My Academic Track

Sebastia Xambo-Descamps (SX)Jordi Girona 1-3, UPC/Omega/428, Barcelona 08034

sebastia.xambo@upc.edu

Abstract

This is an extension of the document presented in Spring 2015 to the Re-search and Academic Committees of the Universitat Politecnica de Catalunya(UPC)1 by the Faculty of Mathematics and Statistics (FME), The Facultyof Informatics (FIB) and the Department of Mathematics (MAT) proposingSX as Emeritus Professor of Mathematics. The main additions are: Section1, Short CV; a list of published materials at the end; the main academicproductions in the last two years; an update of the main current projects;and the paragraphs Further comments appended to the original sections orsubsections.

General justification of the proposal

SX fulfills the requirements to be nominated as Emeritus Professor of Math-ematics of the UPC: he has a positive evaluation of the maximum numberof five-year teaching stages and of six-year administration stages. His mainresponsibilities and achievements in the service of the University and of themathematics community for 46-years, with emphasis on the last 22 as a FullProfessor of Information and Coding Theories at UPC, are described in thesections 2-12. For a more complete list of the published materials, see theReferences at the end added to this version in a time-line style. For a morestructured view, see SX’s Web page.

1. Short CV

EducationPhD in Mathematics, UB (1981)

1To ease the reading, acronyms have been collected in section 15, page 17. The firstoccurrence of an acronym is only occasionally preceeded by its definition.

MSc Mathematics, Brandeis University (1978)Licenciado en Matematicas con Grado, UB (five-year degree, winner ofthe Extraordinary Prize)Languages: Catalan & Spanish (native); English & French (fluent);German, Italian, Portuguese (reading)

StatusProfessor Emeritus of Mathematics, UPC (since 2015).

Positions heldFull Professor of Information and Coding Theory, UPC (1993-2015).Vice-rector of Information and Documentation Systems, UPC(1998-2002).Full Professor of Algebra and Algebraic Geometry, UCM (1989-1993).Profesor Titular (tenured), UB (1982-1989).Fulbright-Hays Grant, Brandeis University (1977-1979).Several temporary positions at the UB (1969-1977 and 1979-1981) andUAB (1972-1976).

Main subjects taughtGeometry (sophomore), Mathematics for Physicists (sophomore), Math-ematical Models of Physics (junior), Coding Theory (senior or gradu-ate), Algebra (junior), Commutative Algebra (senior), Algebraic Ge-ometry (senior and graduate), Data and Image Processing (senior).

Main reseach interestsAlgebraic Geometry, Intersection Theory, Enumerative Geometry.Information Theory and Coding Theory, Error-Correcting Codes.Effective Methods for Computer Mathematics, Symbolic Computation.Mathematical Models in Physics and Engineering. Geometric Algebraand Geometric Calculus.

Some Research VisitsEmmy Noether Institute (Eilat, Israel, January 2003)Steklov Institute (Moscow, October 1991)Max Planck Institute fur Mathematik (Bonn, Germany, June and July1988) and Copenhagen Mathematics Institute (August 1988).

Major Research & Development AwardsMember of the mOlto project, 7th EU FP(ICT-2009, 2 M€; 2010-2013).Member of JEM, eContentPlus Thematic Network (800 K€; 2006-2009).

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Member of WebALT, eContent Project supported by the EuropeanCommission (2.5 M€; 2005 and 2006).Coordinator the project that led to the Wiris mathematical platformand founding member of M4M (1994-2001).Several grants, as main researcher, of the Spanish Science Council.

Selected Service ActivitiesPresident of the Catalan Mathematical Society (1995-2002).President of the Executive Committee of the 3rd European Congressof Mathematics (2000).President of the Spanish Conference of Deans of Mathematics (1995-2002).

2. Stage 1969-1976 (UB and UAB)

Assistant Professor at the Facultat de Matematiques (FM) of the Universitatde Barcelona (UB) since 1969 (the same year of finishing the five-year “Licen-ciatura en Ciencias (Matematicas)” with “Premio Extraordinario”) and also,since 1972, Assistant Professor at the Universitat Autonoma de Barcelona(UAB). The subjects taught were Geometry (sophomore), Commutative Alge-bra (senior) and Mathematics for Physicists (sophomore). In December 1973wins the “Catedra de Matematiques” of the High School “Jaume Balmes”and for the remaining three years combines the teaching there with that atthe UB and UAB.

