Andrew S. Toms Curriculum Vitae

Contact Information Personal Information

Department of Mathematics Born March 12, 1975, Montreal, PQ Purdue University Married with two sons 150 N. University St., West Lafayette, IN Canadian and British citizen 47907-2067 US Permanent Resident Telephone: (765) 494-1901 [email protected]

Education 1999–2002 Ph.D. University of Toronto 1997–1999 M.Sc. University of Toronto 1993–1997 B.Sc.H. Queen’s University

Employment 2013–2018 University Faculty Scholar, Purdue University 2013–present Professor, Purdue University 2010–2013 Associate Professor, Purdue University 2008–2010 Associate Professor, York University 2006–2008 Assistant Professor, York University 2004–2006 Assistant Professor, University of New Brunswick 2003–2004 NSERC Postdoctoral Fellow, Copenhagen University

Honours and Awards 1. Purdue University Faculty Scholar, 2013-2018 2. AMS Centennial Fellowship 2011-12 3. CMS Gilbert de Beauregard Robinson Award (with Wilhelm Winter) 4. Israel Halperin Prize 20101 5. Canada Research Chair Nomination, 2009 (declined) 6. Ontario Early Researcher Award2, 2008–2013 7. NSERC Postdoctoral Fellowship, 2003–2004 8. Daniel B. DeLury Teaching Award, University of Toronto, 2003 9. Israel Halperin Graduate Award, University of Toronto, 2001–2002 10. NSERC Postgraduate Scholarship, 1997–2001 11. Governor General’s Medal3, Queen’s University, 1997 12. Prince of Wales Prize4, Queen’s University, 1997

1Awarded every ﬁve years to the mathematician from the Canadian community within 10 years of his/her Ph.D. deemed to have made the greatest contribution to operator algebras. 2Comparable an NSF CAREER Award in terms of funds to researcher. 3Awarded to the graduate with the highest aggregate GPA. 4Awarded to the graduate deemed by the Chancellor to have the best academic record. 1 2

Research Interests Operator algebras and their classiﬁcation, K-theory; a particular interest in points of contact between operator algebras and algebraic and differential topology, dynamics, and set theory.

Publications

1. Minimal dynamics and K-theoretic rigidity: Elliott’s Conjecture (with W. Winter) Geometric and Functional Analysis (in press), 13p. 2. The descriptive set theory of C∗-algebra invariants (with I. Farah and A. Tornquist)¨ International Mathematics Research Notices (in press), 27p. 3. C∗-algebras, dynamics, and classification (with T. Giordano, D. Kerr, and N. C. Phillips) Solicited volume for Birkhauser’s CRM Advanced Course series (in press, approx. 200p.) 4. Turbulence, orbit equivalence, and the classification of nuclear C∗-algebras (with I. Farah and A. Tornquist)¨ Journal fur¨ die reine und angewandte Mathematik (in press), 46p. 5. Characterizing classifiable AH algebras Mathematical Reports of the Royal Society of Canada (in press), 4p. 6. The radius of comparison: an algebraic approach (with B. Blackadar, L. Robert, A. Tikuisis, and W. Winter) Transactions of the American Mathematical Society (in press), 18p. 7. K-theoretic rigidity and slow dimension growth Inventiones Mathematicae 183 (2011), 225-244 8. The Cuntz semigroup and the classification of C∗-algebras (with P. Ara, N.P. Brown, D. Guido, F. Lledo, and F. Perera, Lecture notes for Summer School at UIMP, San- tander, Spain, in July 2008) Contemporary Mathematics 534 (2011), vii+168p. 9. Ranks of operators in simple C∗-algebras (with M. Dadarlat) Journal of Functional Analysis 259 (2010), 209-229 10. Minimal dynamics and the classification of C∗-algebras (with W. Winter) Proceedings of the National Academy of Sciences of the United States of America 106 (2009), 16942-16943 11. Z-stability and infinite tensor powers of C∗-algebras (with M. Dadarlat) Advances in Mathematics 220 (2009), 341-366 12. A class of simple C∗-algebras with stable rank one (with G. A. Elliott and T. Ho) Journal of Functional Analysis 256 (2009), 307-322 13. Comparison theory and smooth minimal C∗-dynamics Communications in Mathematical Physics 289 (2009), 401-433 3

