Papers and preprints

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Book draft (with Guoliang Yu): Higher Index Theory
This is more-or-less a complete draft. The book has now been published by Cambridge University Press, with the published version a little different.
This document contains errata to the published version. Any comments appreciated!

Papers (ordered more-or-less by date of completion, with the most recent first).

• Conditional representation stability, classifying *-homomorphisms, and relative eta invariants. pdf
   Preprint.
  
  
• The rational HK-conjecture: transformation groupoids and a revised version. pdf
   Joint work with Robin Deeley.
   To appear, Münster Journal of Mathematics.
  
  
• Coarse equivalence versus bijective coarse equivalence of expander graphs. pdf
   Joint work with Florent Baudier, Bruno de Mendonça Braga, Ilijas Farah, and Alessandro Vignati.
   Mathematische Zeitschrift, 307 (2024), 44.
  
  
• Embeddings of von Neumann algebras into uniform Roe algebras and quasi-local algebras. pdf
   Joint work with Florent Baudier, Bruno de Mendonça Braga, Ilijas Farah, and Alessandro Vignati.
   Journal of Functional Analysis, 286 (2024), 110186.
  
  
• Complexity rank for C*-algebras. pdf
   Joint work with Arturo Jaime.
   Münster Journal of Mathematics, 16 (2023), 51-94.
  
  
• Uniform Roe algebras of uniformly locally finite metric spaces are coarsely rigid. pdf
   Joint work with Florent Baudier, Bruno de Mendonça Braga, Ilijas Farah, Ana Khukhro, and Alessandro Vignati.
   Inventiones Mathematicae, 230 (2022), 1071-1100.
  
  
• The UCT for C*-algebras with finite complexity. pdf
   Joint work with Guoliang Yu.
   Memoirs of the European Mathematical Society, 8 (2024).
  
  
• Controlled KK-theory, and a Milnor exact sequence. pdf
   Joint work with Guoliang Yu.
   Preprint.
  
  
• Dynamic asymptotic dimension and Matui's HK conjecture. pdf
   Joint work with Christian Bönicke, Clément Dell'Aiera, and Jamie Gabe.
   Proceedings of the London Mathematical Society, 126 (2023), 1182-1253.
  
  
• The UCT problem for nuclear C*-algebras. pdf
   Joint work with Nate Brown, Sarah Browne, and Jianchao Wu.
   Rocky Mountain Journal of Mathematics, 52 (2022), 817-827.
  
  
• Amenability and weak containment for actions of locally compact groups on C*-algebras. pdf
   Joint work with Alcides Buss and Siegfried Echterhoff.
   To appear, Memoirs of the American Mathematical Society.
  
  
• Bounded derivations on uniform Roe algebras. pdf
   Joint work with Matthew Lorentz.
   Rocky Mountain Journal of Mathematics, 50 (2020), 1757-1758.
  
  
• Approximate ideal structures and K-theory. pdf
   New York Journal of Mathematics, 27 (2021), 1-52.
  
  
• Injectivity, crossed products, and amenable group actions. pdf
   Joint work with Alcides Buss and Siegfried Echterhoff.
   Contemporary Mathematics, 749 (2020), 105-137.
  
  
• Bott periodicity and almost commuting matrices. pdf
   Contemporary Mathematics, 749 (2020), 379-388.
  
  
• Topological property (T) for groupoids. pdf
   Joint work with Clément Dell'Aiera.
   Annales de l'Institut Fourier, 72 (2022), 1097-1148.
  
  
• The maximal injective crossed product. pdf
   Joint work with Alcides Buss and Siegfried Echterhoff.
   Ergodic Theory and Dynamical Systems, 40 (2020), 2995-3014.
  
  
• The minimal exact crossed product. pdf
   Joint work with Alcides Buss and Siegfried Echterhoff.
   Documenta Mathematica, 23 (2018), 2043-2077.
  
  
• Cartan subalgebras of uniform Roe algebras. pdf
   Joint work with Stuart White.
   Groups, Geometry, and Dynamics, 14 (2020), 949-989.
  
  
• Low dimensional properties of uniform Roe algebras. pdf
   Joint work with Kang Li.
   Journal of the London Mathematical Society, 97 (2018), 98-124.
  
  
• Localization C*-algebras and K-theoretic duality. pdf
   Joint work with Marius Dadarlat and Jianchao Wu.
   Annals of K-theory, 3 (2018), 615-630.
  