Publishes the two-volume book Algebra Lineal y Geometrıas Lineales (ap-peared in 1977 and 1978, respectively) and a short memoir on the axiomaticfoundations of projective geometry. Research initiation in Algebraic Geom-etry through the seminars run by Federico Gaeta at UPC (Summer 1975and Summar 1976).Further comments. The two volumes [2, 3], with well over 900 pages in all,had a substantial influence in several generations. They were concerned withapplications in Mathematics, like the foundations of the minimum squaresmethod and of linear programming, and in Physics, like the dynamics of rigidbodies or the deduction of the Lorentz transformations without assumingthat c is a constant. The algorithmic and computational points of view wereimportant threads.

The aim of the memoir, Fundamentos de Geometrıa Proyectiva, was abrief account of how the linear algebra structure emerges from purely geo-metric axioms (see [1]; a recent revision was included as the first part of [95].The Gaeta seminars paved the way for next stage.

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3. Fulbright-Hays grant

Spent the terms 1977-78 and 1978-79 at the University of Brandeis (Waltham,Massachusetts, USA) with a Fulbright-Hays grant and a leave of abasencefrom the Balmes High School. Takes advanced courses in Geometric Analysis(Nolan Wallach), Algebraic Topology and Characteristic Classes (JeromeBruner). In 1978 obtains the MSc/Mathematics under the supervisionof David Buchsbaum and Teruhisa Matsusaka. Participates in the dis-cussions in the Matsusaka Seminar. Later was guided in the research ofalgebraic geometry and commutative algebra by David Eisenbud. Attendedregularly the weekly colloquium Brandeis-Harvard-MIT.

4. PhD and UB tenure (1979-1988)

Returns to Barcelona in 1979. While still committed to the Balmes job,teaches Projective Geometry and Algebraic Geometry at the UB under a part-time contract. In 1981 defends the PhD thesis, Variedades de grado mınimo(cum laude). In 1982 wins a tenured full-time position at the Department ofAlgebra and Geometry of the UB.

In 1983 organizes, in collaboration with Eduard Casas and Gerald Wel-ters, the international conference Week of Algebraic Geometry held in Sitges(Barcelona) and is coeditor of the corresponding proceedings volume as LNiM1124 (416 p; see [9]). One year later publishes, in collaboration with EduardCasas, The enumerative theory of conics after Halphen as LNiM 1196 (130pag.; see [11]). In 1987 organizes, in collaboration with Eduard Casas, theinternational conference Enumerative Geometry, again in Sitges, and editsthe corresponding proceedings as LNiM 1436 (303 p; see [17]).

In 1986 justifies, in collaboration with Steven L. Kleiman (MIT) andStein Arild Strømme (Bergen), with contemporary techniques, the number,given by Schubert, of quadrics that are tangent to 12 given quadrics (see[14]). For an extensive review of the Enumerative Geometry in Barcelona inthis period, see the article in memoriam of S. A. Strømme in the September2014 EMS Newsletter (see [94]).

The Summer of 1988 visits for two months the Max-Planck Institutein Bonn, invited by Fredrich Hirzebruch, and afterwards the CopenhagenMathematics Institute for one month, invited by Anders Thorup and StevenL. Kleiman.

In this period supervises the PhD theses of Rosa M. Miro-Roig withthe title Haces reflexivos en espacios proyectivos and of Francesc Rossellowith the title Calcul de grups de Chow i aplicacions.

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Further comments. For a condensed version of the PhD thesis, see [5]. Seealso the papers [6, 7]. Papers related to the book with Casas: [10, 13]. Anoffshoot of the 1981 memoir [4] was the paper [12] with Rossello, withwhom also published [15, 19]. The visits to Max-Planck and Copenhagencontributed significantly in making possible to win in the next year the com-petition for a full-professorship at UCM.

Interest for the history of mathematics, and particularly biography, hasbeen constant since the undergraduate times. One early paper, [8], is awrite-up of an invited lecture in a day devoted to the history of Geometry.

5. Full Professor at UCM, 1989-1993

In 1989 wins the competion for a full professorship of Algebra and AlgebraicGeometry in the “Departamento de Algebra” of the UCM. In this periodwrites, in collaboration with Felix Delgado and Concha Fuertes, Intro-duccion al Algebra (three volumes) that were published in 1992, 1998 and2000 (see [22, 32, 40]).