14. The Elliott conjecture for Villadsen algebras of the first type (with W. Winter) Journal of Functional Analysis 256 (2009), 1311-1340 15. The Jiang-Su algebra does not always embed (with M. Dadarlat, I. Hirshberg, and W. Winter) Mathematical Research Letters 16 (2009), 23-26 16. A direct proof of Z-stability for AH algebras of bounded dimension (with M. Dadarlat and N. C. Phillips) Bulletin of the London Mathematical Society 41 (2009), 639-653 17. The Cuntz semigroup, the Elliott conjecture, and dimension functions on C∗-algebras (with N. P. Brown and F. Perera) Journal fur¨ die reine und angewandte Mathematik 621 (2008), 191-211 18. Inductive limits of K-theoretic complexes with torsion coefficients (with S. Eilers) Journal of K-theory 1 (2008), 145-168 19. Z-stable ASH algebras (with W. Winter) Canadian Journal of Mathematics 60 (2008), 703-720 20. Stability in the Cuntz semigroup of a commutative C∗-algebra Proceedings of the London Mathematical Society 96 (2008), 1-25 21. Regularity properties in the classification program for separable amenable C∗-algebras (survey, with G. A. Elliott) Bulletin of the American Mathematical Society 45 (2008), 229-245 22. On the classification problem for nuclear C∗-algebras Annals of Mathematics 167 (2008), 1059-1074 23. An infinite family of non-isomorphic C∗-algebras with identical K-theory Transactions of the American Mathematical Society 360 (2008), 5343-5354 24. Strongly self-absorbing C∗-algebras (with W. Winter) Transactions of the American Mathematical Society 359 (2007), 3999-4029 25. Recasting the Elliott conjecture (with F. Perera) Mathematische Annalen 338 (2007), 669-702 26. Three applications of the Cuntz semigroup (with N. P. Brown) International Mathematics Research Notices, Vol. 2007, Article rnm068, 14p. 27. Dimension growth for C∗-algebras Advances in Mathematics 213 (2007), 820-848 28. Cancellation does not imply stable rank one Bulletin of the London Mathematical Society 38 (2006), 1005-1008 29. Flat dimension growth for C∗-algebras Journal of Functional Analysis 238 (2006), 678-708

30. Inﬁnitely generated perforated ordered K0-groups Mathematica Scandinavica 36 (2005), 147-160 31. On the independence of K-theory and stable rank Journal fur¨ die reine und angewandte Mathematik 578 (2005), 185-199 4

∗ 32. Strongly perforated K0-groups of simple C -algebras Canadian Mathematical Bulletin 46 (2003), 457-472 33. Comparison of four SNR estimators for QPSK modulations (with N. C. Beaulieu and D. R. Pauluzzi) IEEE Communications Letters 4 (2000), 43-45

Manuscripts submitted or in preparation 1. Z-stability and ﬁnite dimensional extreme tracial boundaries Submitted to IMRN 2. Ranks of operators in simple C∗-algebras II (with A. Tikuisis), Submitted to Illinois Journal of Mathematics 3. The Cuntz semigroup and perturbations of C∗-algebras (with F. Perera, S. White, and W. Winter), Submitted to Analysis and PDE 4. Isomorphism of separable C∗-algebras is below a group action (with G. Elliott, I. Farah, V. Paulsen, C. Rosendal, and A. Tornquist)¨ Submitted to Proceedings of the National Academy of Sciences of the United States of America 5. Mean dimension and the structure of crossed products (with T. Hines and N. C. Phillips), working draft, 70p.

