Pedro Resende

Professor at Mathematics Department, Instituto Superior Técnico

Member of Center for Mathematical Analysis, Geometry, and Dynamical Systems

Postal address:
Departamento de Matemática
Instituto Superior Técnico
Av. Rovisco Pais
1049-001 Lisboa, Portugal

Tel: +351-218417131
Fax: +351-218417035 / 598
E-mail: pmr (at) math.tecnico.ulisboa.pt
Web: http://www.math.tecnico.ulisboa.pt/~pmr/
Office: 4.28

Selected publications and preprints

Editorial: Mathematical and empirical foundations of models of consciousness, with Xerxes D. Arsiwalla, Johannes Kleiner, Sean Tull, Koby Kremnitzer, Front. Appl. Math. Stat., Vol. 9 (2023); DOI 10.3389/fams.2023.1214939.
Qualia as physical measurements: a mathematical model of qualia and pure concepts (2022); arXiv:2203.10602.
On the geometry of physical measurements: topological and algebraic aspects, J. Geom. Phys. 185 (2023) 104730; DOI 10.1016/j.geomphys.2022.104730; arXiv:2005.00933.
An abstract theory of physical measurements, Found. Phys. 51, 108 (2021); DOI 10.1007/s10701-021-00513-1; arXiv:2102.01712.
Morita equivalence of pseudogroups, with Mark V. Lawson, J. Algebra 586 (2021) 718-755; DOI 10.1016/j.jalgebra.2021.06.036; arXiv:2011.14335.
Actions of étale-covered groupoids, with Juan Pablo Quijano, J. Algebra 566 (2021) 222-258; DOI 10.1016/j.jalgebra.2020.08.032; arXiv:2002.02294.
Functoriality of groupoid quantales. II, with Juan Pablo Quijano, Appl. Categ. Structures (2021); DOI 10.1007/s10485-021-09628-y; arXiv:1803.01075.
Effective equivalence relations and principal quantales, with Juan Pablo Quijano, Semigroup Forum 99 (2019) 754-787; DOI 10.1007/s00233-019-09994-z; arXiv:1807.08979.
The many groupoids of a stably Gelfand quantale, J. Algebra 498 (2018) 197-210, DOI 10.1016/j.jalgebra.2017.11.042; arXiv:1706.06545.
Open maps of involutive quantales, Appl. Categ. Structures 26(4) (2018) 631-644, DOI 10.1007/s10485-017-9506-y; arXiv:1706.04909.
Quantales and Fell bundles, Adv. Math. 325 (2018) 312-374, DOI 10.1016/j.aim.2017.12.001; arXiv:1701.08653.
Linear structures on locales, with João Paulo Santos, Theory Appl. Categ. 31 (2016) 502-541.
Open quotients of trivial vector bundles, with João Paulo Santos, Topol. Appl. 224C (2017) 19-47, DOI 10.1016/j.topol.2017.04.001; arXiv:1510.06329.
Invariant means on Boolean inverse monoids, with Ganna Kudryavtseva, Mark V. Lawson, Daniel H. Lenz, Semigroup Forum 92 (2016) 77-101, DOI 10.1007/s00233-015-9768-3; arXiv:1503.03733.
Functoriality of groupoid quantales. I, J. Pure Appl. Algebra 219 (2015) 3089-3109, DOI 10.1016/j.jpaa.2014.10.004; arXiv:1401.8116.
Quantales of open groupoids, with M.C. Protin, J. Noncommutative Geom. 6 (2012) 199-247, DOI 10.4171/JNCG/90; arXiv:0811.4539v2.
Groupoid sheaves as quantale sheaves, J. Pure Appl. Algebra 216 (2012) 41-70, DOI 10.1016/j.jpaa.2011.05.002; arXiv: 0807.4848v3.
Étale groupoids as germ groupoids and their base extensions, with D. Matsnev, Proc. Edinb. Math. Soc. 53 (2010) 765-785; arXiv: 0807.3916.
Sheaves as modules, with E. Rodrigues, Appl. Categ. Structures 18 (2010) 199-217; arXiv:0711.4401.
An algebraic generalization of Kripke structures, with S. Marcelino, Math. Proc. Cambridge Philos. Soc. 145 (2008) 549-577; arXiv:0704.1886.
Étale groupoids and their quantales, Adv. Math. 208 (2007) 147-209, DOI 10.1016/j.aim.2006.02.004; arXiv:math/0412478.
A note on infinitely distributive inverse semigroups, Semigroup Forum 73 (2006) 156-158, DOI 10.1007/s00233-005-0547-4; arXiv:math/0506454.
Lectures on étale groupoids, inverse semigroups and quantales, Lecture Notes for the GAMAP IP Meeting, Antwerp, 4-18 September, 2006, 115 pp.
A noncommutative theory of Penrose tilings, with C.J. Mulvey, Internat. J. Theoret. Phys. 44 (2005) 655-689.
On quantales that classify C*-algebras, with D. Kruml, Cah. Topol. Géom. Différ. Catég. 45 (2004) 287-296.
Sup-lattice 2-forms and quantales, J. Algebra 276 (2004) 143-167.
On quantales and spectra of C*-algebras, with D. Kruml, J.W. Pelletier, J. Rosický, Appl. Categ. Structures 11 (2003) 543-560.
Localic sup-lattices and tropological systems, with S.J. Vickers, Theoret. Comput. Sci. 305 (2003) 311-346.
Tropological systems are points of quantales, J. Pure Appl. Algebra 173 (2002) 87-120.
Quantales, finite observations and strong bisimulation, Theoret. Comput. Sci. 254 (2001) 95-149.
Quantales and observational semantics, In B. Coecke, D. Moore, A. Wilce, editors, Current Research in Operational Quantum Logic: Algebras, Categories and Languages, 263-288, Fund. Theories Phys. 111, Kluwer Acad. Publ., 2000.
Modular specification of concurrent systems with observational logic, In J.L. Fiadeiro, editor, Recent Trends in Algebraic Development Techniques (Lisbon 1998), 310-325, Lecture Notes in Comput. Sci. 1589, Springer, Berlin, 1999.

