Tristan Bice

B [email protected] Í www.tristanbice.com

Degrees 1998 High School Certificate (Universities Admission Index 99.9/100). Lake Ginninderra College, Canberra, Australia

2004 Bachelor of Asian Studies (Japanese and Linguistics). Australian National University, Canberra, Australia

2005 Bachelor of Science with First Class Honours (Mathematics). Australian National University, Canberra, Australia

2009 Masters (Mathematical Logic). Kobe University, Kobe, Japan

2012 PhD (Mathematical Logic). Kobe University, Kobe, Japan

Scholarships and Prizes 1999-2005 2005 2006-2012 2012 2013 2013-2014 2014-2016

Australian National University Undergraduate Scholarship. Hanna Neumann Prize, for best Honours thesis in Mathematics. Mombukagakusho (Japan) Post-Graduate Scholarship. Fields Institute Post-Doctoral Fellowship. York University Post-Doctoral Fellowship. CAPES (Brazil) Post-Doctoral Fellowship. IMPA (Brazil) Post-Doctorate of Excellence.

Teaching Experience 1999-2005 Private Tutor, Mathematics, Physics and Japanese. 2007-2011 Teaching Assistant, Kobe University, Calculus and Linear Algebra. 2012-2013 Substitute Lecturer, York University, Analysis, Calculus and Linear Algebra.

Languages English Native Japanese Fluent Portuguese Advanced

Successfully completed the Japanese Language Proficiency Test Level 1

Talks Contributed November 16 Cardinal Invariants of Projections in the Calkin Algebra. 2009 Set Theory Workshop, Kyoto University Research Institute of Mathematical Sciences January 27 Cardinal Invariants of Projections in the Calkin Algebra. 2010 Third Indian School on Logic and its Applications, University of Hyderabad 1/3

October 27 MAD families of projections and real-valued functions on ω. 2010 Set Theory Workshop, Kyoto University Research Institute of Mathematical Sciences February 3 Playing With Projections. 2011 Winter School in Abstract Analysis: Set Theory & Topology, Hejnice, Charles University/Academy of Sciences of the Czech Republic

October 20 Filters of Projections in the Calkin Algebra. 2011 Set Theory Workshop, Kyoto University Research Institute of Mathematical Sciences

Invited (Conferences) June 19 States, Projections and C*-Algebras of Real Rank Zero. 2012 Workshop on Applications of Descriptive Set Theory to Functional Analysis, Banff International Research Station, Canada

September 22 Traces and Ultrapowers. 2012 Workshop on Applications to Operator Algebras, The Fields Institute for Research in Mathematical Sciences

March 11 Traces and Ultrapowers. 2013 Miniworkshop on Operator Algebras IV, Tokyo University May 9 Traces and Ultrapowers. 2013 North American Annual ASL Meeting, University of Waterloo June 11 Set Theory and Operator Algebras. 2013 6th Young Set Theory Workshop, Oropa, Italy February 20 Annihilators in C*-Algebras. 2014 Geometric Functional Analysis and Group Actions, Federal University of Santa Catarina April 30 Annihilators in C*-Algebras. 2014 Colloquium III of the Southern Region, Federal University of Santa Catarina January 11 Hereditary C*-Subalgebra Lattices. 2015 Joint Mathematics Meetings AMS Special Session on Classification Problems in Operator Algebras, San Antonio, Texas

January 21 Hereditary C*-Subalgebra Lattices. 2015 Summer Thematic Program: Logic and Topology, Federal University of Bahia

February 23 Hereditary C*-Subalgebra Lattices. 2015 Workshop on Functional Analysis and Dynamical Systems, Federal University of Santa Catarina

May (TBA). 2016 Workshop on Operator Algebras and Dynamical Systems, University of Ottawa July (TBA). 2016 Institute of Mathematics, Polish Academy of Sciences Conference: Transfinite methods in Banach spaces and algebras of operators, Be¸dlewo, Poland

Invited (Lecture Series) February 3-7 Ortholattices and Operator Algebras. 2014 15th Annual Summer School, Federal University of Santa Catarina November 23-27 Non-Commutativity in Topology, Analysis, Algebra and Set Theory. 2015 University of São Paulo

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Publications Journal Articles with Charles A. Hereditary C*-subalgebra lattices. Akemann Adv. Math. 285 (2015) 101-137 doi:10.1016/j.aim.2015.07.027 with Ilijas Farah Traces, Ultrapowers and the Pedersen-Petersen C*-Algebras. Houston J. Math 41(4) (2015) 1175-1190 http://math.uh.edu/~hjm/Vol41-4.html

*-Annihilators in proper *-semigroups. Semigroup Forum 90(2) (2015) 425-448 doi:10.1007/s00233-014-9611-2

Type Decomposition in Posets. Math Slovaca (to appear) ArXiv:1403.4172

The Projection Calculus. Münster J. Math. 6 (2013), 557-581 http://wwwmath.uni-muenster.de/mjm

Filters in C*-Algebras. Canad. J. Math. 65 (2013), 485-509 doi:10.4153/CJM-2011-095-4

The Order on Projections in C*-Algebras of Real Rank Zero. Bull. Polish Acad. Sci. Math. 60 (2012) 37-58 doi:10.4064/ba60-1-4

MAD families of projections on `2 and real-valued functions on ω. Arch. Math. Logic 50(7-8) (2011) 791-801 doi:10.1007/s00153-011-0249-4

Preprints (under review) *-Accretives in *-Rings. (2016) ArXiv:1601.02270 (submitted to J. Algebra)

Distances. (2015) ArXiv:1503.03147 (submitted to Topology Appl.)

Conference Proceedings Generalized Mathias Forcing. Set Theory Workshop: Interplay between large cardinals and small cardinals, October 25-28 (2010) 1-5 Editor: Hiroshi Sakai, Kyoto RIMS http://hdl.handle.net/2433/171199

Meagre Subsets of ω [0, 1] and B(l2 ). Set Theory Workshop: Combinatorial set sheory and forcing theory, November 16-19 (2009) 1-15 Editor: Teruyuki Yorioka, Kyoto RIMS http://hdl.handle.net/2433/141474

Theses PhD Set Theory of the Calkin Algebra. Kobe University (2012)

Masters Set Theory of Hilbert Spaces and Hilbert Space Operators. Kobe University (2009)

Honours Kaplansky’s Uniform Norm Problem and the Super-Real Fields. Australian National University (2005)

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