Conference Presentations (includes accepted invitations, all talks plenary save AMS/CMS Sessions) 1. Workshop on C∗-algebras (50 minutes), Oberwolfach, 08/13 2. Canadian Operator Symposium (50 minutes), Toronto, 05/13 3. ICMS workshop on C∗-algebras (50 minutes), Edinburgh, 04/13 4. Fields Institute 20th Anniversary Colloquium Series (50 minutes), Toronto, 09/12 5.C ∗-algebras (50 minutes), Shanghai, 04/12 6. Conference for Eberhard Kirchberg’s 65th birthday (50 minutes), Copenhagen, 11/11 7. Virginia Operator Theory and Complex Analysis Symposium (keynote speaker, 2 x 50 minutes), 11/11 8.C ∗-algebras and related topics (50 minutes), RIMS Kyoto, 09/11 9. Conference for David Handelman’s 65th birthday (50 minutes), Ottawa, 8/11 10.C ∗-algebras, dynamics, and classiﬁcation (50 minutes), CRM Barcelona, 06/11 11. Canadian Operator Algebras Symposium (50 minutes), Victoria, 05/11 12. Great Plains Operator Theory Symposium (50 minutes), Phoenix, 05/11 13. North British Functional Analysis Seminar (2x60 minutes), Glasgow, 11/10 14. East Coast Operator Algebras Symposium (50 minutes), Dartmouth College, 10/10 15. Midwest Topology Seminar (50 minutes), Wayne State, 10/10 16. Canadian Operator Symposium (50 minutes), Fredericton, 06/10 17.C ∗-algebras (40 minutes), Oberwolfach, 03/10 5

18. AIM workshop ”The Cuntz Semigroup” (50 minutes), Palo Alto, 11/09 19. West Coast Operator Algebras Symposium (50 minutes), Reno, 10/09 20. Operator Algebras (50 minutes), Qinhuangdao, China, 09/09 21. CMS Winter Meeting (25 minutes), Ottawa, 12/08 22. East Coast Operator Algebras Symposium (25 minutes), Penn State, 10/08 23. Wabash Mini-conference (50 minutes), IUPUI, 09/08 24.C ∗-algebras (40 minutes), Oberwolfach, 08/08 25. Canada-France Math Congress (50 minutes), Montreal, 06/08 26. Canadian Operator Symposium (25 minutes), Toronto, 05/08 27. AMS Meeting, Session on Operator Algebras (25 minutes), Bloomington, 04/08 28.C ∗-algebras Workshop (50 minutes), Fields Institute, 11/07 29. East Coast Operator Algebras Symposium (25 minutes), Wellesley College, 09/07 30. Operator Algebras (50 minutes), East China Normal University, Shanghai, 06/07 31.C ∗-algebras and their Invariants (50 minutes), CRM Barcelona, 06/07 32. AMS Meeting, Session on Operator Algebras (25 minutes), Tucson, 04/07 33. Wabash Modern Analysis Seminar (50 minutes), Wabash College, 04/07 34. Wabash Mini-conference (50 minutes), IUPUI, 09/06 35. Great Plains Operator Symposium (25 minutes), Iowa City, 05/06 36. Operator Algebras and Mathematical Physics (50 minutes), Settat, Morocco, 12/05 37.C ∗-algebras (50 minutes), Oberwolfach, 08/05 38. Canadian Operator Symposium (25 minutes), Ottawa, 06/05 39. Banff International Research Station Workshop on Amenable Systems (25 minutes), 10/04 40. Canadian Operator Symposium (25 minutes), Waterloo, 05/04 41. Weekend Meeting on Operator Algebras (50 minutes), Fields Institute, 03/04 42. Operator Algebras and Mathematical Physics 2 (25 minutes), Sinaia, Romania, 07/03 43. Canadian Operator Symposium (25 minutes), Thunder Bay, 05/02 44. AMS Meeting, Session on Operator Algebras (25 minutes), San Francisco, 10/00 45. Canadian Operator Symposium (25 minutes), Charlottetown, 05/99 46. CMS Winter Meeting (25 minutes), Kingston, 12/98

Summer Schools and Lecture Series 1. Appalachian Set Theory Workshop, 6 x 1 hour, Fields Institute, 9/12 2. Master Class on the Nuclear Dimension of C∗-algebras, 5 x 1 hour, Copenhagen University, 11/11 3. Advanced Course on C∗-algebras, Dynamics, and Classification, 5 x 1 hour, Centre de Re- cerca Matematica, Bellaterra, Spain, 06/11 4. Classification of separable amenable C∗-algebras, 5 x 1 hour, Pacific Institute for the Mathematical Sciences Summer School, University of Victoria, 07/10 5. The Cuntz semigroup and the classification of C∗-algebras, 4 x 45 minutes, EU Semester on Non-commutative Geometry, University of Copenhagen, 11/09 6. Classifying the C∗-algebras of smooth dynamical systems, 3 x 1 hour, Texas A&M Concentration Week on C∗-algebras and Dynamics, 07/08 6