Was main organizer of the Algebraic Geometry Seminar, visited by a longlist of international experts, as for example Steven L. Kleiman (MIT) andDavid Eisenbud (University of California at Berkeley).

Supervises the PhD thesis of Carles Victoria (1964-2004), with the titleContribuciones al estudio de las supervariedades (defended in 1993).Further comments. Continues a productive collaboration with Josep M. Miretfocused on understanding and completing Schubert’s numbers about sin-gular cubics: [16, 18, 20, 24]. The paper [20] appeared in the Proceedings ofthe 1989 Zeuthen Symposium, attended by the authors, and also the paper[21] written in collaboration with Claudio Procesi. Another contributionto a conference (Cortona, Italy, 1992) was [25].

At the end of this period, was invited by Sevın Recillas to teach anintensive course on intersection theory in Mexico (Morelia y Guanajuato).The notes were published as a book that appeared in 1996 (see [30]).

In the previous period, collaborated with a group of physicists of the UB,including Joaquim Gomis and Josep M. Pons, in trying to understand stringtheories. SX participated in the seminar with several lectures on geometricmethods in Physics, a contribution that was replicated in the University ofFlorence in 1987. The paper [27] was written after the discovery of a deepconnection between string theories and enumerative geometry. The alreadyquoted paper [94] gives an account of the evolution of these ideas up to ourdays.

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Another reflection stemmed from Jose M. Montesinos asking how toexplain that the word ‘spectrum’ was used to denote the space of maximal(or prime) ideals of a ring. The answer was [26].

6. Full Professor at UPC (since 1993)

In 1993 wins the competion for the full-professorship of Information The-ory and Coding Theory at the the Department of Applied Mathematics ofthe UPC with teaching assigned at the newly launched FME. The memoirprepared for this opening meant a deep immersion in the algorithmic andapplied aspects of Algebra, Algebraic Geometry and Number Theory. Thebenefit of this effort is most visible in the Coding Theory course (senior)taught at the FME for over a decade. It is in the context of this disciplinethat the project Omega was conceived (1994) and developed. The projectlead to the preparation of several “Technological projects” (equivalent to amaster’s thesis), including those of Ramon Eixarch and Daniel Marques.This initiative evolved into the creation in 1999 of the company M4M jointlywith students that had contributed to Omega. The star product turned outto be Wiris, a powerful, versatile, multilingual and interactive computationalplatform which has since been a computational facility in many educationaland research environments around the world. An example of its use was tosupport the computations related to the book Block Error-Correcting Codes,a Computational Primer (Springer, 2003, 265 p; see [48]).

In addition to Coding Theory, he has also taught Geometry (second year)and Mathematical Models of Physics (third year) for several years. Thebook written for teaching Geometry won the 1996 teaching innovation prizeawarded by UPC and was published by “Edicions UPC” in 1997, with asecond edition in 2001 (see [31]).

In this period supervised the PhD thesis of Josep M. Miret, with the titleContribuciones al estudio de la geometrıa enumerativa de la curvas cubicascuspidales (defended in 2000, it won the “Premio extraordinario de doctora-do” of the UPC); of Josep Elgueta, with the title Cohomologıa y Teorıa dedeformaciones de 2-categorıas semigrupales, defended in 2002 (cosupervisedby Louis Crane, of the University of Kansas); and of Maria Bras, with thetitle Improving evaluation codes, defended in 2003 (cosupervised by MichaelO’Sullivan, of the University of California at San Diego).

Also supervised several master thesis in Applied Mathematics and Math-ematical Engineering:

• 2007/08: Juanjo Rue, Un model matematic per a la computacio quan-tica: fonaments, algorismes i implementacions.

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• 2008/09: Gerard Tarrago, Algorismes PBP per a la visio estereo.The context of this thesis was the Visio Project that will be consideredlater.

• 2010/11: Jordi Tura, Mathematical and Technological Aspects of Quan-tum Information Processing.

• 2011/12: Narcıs Sayols, Mathematical methods of signal processing.

• 2011/12: Jose Tejedor, On the quantization of Yang-Mills equations.

In the case of Rue, Tura and Sayols, also supervised the Final Projectfor their degree in Telecommunications Engineering.Further comments. On the first term at the FME, was invited to deliver theopening lecture, which was printed as a booklet: [23].

