### Invited talks

*Ideal free quotients of Cuntz semigroups: the dynamical Cuntz semigroup*, Minisymposium on Operator Algebras, 9ECM, July 15-19, 2024.*Pure C*-algebras*, Noncommutativity in the North – MikaelFest, Chalmers University, June 17-20, 2024.*A notion of almost finiteness for C*-dynamical systems and categorical crossed products*, C*-days in Prague, May 30-June 1, 2023.*An introduction to the modern theory of Cuntz semigroups*(joint mini-course with Eusebio Gardella), Workshop Cuntz Semigroups 2022, Kiel University, September 19-23, 2022.*A notion of almost finiteness for C*-dynamical systems and its relation to dynamical strict comparison*, The 17th Special Week on Operator Algebras, East China Normal University, August 1-5, 2022.*General quotient Cuntz semigroups and dynamical Cuntz semigroups*, Worskhop Cuntz Semigroups 2021, Münster Universität, July 12-16, 2021.*Ultraproducts of C*-algebras, their Cuntz semigroups, and their (quasi)traces*, International Conference in the Thematics Research Program: Operator Algebras, Groups, and applications to Quantum Information, June 17-21, 2019, ICMAT (Madrid).*C*-algebras of stable rank one and their Cuntz semigroup*, Research school on evolution algebras and non associative algebraic structures, October 15-17, 2018, Universidad de Málaga.*Existence of infima in the Cuntz semigroup and applications to the structure of C*-algebras with stable rank one*, IWOTA 2018, July 23-27, Shanghai.*The Cuntz semigroup as an invariant for C*-algebras*, Mini-workshop on the Cuntz semigroup, June 18-20, 2018, University of Houston.*The dynamical Cuntz semigroup: some categorical aspects*, Future targets in the classification program for amenable C*-algebras, September 4-8, 2017, BIRS (Banff).*The category of Cuntz semigroups*, Czech-Slovenian-Austrian-Slovak-Catalan Mathematical Societies Meeting, Session on Applications of Categories in Algebra and Topology, September 20-23, 2016, IEC (Barcelona).*Near unperforation, almost unperforation, and almost algebraic order*, Workshop on Classification and Dynamical Systems I, February 22-26, 2016, Mittag Leffler Institute (Stockholm).*Near unperforation for Z-stable C*-algebras*, First Joint Meeting Brazil-Spain in Mathematics, Special Session in Operator Algebras, December 7-10, 2015, Fortaleza (Brazil).*Abstract bivariant Cuntz semigroups*, Workshop on C*-algebras: Geometry and Actions, Focus Programme in C*-algebras, July 13-17, 2015, Münster Universität.*Tensor products in the category Cu and structure of Cu-semirings*, Classification, Structure, Amenability, and Regularity Conference, September 1-5, 2014, University of Glasgow.*The Cuntz semigroup and its impact into classification*, First Joint International Meeting RSME-SCM-SEMA-SIMAI-UMI, Special Session on Operator Algebras and Applications to Quantum Physics, June 30- July 1, 2014, Universidad del País Vasco (Bilbao).*Structural aspects of the category Cu*, Workshop on C*-algebras and dynamical systems, June 16-20, 2014, The Fields Institute (Toronto).*Geometric structure of dimension functions of certain continuous fields*, Classifying structures for Operator Algebras and Dynamical Systems, September 16-20, 2013, University of Aberystwyth.*Geometric structure of dimension functions on some C(X)-algebras*, Graph algebras: Bridges between Leavitt path algebras and graph C*-algebras, April 21-26, 2013, BIRS (Banff).*Regularity properties of the Cuntz semigroup*, The structure and classification of nuclear C*-algebras, April 15-19, 2013, ICMS (Edinburgh).*Semigroup valued lower semicontinuous functions (with applications to the Cuntz semigroup)*, Classification of amenable C*-algebras, September 19-24, 2010, BIRS (Banff).*Monoids of lower semicontinuous functions with applications to the Cuntz semigroup*, Workshop on C*-algebras, September 7-10, 2010, The University of Nottingham.*The Cuntz semigroup, the corona factorization property, and completions of semigroups*, Masterclass on the Classification of C*-algebras, November 16-27, 2009, University of Copenhagen.*Purely infinite corona algebras and the corona factorization property*, Workshop on the Cuntz semigroup, November 2-6, 2009, AIM (Palo Alto).*The Cuntz semigroup and its impact into classification*, II Encuentro Ibérico, October 3-5, 2008, Universidad de Extremadura.*Purely infinite corona algebras of simple stable C*-algebras*, International Conference on Operator Algebras and Applications in Morocco, April 14-18, 2008, Marrakech.- Representing semigroups as semigroups of projections of C*-algebras, Workshop on Structure of C*-algebras, November 12-16, 2007, The Fields Institute (Toronto).
*The quest for algebraic analogues: extremal richness, the QB-property, and non-stable K-theory*, Symposium honoring the memory of G. K. Pedersen, April 29 to May 1, 2005, University of Copenhagen.*Multiplier algebras have algebraic cousins*, 2nd Oresund Meeting in Non-commutative Analysis and Non-commutative Geometry, May 2, 2003, University of Copenhagen.*A closure operation in rings*, 8th Danish-Norwegian Meeting on Operator Algebras, August 2001, Lysebu.*Extremally rich C*-algebras and their algebraic relatives*, Symposium in honour of G. K. Pedersen’s 60th anniversary, May 2000, The Carlsberg Academy (Copenhagen).*Algebraic aspects in the classification of C*-algebras*, C*-algebras at Queen’s, May 1999, Queen’s University Belfast.