7. The Cuntz semigroup, 3 x 1.5 hours, Summer School at the Universidad Internacional Menendez Pelayo, Santander, Spain, 07/08 8. K-theory and the structure of stably ﬁnite C∗-algebras, 4 x 2 hours, Subsection of Fields Institute Graduate Course, 09/07 9. K-theory for Operator Algebras, 2 x 2 hours, Mini-course on Operator Theory, University of New Brunswick, 06/06

Seminars and Colloquia 1. Colloquium, Indiana University, 10/11 2. Subfactors Seminar, Vanderbilt, 01/11 3. Colloquium, Wayne State University, 11/10 4. Colloquium, Washington University, 08/10 5. Colloquium, University of Nevada, Reno, 10/09 6. Colloquium, University of Oregon, 10/09 7. Functional Analysis Seminar, University of Nevada, Reno, 10/09 8. Functional Analysis Seminar, University of Oregon, 10/09 9. Functional Analysis Seminar, Nottingham University, 06/09 10. Operator Algebras Seminar, Fields Institute, 01/09 11. Colloquium, University of Ottawa, 12/08 12. Colloquium, Purdue University, 11/08 13. Topology Seminar, Wayne State University, 11/08 14. Functional Analysis Seminar, Texas A&M University, 11/08 15. Colloquium, Texas A&M University, 11/08 16. Colloquium, Queen’s University, 10/08 17. Colloquium, Penn State University, 10/08 18. Colloquium, Purdue University, 09/08 19. Colloquium, Dartmouth College, 04/08 20. Colloquium, University of Toronto, 11/07 21. Analysis Seminar, Guelph University, 09/07 22. Probabilistic Operator Algebras Seminar, Queen’s University, 07/07 23. Functional Analysis Seminar, Tongji University, Shanghai, 06/07 24. Ring Theory Seminar, Universitat Autonoma de Barcelona, 06/07 25.C ∗-algebras Seminar, Arizona State University, 04/07 26. Functional Analysis Seminar, University of Illinois at Urbana-Champaign, 04/07 27. Toronto Set Theory Seminar, 02/07 28. Operator Theory Seminar, University of Toronto, 01/07 29. Operator Algebras Seminar, Purdue University, 12/06 30. Geometric and Functional Analysis Seminar, Penn State University, 11/06 31. Analysis Seminar, SUNY Buffalo, 10/06 32. Operator Theory Seminar, University of Toronto, 10/06 33. Operator Algebras Seminar, Fields Institute, 09/06 7

34. Colloquium, University of Ottawa, 02/06 35. Colloquium, York University, 01/06 36. Operator Algebras Seminar, Fields Institute, 07/05 37. Ring Theory Seminar, Universitat Autonoma de Barcelona, 05/05 38. Colloquium, University of Prince Edward Island, 03/05 39. Colloquium, University of New Brunswick, 01/04 40. Non-commutative Geometry Seminar, University of Munster,¨ 10/03 41. Operator Algebras Seminar, University of Southern Denmark, 10/03 42. Operator Algebras Seminar, Queen’s University, 09/03 43. Mathematical Physics Seminar, McGill University, 09/03 44. Functional Analysis Seminar, Waterloo University, 09/03 45. Colloquium, University of Toronto, 09/03 46. Operator Algebras Seminar, University of Southern Denmark, 03/03 47. Operator Algebras Seminar, Copenhagen University, 02/03 48. Operator Algebras Seminar, MSRI, 11/00

Visiting Positions (one month or more) 1. Centre de Recerca Matematica, Barcelona, 06/11 2. Fields Institute, 07/07–12/07 3. Centre de Recerca Matematica, Barcelona, 05/07 4. Fields Institute, 07/05 5. Centre de Recerca Matematica, Barcelona, 05/05 6. Mathematical Sciences Research Institute, 09/00–12/00