Selected talks and short courses

The emergence of geometric worldviews in qualia space (remote talk), Third International Symposium on the Mathematics of Neuroscience, Heraklion, Crete, 24-25 September 2022.
Revisiting the measurement problem and qualia, Models of Consciousness 2021 (MoC2), on-line conference, September 27, 2021.
Revisiting quantum mechanics via quantales and groupoid C*-algebras (invited on-line talk), CLAM 2021, VI Congreso Latinoamericano de Matemáticos, session on Operator Algebras, Montevideo, Uruguay, September 16, 2021.
An abstract theory of physical measurements, on-line poster at Vienna Quantum Foundations Conference (VQF-CON 2021), Vienna, Austria, September 7-10, 2021.
An abstract theory of physical measurements, on-line poster at 18th International Conference on Quantum Physics and Logic (QPL 2021), Gdansk, Poland, June 7-11, 2021.
Sketches of a mathematical theory of qualia, Workshop on Models of Consciousness, Univ. Oxford, September 9-12, 2019.
Generalized C*-diagonals via maps of quantales, Workshop on Analysis and Synthesis for Operator Algebras, IWOTA 2019, Instituto Superior Técnico, Lisboa, Portugal, July 22-26, 2019.
A mathematical model of qualia, poster at 26th International Interdisciplinary Conference on The Science of Consciousness, Interlaken, Switzerland, June 25-28, 2019.
A quantale model of cognition, Workshop on Algebra, Logic and Topology, Univ. Coimbra, September 27-29, 2018.
Quanta and qualia, Workshop on Combining Viewpoints in Quantum Theory, ICMS, Edinburgh, March 19-22, 2018.
Quantales and Fell bundles, Workshop on Applications of Operator Algebras: order, disorder and symmetry, ICMS, Edinburgh, June 26-30, 2017.
Groupoid quantales, 37th Linz Seminar on Fuzzy Set Theory - Enriched Category Theory and Related Topics, Bildungszentrum St. Magdalena, Linz, Austria, February 7-10, 2017.
Linear structures on locales, Workshop on Dualities 2016, Univ. Coimbra, September 19-21, 2016.
Stably Gelfand quantales and C*-algebras, Fields Institute Workshop on New Directions in Inverse Semigroups, Univ. Ottawa, Canada, 1-4 June, 2016.
Étale groupoids and their quantales: functoriality, Workshop on Categorical Methods in Algebra and Topology, Univ. Coimbra, January 24-26, 2014.
Inverse semigroups and groupoids via quantales, Edinburgh Workshop on Semigroup Representations 2013, Univ. Herriot-Watt, 10-12 April 2013.
Quantales of open groupoids, Fields Institute Workshop on Semigroups and Categories, Univ. Ottawa, Canada, 2-4 Mat 2010.
Stably Gelfand quantales, groupoids and Cartan sub-C*-algebras, Fifth Workshop on Categories, Logic and Foundations of Physics, Imperial College, London, August 6, 2009.
Sheaves on groupoids and quantales (2 x 45 mins.), Workshop on Sheaves in Geometry and Quantum Theory, Nijmegen, Netherlands, 3-5 September 2008.
Noncommutative geometry and Bohr's doctrine of classical concepts, Applications of Noncommutative Geometry, Minisymposium of 5th European Congress of Mathematics (5ECM), Amsterdam, Netherlands, 17 July 2008.
Quantales and toposes, International category Theory Conference, Calais, France, 22-28 June 2008.
Quantale-valued sets, quantale modules, and groupoid actions, International Category Thery Conference, Carvoeiro, Portugal, 17-23 June 2007.<\li>