For accounts of the early Omega endeavours, see [28] and [29]. The pro-totype of the full Omega engine was programmed in Haskel (see [33]). Thewhole system (Omega and Wiris) were described in [35] and [46]. The papers[36] and [41] were forerunners of the book [48] and of future research.

The interface Physics-Geometry continued to be present: see the book[37] for another witness. The ideas of the editors in organizing the meet-ing were “to stimulate the physicists and mathematicians of our country toparticipate in, and share some of the current excitement about the most dy-namic interactions between these two fields”. Among the speakers were A.Ashtekar, A. Connes, G. F. R. Ellis, and B. B. Mandelbrot.

The reflections with Rue on the mathematical structure of quantum com-putating were disseminated with [72] and [85, 86]. See also the lecture [90].

A very sad news for a large mathematical community was the untimelydeath of Fernando Serrano (1957-1997) and a great distress for the authorsof [34].

7. President of the Catalan Mathematical Society (1995-2002)

Among the initiatives promoted during the two mandates as President of theSCM, the most outstanding was winning the bid to organize the 3ecm (3rdEuropean Congress of Mathematics) in the 1996 EMS Council in Buda-Peston the occasion of the 2ecm (the other bidders were Copenhagen, Brightonand Turin) and then coordinating, as President of the Executive Committeeand of the Organizing Committee, the Catalan mathematical community,whose response was admirable, to achieve that goal (July 2000, 1500 partic-ipants). For many, the 3ecm has been the best of the seven EMS congressesorganized so far.

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Coeditor of Proceedings (2 volumes, above 1222 p) and of the volumedevoted to the round tables (203 p). See [44, 45].

The year 2000 was also the World Mathematical Year (WMY) and theSCM played a leading role in contributing to make Mathematics visible tothe socienty at large.

During the two periods in office (3+3 years), the “Proves Cangur” werelaunched in 1996, a participating mathematical contest that in 2017 has en-rolled more that one hundred thousand students. The publication SCM/Notı-cies was started. The number of affiliates grew from about 350 to more than1000.Further comments. Being the president of a society such as SCM, and themore so with all the fireworks concomitant to the 3ecm organization and theWMY, entails that one has to speak and write in unsuspected places. Hereis a sample: [38], [39], [42], [43], [47], and [50] (the latter belongs to the sameseries, but with some sort of retarded effect).

8. Vicerector UPC (1998-2002)

Was Vicerector of Information and Documentation Systems (in charge ofcomputing and communication systems, libraries and the language and ter-minology service) in the team of the Rector Jaume Pages. During that pe-riod, the Atenea platform for managing teaching and the Paideia program forthe UPC libraries were launched. The company UPCnet was founded. Theactive participation in the “Xarxa Lluıs Vives” culminated with the UPCchairing the net during the first semester of 2000. Membership in Universia(Latinamerican universities netword) started.

9. Dean of the FME (2003-2009)

During the two periods (3+3) as Dean of the FME, promoted the dedicationof each term to a historical personality and was the editor of the six volumescollecting the lectures delivered in each of the six occasions: Poincare,Einstein, Gauss, Euler, Riemann and E. Noether. See [51, 52, 53,60, 62, 68].

During the Riemann term (2007-2008), promoted the nomination of Pro-fessor Sir Michael Atiyah (Fields Medal 1966, Abel Prize 2004) as DoctorHonoris Causa by the UPC. In addition to the Laudatio [64], prepared thematerials [65]. Previously, transcribed the two key-note lectures delivered byAtiyah in December 2007 as part of the Riemann term program and included

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them in [62]. These lectures are now featured in the 7th volume of Atiyah’scollected works.

In the same term, promoted the distinction Magister Honoris Causa bythe FME. The first was awarded to Josep Pla i Carrera and the second,in 2008, to Jaume Pages Fita.

Concerning administration initiatives, the new bachelor and master’s de-grees were launched following the guidelines of the European Space for HigherEducation, including a bachelor’s degree in Statistics in collaboration withthe UB.