Grants and Other Support (I am PI unless otherwise noted.) 1. Agency: Purdue University Title: University Faculty Scholar Amount: $50,000 Duration: 07/13–06/18 2. Agency: American Mathematical Society Title: 2011 AMS Centennial Fellowship Amount: $86,900 Duration: 07/11–06/13 3. Agency: National Science Foundation Title: Ninth East Coast Operator Algebras Symposium (DMS-1139717) Amount: $28,080 Duration: October 14–16, 2011 4. Agency: Centre de Recerca Matematica Title: Visiting Fellowship Amount: $2,500 Duration: 06/11 5. Agency: National Science Foundation Title: The Cuntz semigroup and the classiﬁcation of C∗-algebras (DMS-1067890) 8

Amount: $80,500 (co-PI with Nate Brown, funds primarily used to support untenured researchers participating in a CRM thematic program) Duration: 03/11–02/12 6. Agency: National Science Foundation Title: Hilbert modules and the structure of C∗-algebras (DMS-0969246) Amount: $152,800 Duration: 07/10–06/13 7. Agency: Mitacs Title: Matching grant for postdoctoral fellowship Amount: $25,000 Duration: 05/10–04/11 8. Agency: Natural Sciences and Engineering Research Council of Canada Title: Discovery Grant Amount: $24,000 Duration: 04/10–03/11 9. Agency: Mitacs Title: Matching grant for postdoctoral fellowship Amount: $25,000 Duration: 07/08–06/09 10. Agency: Ontario Ministry of Research and Innovation Title: Early Researcher Award Amount: $190,000 Duration: 04/08–03/13 11. Agency: Fields Institute for the Mathematical Sciences Title: Teaching Buyout Grant Amount: $7,000 Duration: 09/07–12/07 12. Agency: Centre de Recerca Matematica Title: Visiting Fellowship Amount: $6,000 Duration: 05/07 13. Agency: Centre de Recerca Matematica Title: Visiting Fellowship Amount: $6,000 Duration: 05/05 14. Agency: Natural Sciences and Engineering Research Council of Canada Title: Discovery Grant Amount: $65,000 Duration: 04/05–03/10 9

Conferences and Research Programs Organized 1. Member of the Organizing Committee, Fields Institute Thematic Program on Abstract Harmonic Analysis, 01/14–06/14 2. Member of the Organizing Committee, Banff International Research Station 5-day Workshop on C∗-algebras and Dynamics: Amenability and Soficity 3. Member of the Organizing Committee, Great Plains Operator Theory Symposium, 06/14 4. Member of the Organizing Committee, International Centre for Mathematical Sci- ences (Edinburgh) workshop on The Structure and Classification of Nuclear C∗-algebras, 04/13 5. Member of the Organizing Committee, Oberwolfach workshop on C∗-algebras, dynamics, and classification, 11/12 6. Member of the Organizing Committee, Fields Institute workshop on Set Theory and C∗-algebras, 10/12 7. Contact Organizer, Banff International Research Station 5-day Workshop on Set The- ory and Functional Analysis, 06/12 8. Member of the Organizing Committee, East Coast Operator Algebras Symposium, 09/11 9. Member of the Organizing Committee, 6-month program “Classification of C∗-algebras and the Cuntz semigroup”, Centre de Recerca Matematica (CRM), Bellaterra, Spain, 01/11–06/11 10. Contact Organizer, Banff International Research Station 5-day Workshop on Classifi- cation of C∗-algebras, 09/10 11. Member of the Organizing Committee, American Institute of Mathematics 5-day Work- shop on the Cuntz semigroup, 11/09 12. Member of the Organizing Committee, Texas A&M Concentration Week on C∗-algebras and Dynamics, 07/08 13. Budgeting/local organization, Fields Institute Thematic Program on Operator Alge- bras, 07/07–12/07 14. Member of the Organizing Committee, 2008 Canadian Operator Symposium, 05/08 15. Member of the Organizing Committee, Fields Institute 5-day Workshop on C∗-algebras, 11/07 16. Contact Organizer, Banff International Research Station 5-day Workshop on C∗-algebras Associated to Discrete and Dynamical Systems, 01/08 17. Main Organizer, University of New Brunswick Mini-course on Operator Theory, 06/06 18. Co-organizer, Functional Analysis Session at the Atlantic Provinces Council on the Sciences Fall Meeting, 10/04

