PhD Thesis

**Continuous Fields of C*-algebras, their Cuntz Semigroup and the Geometry of Dimension Functions,**Universitat Autònoma de Barcelona, 26 September 2013. [pdf of Thesis] [Presentation] Supervisor: Francesc Perera (UAB).

Publications

- With M. Christensen
**"The failure of the Corona Factorization Property for the Villadsen algebra V_\infty "**, Maths. Scan, to appear. [pdf]- With H. Petzka,
**"Comparison properties of the Cuntz semigroup and applications to C*-algebras"**, Canadian J. of Mathematics, to appear. [pdf]- With P. Ara, R. Hazrat and A. Sims,
**"Reconstruction of graded groupoids from graded Steinberg algebras"**, Forum Mathematicum, to appear. [pdf]- With G. Tornetta and J. Zacharias,
**"Open projections and suprema in the Cutnz semigroup"**, Mathematical Proceedings Cambridge Philosophical Society, to appear. [pdf]- With N. Brown, Y. Sato, A. Tikuisis, S. White, W. Winter,
**"Covering Dimension of C*-algebras and 2-coloured classification"**, Memoirs of the American Mathematical Society, to appear. [pdf]- With Marius Dadarlat,
**"Local triviality for continuous field C*-algebras"**, International Mathematics Research Notices (IMRN) 4 (2015), pp 1044-1055. [pdf] - With H. Petzka,
- With Ramon Antoine, Francesc Perera and Henning Petzka,
**"Geometric structure of dimension functions on certain continuous fields"**, J. Funct. Anal., 266 (2014), no.4, pp. 2403-2423. [pdf] - With Ramon Antoine and Francesc Perera,
**"The Cuntz semigroup of Continuous Fields"**, Indiana Univ. Math. J. 62 (2013), no.4, pp. 1105-1131. [pdf] - With Ramon Antoine and Francesc Perera,
**"Completions of monoids with applications to the Cuntz Semigroup"**, in International Journal of Mathematics, 22 (6) (2011), pp. 837-861. [pdf]

In press:

Preprints

- With G. Tornetta and J. Zacharias,
**"A Bivariant Theory for the Cuntz Semigroup"**. [pdf]

Research Stays

**Institut Mittag-Leffler.**Invited researcher during the Classification of Operator algebras: Complexity, Rigidity, and Dynamics Programme. February 2016**University of Muenster.**Invited researcher during the Focus Programme on C*- Algebras. April-May 2015**Fields Institute of Toronto.**Invited researcher during the Theme Period on C*-Algebras and Dynamical Systems. June 2014

### Talks

#### Comunications

**"Classification of C*-algebras. Comparison Properties of the Cuntz semigroup and applications to C*-algebras"**, presented at Special weeek on Operator Algebras, Research Center of Op. Algebras, East China Normal University, Shanghai, China. June 2016.**"Comparison properties on Cu-semigroups, with applications to C*-algebras"**, presented in "Workshop Classification and Dynamical systems I:C*-algebras", Mittag-Leffler Institute, Stockholm. February 2016.**"Covering Dimension and 2-coloured classification"**, presented in "Edinburgh Math. Soc.-Soc. Catalana de Mat. joint meeting", Barcelona. May 2015.**"Equivalent definitions of the Corona Factorization Property"**, presented in "Workshop on C*-algebras: Structure and Classification", University of Muenster. April 2015.**"Nuclear Dimension of Kirchberg Algebras"**, presented in "Conference of Classification, Structure, Amenability and Regularity (CSTAR)", University of Glasgow. September 2014.**"The Category Cu. Which maps are the correct ones? *-homomorphisms or cpc order zero maps?"**, presented in "Workshop on C*-algebras and Dynamical Systems" Fields Institute of Toronto. June 2014.**"The Category Cu. Which maps are the correct ones? *-homomorphisms or cpc order zero maps?"**, presented in "Scottish Operator Algebras Seminar", University of Glasgow. March 2014.**"Local triviality for Continuous Fields of C*-algebras"**, presented in "School and Workshop: Topics in Operator Algebras and Applications" ICMAT-International Ciencias Matemáticas. September 2013.**"Local triviality of Continuous Fields"**,presented in "The structure and classification of nuclear C*-algebras" ICMS-International Centre for Mathematical Sciences April 2013.**"Dimension functions on C(X,A)"**, presented in "Wabash Modern Analysis Mini-conference" Indiana University-Purdue University. September 2012.**"The Cuntz semigroup of Continuous Fields"**, presented in "Jornadas Españolas de Teoríax de Anillos" Universidad de Granada. June 2012.**"Dimension functions on C*-algebras"**, presented in "Master Class on the Nuclear Dimension of C*-algebras" University of Copenhaguen. November 2011.**"The Cuntz semigroup of certain C(X)-algebra"**,presented in "Conference on Structure and Classification of C*-algebras" CRM-Centre Recerca Matemàtica, Bellaterra. June 2011.**"The Cuntz semigroup of a C(X)-algebra"**,presented in "Great Plains Operator Theory Symposium 2011" University of Phoenix. May 2011.**"C*-algebras and their classification"**, presented in "Jornada de Joves Matemàtics de la Societat Catalana de Matemàtiques (SCM)" Barcelona. November 2010.**"Classification of Monoids. Applications to the Cuntz semigroup"**, presented in "Master Class on Classification of C*-algebras", University of Copenhaguen. November 2009.