### Communications

*Almost elementary dynamical systems*, C*-dynamics and Set Theory in Paris, August 1-5, 2022.*The Cuntz semigroup and the category Cu*, TACL 2017, June 26-30, Praha,*Inverse limits of rings and multiplier rings*, British Mathematical Colloquium, April 2004, Queen’s University Belfast.*Límites inversos de anillos y anillos de multiplicadores,*Octavas Jornadas Españolas en Teoría de Anillos, Febrere 2004, Universidad de Oviedo.*The exchange property for Gromov translation algebras*, Algebras, Rings, and Modules, July 2003, University of Lisbon.*Analysing the ideal lattice of C*-algebras with real rank zero via AF algebras*, Noncommutative Geometry and Operator Algebras, May 2003, University College Cork.*Non-stable K-Theory and index theory for exchange rings and QB-rings*, Algebra Conference, June 2002, Venice.*Stable finiteness of group rings in arbitrary characteristic*, All Ireland Algebra Days, May 2001, Queen’s University Belfast.*Finitud estable para anillos de grupo en característica arbitraria*, Sextas Jornadas Españolas en Teoría de Anillos, April 2001, Universidad de Almería.*Index Theory for exchange rings and C*-algebras with real rank zero*, C*-algebras at Queen’s and North British Functional Analysis Seminar, May 2001, Queen’s University Belfast.*Teoría del índice para anillos de intercambio*, Quintas Jornadas Españolas en Teoría de Anillos, March 2001, Universidad de Cádiz.*Extremal richness of multiplier and corona algebras for some simple C*-algebras with real rank zero,*C*-algebras and their invariants, August 1998, University of Copenhagen.*Anillos de multiplicadores y anillos regulares*, Terceras Jornadas Españolas en Teoría de Anillos, June 1998, Universidad de Granada.*Multipliers of von Neumann regular rings and C*-algebras*, Ring Theory and Representations of Algebras, January 1998, Universidad de Murcia.*Ideales de anillos de multiplicadores de anillos regulares y C*-álgebras*, Segundas Jornadas Españolas en Teoría de Anillos, April 1997, Centre de Recerca Matemàtica (Barcelona).*Comparability relations for C*-algebras with real rank zero*, Primeras Jornadas Españolas en Teoría de Anillos, April 1996, Universidad de Murcia.