymptotic dimension growth. 1(1), 129-144.
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Chen, X., Tessera, R., Wang, X., & Yu, G.
(2008).
Metric sparsification and operator norm localization. Advances in Mathematics.
218(5), 1496-1511.
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Kasparov, G., & Yu, G.
(2006).
The coarse geometric Novikov conjecture and uniform convexity. Advances in Mathematics.
206(1), 1-56.
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Yu, G.
(2005).
Hyperbolic groups admit proper affine isometric actions on lp-spaces. GEOMETRIC AND FUNCTIONAL ANALYSIS.
15(5), 1144-1151.
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Chen, X., Dadarlat, M., Guentner, E., & Yu, G.
(2003).
Uniform embeddability and exactness of free products. Journal of Functional Analysis.
205(1), 168-179.
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Dranishnikov, A. N., Gong, G., Lafforgue, V., & Yu, G.
(2002).
Uniform Embeddings into Hilbert Space and a Question of Gromov. Canadian Mathematical Bulletin.
45(1), 60-70.
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Mineyev, I., & Yu, G.
(2002).
The Baum-Connes conjecture for hyperbolic groups. Inventiones Mathematicae.
149(1), 97-122.
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Skandalis, G., Tu, J. L., & Yu, G.
(2002).
The coarse BaumConnes conjecture and groupoids. Topology.
41(4), 807-834.
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Yu, G.
(2000).
The coarse BaumConnes conjecture for spaces which admit a uniform embedding into Hilbert space. Inventiones Mathematicae.
139(1), 201-240.
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Gong, G., & Yu, G.
(2000).
Volume growth and positive scalar curvature. GEOMETRIC AND FUNCTIONAL ANALYSIS.
10(4), 821-828.
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Kaminker, J., & Yu, G.
(1999).
Boundary Amenability of Groups and Positive Scalar Curvature. K-Theory: interdisciplinary journal for the development, application and influence of K-theory in the mathematical sciences.
18(1), 93-97.
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Yu, G.
(1998).
Asymptotic Fredholm Modules, Vector Bundles with Small Variation and a Nonvanishing Theorem for K-Theoretic Indices. K-Theory: interdisciplinary journal for the development, application and influence of K-theory in the mathematical sciences.
13(4), 331-346.
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Yu, G.
(1998).
The Novikov Conjecture for Groups with Finite Asymptotic Dimension. Annals of Mathematics.
147(2), 325-325.
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Yu, G.
(1997).
Localization algebras and the coarse Baum--Connes conjecture. K-Theory: interdisciplinary journal for the development, application and influence of K-theory in the mathematical sciences.
11(4), 307-318.
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Yu, G.
(1997).
Zero-in-the-spectrum conjecture, positive scalar curvature and asymptotic dimension. Inventiones Mathematicae.
127(1), 99-126.
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YU, G.
(1997).
K-Theoretic Indices of Dirac Type Operators on Complete Manifolds and the Roe Algebra. K-Theory: interdisciplinary journal for the development, application and influence of K-theory in the mathematical sciences.
11(1), 1-15.
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Yu, G. L.
(1995).
Cyclic Cohomology and Higher Indexes for Noncompact Complete Manifolds. Journal of Functional Analysis.
133(2), 442-473.
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Douglas, R. G., Glazebrook, J. F., Kamber, F. W., & Yu, G.
(1995).
Index formulas for geometric Dirac operators in Riemannian foliations. K-Theory: interdisciplinary journal for the development, application and influence of K-theory in the mathematical sciences.
9(5), 407-441.
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Yu, G.
(1995).
Baum-Connes conjecture and coarse geometry. K-Theory: interdisciplinary journal for the development, application and influence of K-theory in the mathematical sciences.
9(3), 223-231.
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Yu, G.
(1995).
Coarse Baum-Connes conjecture. K-Theory: interdisciplinary journal for the development, application and influence of K-theory in the mathematical sciences.
9(3), 199-221.
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Higson, N., Roe, J., & Yu, G.