  
• Dynamical complexity and controlled operator K-theory. pdf
   Joint work with Erik Guentner and Guoliang Yu.
   To appear, Astérisque.
  
  
• Roe C*-algebras for groupoids and generalized Lichnerowicz vanishing theorem for foliated manifolds. pdf
   Joint work with Xiang Tang and Yi-Jun Yao.
   Mathematische Zeitschrift, 290 (2018), 1309-1338.
  
  
• Exotic crossed products. pdf
   Joint work with Alcides Buss and Siegfried Echterhoff.
   Operator Algebras and Applications (Proceedings of the Abel Symposium 2015), 61-108.
  
  
• Exactness and the Kadison-Kaplansky conjecture. pdf
   Joint work with Paul Baum and Erik Guentner.
   Contemporary Mathematics, 671 (2016).
  
  
• A non-amenable groupoid whose maximal and reduced C*-algebras are the same. pdf
   Münster Journal of Mathematics, 8 (2015), 241-252.
  
  
• Dynamic asymptotic dimension: relation to dynamics, topology, coarse geometry, and C*-algebras. pdf
   Joint work with Erik Guentner and Guoliang Yu.
   Mathematische Annalen, 367 (2017), 785-829.
  
  
• Exotic crossed products and the Baum-Connes conjecture. pdf
   Joint work with Alcides Buss and Siegfried Echterhoff.
   Journal für die Reine und Angewandte Mathematik, 740 (2018), 111-159.
  
  
• A metric approach to limit operators. pdf
   Joint work with Ján Špakula.
   Transactions of the American Mathematical Society, 369 (2017), 263-308.
  
  
• Random graphs, weak coarse embeddings, and higher index theory. pdf
   Journal of Topology and Analysis, 7 (2015), 361-388.
  
  
• Geometric property (T). pdf
   Joint work with Guoliang Yu.
   Chinese Annals of Mathematics Series B, 35 (2014), 761-800.
  
  
• Expanders, exact crossed products, and the Baum-Connes conjecture. pdf
   Joint work with Paul Baum and Erik Guentner.
   Annals of K-theory, 1 (2016), 155-208.
  
  
• Ghostbusting and property A. pdf
   Joint work with John Roe.
   Journal of Functional Analysis, 266 (2014), 1674-1684.
  
  
• A finite dimensional approach to the strong Novikov conjecture. pdf
   Joint work with Daniel Ramras and Guoliang Yu.
   Algebraic and Geometric Topology, 13 (2013), 2283-1316.
  
  
• Uniform local amenability. pdf
   Joint work with Jacek Brodzki, Graham Niblo, Ján Špakula, and Nick Wright.
   Journal of Noncommutative Geometry 7 (2013), 583-603.
  
  
• On rigidity of Roe algebras. pdf
   Joint work with Ján Špakula.
   Advances in Mathematics 249 (2013), 289-310.
  
  
• Property A and girth of graphs. pdf
   Journal of Topology and Analysis 3 (2011), 377-384.
  
  
• Higher index theory for certain expanders and Gromov monster groups II. pdf
   Joint work with Guoliang Yu.
   Advances in Mathematics 229 (2012), 1762-1803.
  
  
• Higher index theory for certain expanders and Gromov monster groups I. pdf
   Joint work with Guoliang Yu.
   Advances in Mathematics 229 (2012), 1380-1416.
  
  
• Maximal and reduced Roe algebras of coarsely embeddable spaces. pdf
   Joint work with Ján Špakula.
   Journal für die Reine und Angewandte Mathematik, 678 (2013), 35-68.
  
  
• An index theorem for band-dominated operators with slowly oscillating coefficients (after Deundyak and Shteinberg). pdf
   Integral Equations and Operator Theory 69 (2011), 301-316.
  
  
• Some 'homological' properties of the stable Higson corona. pdf
   Journal of Noncommutative Geometry 7 (2013), 203-220.
  
  
• Band-dominated operators and the stable Higson corona. pdf
   Thesis, Penn State University, 2011.
  
  
• Some notes on Property A. pdf
   Limits of Graphs in Group Theory and Computer Science, 191-281, EPFL press, Lausanne 2009.

My research is currently supported by NSF grant DMS 2247968 and Simons Foundation Travel Grant MP-TSM-00002363.