#### Seminar Talks

**"Comparison Properties of the Cuntz Semigroup and applications to C*-algebras"**, Algebra seminar, Universitat Autònoma de Barcelona, May 2016.**"Classification of C*-algebras and the Category Cu"**, Operator Algebra seminar, University of Wollongong, October 2015.**"Classification of maps by traces"**, Operator Algebra seminar, Newcastle University, February 2015.**"Classificationof maps by traces"**, Operator Algebra seminar, University of Muenster, March 2014.**"The Category Cu. Which maps are the correct ones? *-homomorphisms or cpc order zero maps?"**, Geometry-Analysis seminar, Queen Mary-University of London, March 2014.**"The Cuntz semigroup of some Continuous Fields**, Operator algebra seminar, University of Glasgow, December 2013.**"The Cuntz semigroup and Dimension Functions on C(X,A)**, Operator algebra seminar, Purdue University, U.S.A., October 2012.**"The Cuntz semigroup of certain C(X)-algebras"**, Operator algebra talk, CRM-Centre de Recerca Matemàtica, Bellaterr, May 2011.**"Completions of monoids. Applications to the Cuntz Semigroup"**, Operator algebra talk,Department of Mathematical Sciences-University of Copenhaguen, February 2010.**"Complecions de Semigrups: Aplicacions al Semigrup de Cuntz (II)"**, Algebra seminar, Departament de Matemàtiques-Universitat Autònoma de Barcelona, October 2009.**"Complecions de Semigrups: Aplicacions al Semigrup de Cuntz (I)"**, Algebra seminar, Departament de Matemàtiques-Universitat Autònoma de Barcelona, October 2009.

### Organized Scientific Events

- Organizer of
**"Operator Algebra seminars"**, at University of Glasgow since Jan. 2014. - With S. White, W. Winter and J. Zacharias organized the Conference
**"Classification, Structure, Amenability and Regularity (CSTAR)"**, University of Glasgow, 1-5 Set. 2014. - With S. White, W. Winter and J. Zacharias organized the Master Class
**"Classification, Structure, Amenability and Regularity (CSTAR)"**, University of Glasgow, 21-29 May 2014. - With Ramon Antoine, Pere Ara and Francesc Perera organized the Workshop
**"Workshop on Dynamics and C*-algebras"**, in CRM-Centre Recerca Matemàtica, Bellaterra, 6-8 April , 2011. - With Ramon Antoine, Pere Ara and Francesc Perera, organized the Conference
**"Structure and Classification of C*-algebras"**, in CRM-Centre Recerca Matemàtica, Bellaterra, 6-10 June , 2011. - With Ramon Antoine, Pere Ara and Francesc Perera, organized the Advanced course
**"Structure and Classification of C*-algebras"**, in CRM-Centre Recerca Matemàtica, Bellaterra, 6-10 June , 2011.