(1993).
A coarse MayerVietoris principle. Cambridge Philosophical Society: Mathematical Proceedings.
114(1), 85-97.
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Xie, Z., & Yu, G.
(2021).
Delocalized Eta Invariants, Algebraicity, and K-Theory of Group C*-Algebras. 2021(15), 11731-11766.
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book
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Willett, R., & Yu, G.
(2020).
Higher Index Theory. Cambridge University Press.
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Nowak, P. W., & Yu, G.
(2012).
Large Scale Geometry. Samfundslitteratur.
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Willett, R., & Yu, G.
(2020).
Higher Index Theory. Cambridge University Press.
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chapter
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Xie, Z., & Yu, G.
(2019).
Higher invariants in noncommutative geometry. Advances in Noncommutative Geometry.
(pp. 691-751).
Springer Nature.
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Chang, S., Weinberger, S., & Yu, G.
(2017).
Contractible manifolds with exotic positive scalar curvature behavior. Manifolds and -Theory.
(pp. 51-64).
American Mathematical Society (AMS).
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Xie, Z., & Yu, G.
(2015).
Noncommutative Geometry of Discrete Groups. Cheng, S. Y., Ji, L., Poon, Y. S., Xiao, J., Yang, L., & Yau, S. T. (Eds.),
Introduction to Modern Mathematics.
International Press.
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Xie, Z., & Yu, G.
(2019).
Higher invariants in noncommutative geometry. Advances in Noncommutative Geometry.
(pp. 691-751).
Springer Nature.
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conference paper
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Yu, G.
(2006).
Higher index theory of elliptic operators and geometry of groups. 1623-1639.
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Yu, G.
(2006).
Higher index theory of elliptic operators and geometry of groups. 1623-1639.
Research
principal investigator on
- Higher Invariants of Elliptic Operators and Applications awarded by Directorate for Mathematical & Physical Sciences - (Arlington, Virginia, United States) 2020 - 2023
- K-Theory of Operator Algebras and Its Applications awarded by National Science Foundation - (Arlington, Virginia, United States) 2017 - 2020
- FRG: Collaborative Research: Noncommutative Dimension Theories awarded by National Science Foundation - (Arlington, Virginia, United States) 2016 - 2020
- K-theory of Operator Algebras and Its Applications to Geometry and Topology awarded by National Science Foundation - (Arlington, Virginia, United States) 2014 - 2018
- Noncommutative Geometry-Festival awarded by National Science Foundation - (Arlington, Virginia, United States) 2014 - 2015
- Operator K-Theory and its Applications to Geometry and Topology awarded by National Science Foundation - (Arlington, Virginia, United States) 2013 - 2015
co-principal investigator on
- Great Plains Operator Theory Symposium 2019- awarded by National Science Foundation - (Arlington, Virginia, United States) 2019 - 2020
- Conference: International Workshop on Operator Theory and its Applications 2018 awarded by National Science Foundation - (Arlington, Virginia, United States) 2018 - 2020
Teaching
teaching activities
- MATH323 Hnr-linear Algebra Instructor
- MATH409 Advanced Calculus I Instructor
- MATH636 Topology I Instructor
- MATH656 Functional Analysis Ii Instructor
- MATH662 Seminar In Algebra Instructor
- MATH666 Seminar In Geometry Instructor
- MATH685 Directed Studies Instructor
- MATH689 Sptp: Noncommutative Geometry Instructor
- MATH689 Sptp:topological Insulators I Instructor
- MATH691 Research Instructor
- MATH691 Research Instructor
Background
education and training
- Mathematical Sciences Research Institute - (Berkeley, California, United States) , Postdoctoral Training
- Ph.D. in Mathematics, Stony Brook University - (Stony Brook, New York, United States) 1991
awards and honors
Contact
first name
- Guoliang
has last name
- Yu
mailing address
-
Texas A&M University
Mathematics
3368 TAMU
College Station, TX 77843-3368
USA
Other
- guoliangyu@tamu.edu