Refereeing for research articles I have refereed manuscripts for the following journals: Duke Mathematical Journal, American Journal of Mathematics, Advances in Mathematics, Crelle’s Journal, Communications in Mathematical Physics, Mathematische Annalen, Journal of Noncom- mutative Geometry, Journal of Functional Analysis, K-theory, Journal of the London Mathematical 10

Society, Indiana University Journal of Mathematics, Illinois Journal of Mathematics, International Mathematics Research Notices, International Journal of Mathematics, Bulletin of the London Mathe- matical Society, M¨unsterJournal of Mathematics, Proceedings of the American Mathematical Society, Archiv der Mathematik, Canadian Mathematical Bulletin, Canadian Journal of Mathematics, Mathe- matical Reports of the Canadian Royal Society, Journal of Operator Theory.

Reviews for grant proposals I have reviewed funding applications for the following institutes and agencies: 1. National Science Foundation 2. Natural Sciences and Engineering Research Council of Canada 3. Ontario Graduate Scholarships 4. Simons Foundation 5. The Fields Institute

Teaching Experience and Awards Undergraduate: MAT 196 Calculus for Engineering Science (at U. of Toronto) MATH 1823 Calculus for Management Sciences (at U. of New Brunswick) MATH 3343 Graph Theory (x2, at U. of New Brunswick) MATH 3083 Intro to the Mathematics of Finance (at U. of New Brunswick) MATH 3103 Analysis I (at U. of New Brunswick) MATH 1025 Honours Calculus (at U. of New Brunswick) MATH 1025 Linear Algebra (at York) MATH 4010 Honours Analysis (at York) MATH 1013 Differential Calculus (at York) MATH 2320 Discrete Mathematics (at York) MA 341 Introduction to Real Analysis MA 261 Calculus III

Graduate: MATH 6023 Functional Analysis (at U. of New Brunswick) MATH 6280 Measure Theory (at York) MATH 6001 K-theory for C∗-algebras (at York) MATH 6462 Functional Analysis II: Spectral Theory and Operator Algebras (at York) MATH 6461 Functional Analysis I (x3, at York) MA 546 Functional Analysis

Awards: Daniel B. DeLury Teaching Award, University of Toronto, 2003 Teaching Assistant’s Award, Queen’s University, 1999 Douglas Tutorship, Queen’s University, 1994 11

Workshops: Completed new faculty teaching workshops at York University and Purdue Uni- versity.

Supervision Undergraduate: NSERC Summer Student Timothy Mahwhinney Summer 2006 NSERC Summer Student Daniel Hay Summer 2006

Graduate: Ph.D. candidate Taylor Hines September 2010–present Ph.D. candidate Michael Cheong August 2010–present Ph.D. candidate Randombage Silva August 2011–present Ph.D. candidate Wei Zhang October 2011–present

Postdoctoral: Caleb Eckhardt (co-supervisor with M. Dadarlat, August 2010–present Ph.D. UIUC) (Assistant Professor at Miami University)

Ping Wong Ng (co-supervised, Ph.D. UCLA) July 2004–June 2005 (Assistant Professor University of Louisiana)

Toan Ho Minh (Ph.D. Toronto) October 2006–December 2007 (Assistant Professor at Vietnam Academy of Science and Technology, Ha Noi)

Kris Coward (Ph.D. Toronto) September 2007–December 2007 (currently working in the private sector)

Leonel Robert (Ph.D. Toronto) September 2008–August 2010 (Assistant Professor at University of Louisiana)

Ivan Dynov (Ph.D. MPI Bonn) January 2009–August 2010

Adam Sierakowski (Ph.D. Copenhagen) August 2009–August 2010 (currently a postdoctoral fellow at The Fields Institute)

Service

1. Canadian Mathematical Society’s (CMS) Publications Committee, 2008–2011 2. Graduate Committee, 2011–present 3. Scholarship Committee, 2011–present 4. TA Screening Committee, 2011 12

5. Colloquium Chair, 2012–2013