Quantales, groupoids, and C*-algebras (poster), Workshop on Trends in Noncommutative Geometry, Newton Institute, Cambridge, UK, 18-22 December 2006.
Étale groupoids, inverse semigroups and quantales, nine hour course at GAMAP: Geometric and Algebraic Methods oh Physics and Applications, Antwerp, 4-198 September 2006.
Applications of quantale theory to groupoids and inverse semigroups, Canadian Math. Soc. Summer 2006 Meeting (Category Theory session), Calgary, Canada, 3-5 June 2006.
From groupoids and inverse semigroups to supported quantales, Categories and Semigroups Workshop, Univ. Calgary, Canada, June 2, 2006.
Quantales, groupoids, and C*-algebras, Operator Algebra Workshop, Queen's Univ., Belfast, UK, 5-6 May 2006.
Quantale theory, six hour course at GAMAP: Geometric and Algebraic Methods oh Physics and Applications, Antwerp, 5-15 September 2005.
Localic germ groupoids of inverse semigroups, Workshop on Categorical Methods in Algebra, Geometry and Mathematical Physics, Australian National University, Canberra, 18-21 July 2005.
Localic germ groupoids of inverse semigroups, 81st Peripatetic Seminar on Sheaves and Logic (PSSL81), Univ. Coimbra, 9-10 April 2005.
Supported quantales: an interface between modal logic and geometry, Workshop on Logic from Quantales/OASIS seminar, Univ. Oxford, 21 January 2005.
Groupoid quantales, International Category Theory Conference, Univ. British Columbia, Vancouver, 18-24 July 2004.
A quantale that classifies Penrose tilings, European Category Theory Meeting, Haute-Bodeux, Belgium, 7-13 September 2003.
Quantales=1/2-quantization?, Sheaves and Topoi in Theoretical physics, Imperial College, London, 17-18 July 2003.
From algebras to quantales and back, Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories, Fields Institute in Toronto, Canada, 23-28 September 2002.
Quantales, C*-algebras, and Penrose tilings, Workshop on Sheaves and Topoi in Physics, Imperial College, London, 11-12 July 2002.
How quantum are quantales? International Conference on Quantum Structures, Technical Univ. Vienna, Austria, 1-7 July 2002.
On quantales and spectra of C*-algebras, IV Iberoamerican Conference on Topology and Its Applications, Coimbra, 18-21 April 2001.

Grants

FCT EXCL/MAT-GEO/0222/2012, Geometry and Mathematical Physics, 1 May 2013 - 30 April 2016 (non-PI).
FCT POCI/MAT/55958/2004: Groupoids and quantales in geometry and analysis, 14 Jul. 2005 - 13 Jul. 2008
Participation of UTL/IST at the SOCRATES IP 103466-IC-1-2003-1-BE-ERASMUS-IPUC-3: GAMAP: Geometric and Algebraic Methods of Physics and Applications (coordinated by Univ. Antwerp).
CRUP / British Council (Treaty of Windsor) Nos. B-22/04, B-68/05: Quantalic aspects of quasiperiodic tilings, 1 Apr. 2004 - 30 Dec. 2006
FCT POCTI/1999/MAT/33018: Quantales, 1 Oct. 2000 - 30 Jun. 2003
CRUP / British Council (Treaty of Windsor) No. B-29/99: Dynamic observational logic, 1 Apr. 1999 - 30 Apr. 2000

Events

GAMAP IP meeting, Antwerp, September 4-18, 2006.
GAMAP IP meeting, Antwerp, September 5-15, 2005.
Short course: Directed combinatorial homology and noncommutative geometry, Lisbon, February 9-13, 2004.
Meeting on the Theory and Applications of Quantales, Lisbon, July 16-18, 2002.

Seminars

Analysis, Geometry and Dynamical Systems
Groupoids and Noncommutative Geometry (Oct. 2005 - Apr. 2009)
Algebra Seminar (Feb. 2001 - Jul. 2003)
"Geometria em Lisboa"
Colloquium (Oct. 2001 - Dec. 2004)
"Seminário Diagonal" (Mar. 2001 - Jun. 2003)

Editorships

Frontiers Research Topic: Mathematical and Empirical Foundations of Models of Consciousness, special issue of Frontiers in Applied Mathematics and Statistics (2021)
Surv. Math. Appl. (2006-2023)

Teaching

Groups, Rings and Modules (MMAC, Fall 2022)
Algebra (LMAC, Spring 2022)
Category Theory (DMat, Spring 2022)
Topics in Algebra and Topology (DMat, Spring 2022)
Groups, Rings and Modules (MMAC, Fall 2021)
Introduction to Algebra (LMAC, Spring 2021)
Lie Groups and Lie Algebras (Math PhD, Fall 2020)
Differential and Integral Calculus (CDI-II) (MEMec+MEM+LENO: Spring 2020)
Differential and Integral Calculus (CDI-II) (MEMec+MEM+LENO: Spring 2019)
Differential and Integral Calculus (CDI-II) (LEIC+MEC+LEGM: Spring 2017)
Differential and Integral Calculus (CDI-II) (MEC+LEGM: Spring 2016)
Lie Groups and Lie Algebras (Math PhD: Fall 2015)
Differential and Integral Calculus (CDI-II) (MEC+LEGM: Spring 2015)
Differential and Integral Calculus (CDI-II) (MEC+MEFT+LEGM: Fall 2014)
Differential and Integral Calculus (CDI-II) (MEMec: Spring 2014)
Linear Algebra (LMAC+MEFT+MEBiom: Fall 2010)
Topology (LMAC: Spring 2010)
Linear Algebra (AL-3) (MEEC: Fall 2009)
Topology (LMAC: Spring 2009)
Linear Algebra (AL-10) (MEEC: Fall 2008)
Topology (LMAC: Spring 2008)
Linear Algebra (LEIC: Fall 2007)
Linear Algebra ( AL-14, AL-23: Spring 2007)
Linear Algebra (LEIC: Fall 2006)
Category Theory (LMAC, MMA: Fall 2001, Fall 2003, Spring 2005, Spring 2006)
Algebra for Logic and Computer Science (LMAC, LCI, LEIC: Spring 2005, Spring 2006)
Theory of Computation (LEIC: Fall 2005)
Noncommutative Algebra (LMAC, MMA: Spring 2003)
Ordered Algebraic Structures (LMAC, MMA: Fall 2000, Spring 2002)
Algorithms and Data Structures (LEIC: Spring 1997-2001)
Concurrent Processes (LMAC, MEIC: Fall 1996-1998, Fall 2003)

Postdocs

Rachel Dawe Martins, PhD in Mathematical Physics, Nottingham University, 2006. From 2006 to 2014 (with interruptions).
Dmitry Matsnev, PhD in Mathematics, Penn State University, 2005. From 2006 to 2008.
Radu Popescu, Doctorat de Mathematiques, Université Claude Bernard, Lyon 1, France, 2000. From 2005 to 2008.
David Kruml, PhD Math., Univ. Masaryk, Brno, Czech Rep., 2002. From 2003 to 2004.

PhD students

Zan Grad, since 2021.
Juan Pablo Quijano. Sheaves and functoriality of groupoid quantales, 2018.
Elias Rodrigues. Sheaves, local homeomorphisms and local sets as Hilbert locale modules, 2009.
Misha Protin. Quantales of open groupoids, 2008.

MSc students

Luís Dias, Measurement spaces associated to Fell bundles, 2022.
João Carvalho, A not so short introduction to Grothendieck topoi, 2013. Co-supervisor Wojciech Chachólski (KTH).
Cátia Vaz, Supports of quantales and applications to modal logic, 2004.
Vanda Lourenço, Involutive quantales and modules in a non-commutative generalization of the Gelfand representation, 2004.

Membership in scientific societies

AMCS (Association for Mathematical Consciousness Science), since 2021 (founding member).
SPM (Sociedade Portuguesa de Matemática), since 1996.
AMS (American Mathematical Society), 1997-2011.
MAA (Mathematical Association of America), 2007-2009.
EATCS (European Association for Theoretical Computer Science), 1997-2003.