While Dean of the FME, was elected as President of the (Spanish) Con-ference of Deans and Directors of Mathematics (2004-2006). In this period,the legal structure of the institution was consolidated, a strategic plan wasset up, three general meetings were organized (Alacant, Madrid and Pam-plona) to discuss matters of high interest for the mathematical community,and the institutional relations were strengthened and widened, including thepresence with a stand at the ICM-2006 in Madrid and the coordination ofa panel, invited by the Executive Committee of ICM-2006, devoted to e-learning mathematics (this culminated with the paper [56]).Further comments. The collaboration with Miret continued, now also withhis students, and the main contributions in this regard are the papers [49],[61], [70]. All along, worked in an Omega implementation of the Katz-Strømme Schubert package (in Maple) for computations in intersectiontheory. A report on these efforts was the lecture [67]. See also [94] foranother perspective on the approach.

The Gauss volume includes the paper [54] that resulted from discussionswith Yuri Koubychine.

The rather long paper [69] is a scientific biography of Atiyah’s writtenin the context of the honoris causa degree by UPC.

In addition to [60], contributed to commemorate the birth bicentennialof L. Euler with the paper [63].

Since the student days, in which Emil Artin’s Geometric Algebra waspopular, the first serious return to the field is the lecture [71].

10. European projects

WebALT. During its time span (2005 and 2006), was coordinator of theUPC node of the project Web Advanced Learning Technologies (WebALT),which coordinated by Mika Seppala (Helsinki University and Florida StateUniversity). The main contribution of the node was the technology devel-oped in the Wiris research and development as the basis for the automatic

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translation prototype of mathematical exercises that was developed in thosetwo years.

Was coeditor of the Proceedings of the 1st WebALT Conference held inJanuary 2006 at Eindhoven (see [58]).JEM. Member of Joining Educational Mathematics (JEM), eContentPlusThematic Network (2006-2009).Further comments. Here are two papers written in the context of JEM: [58]and [59]. A related woork is [57].mOlto. In the period 2010-2013 was member of the UPC node (this timecoordinated by Jordi Saludes) of the European Project Multilingual OnlineTranslation (mOlto), which was coordinated by Aarne Ranta (University ofGoteborg). The project was oriented toward providing automatic transla-tion with high grammatical quality. The main contribution of the node wasthe development of an environment to develop and validate the methodologyin the case of mathematical texts (cf. Madrid 2013 slides). In 2011 coor-ganized the Summer School Frontiers of Multilingual Technologies (16-26August 2011): Venue.Further comments. The main work in this project was in collaboration withSaludes. The core techniques that were developed are presented in [78],while [79, 80, 81] envision some application scenarios.

11. Other projects

Visio (2008). This was an UPC project in technology transfer developedfrom an initiative of the technological company Imagsa Technologies. It wasoriented to provide a solution to the problem of building sterereoscopic visioncapabilities for compact cameras (programmable in FPGA). Was develpedunder his coordination by a team of FME students (among which GuillemPerarnau, Josep A. Herrero, and Carlos Luna were the more active)together with Gerard Tarrago, a former FME student working for Imagsaand whose research in Visio was the core of his Master’s Thesis in Mathemat-ical Engineering. The resources for the project were granted by CIDEM (nowACCIO), the agency for enterprise competitivity of the Catalan Government,after a positive assessment of Imagsa’s request and the planning to solve it.The final algorithm for solving the problem was called Linear Parallel BeliefPropagation (LPBP) for Stereoscopic Vision and the deliverables were thememoir [66] and an implementation of LPBP in C ready to be transferred toFPGA.WCCI-2010. In 2010 collaborated in the organization of the “2010 IEEE

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World Congress on Computational Intelligence” (18-23 July, Barcelona),which was organized for the first time in Europe. The main activity wasthe edition of [73], the Plenary and Invited Lectures volume (13 lectures inall, 261 p), published by the IEEE Computational Intelligence Society.Imaginary. The year 2011 the RSME celebrated the first centenary. Amongthe projects that were launched for the occasion, one was the successivedeployment of the exhibit “Imaginary—Una mirada matematica” in severalSpanish cities. SX was curator of that exhibit and between January 2011 andJune 2013 managed to bring it to 15 cities (Salamanca, Valladolid, Palmade Mallorca, Bilbao, Pamplona, Gijon, Zaragoza, Madrid, Sevilla, Valencia,Malaga, Barcelona, Albacete, Granada and Santiago de Compostela). In2011 also coordinated the deployment of a museum variation of the itinerantexhibit that was featured in CosmoCaixa (six months in Madrid-Alcobendasand six months in Barcelona). The UPC contributed in supporting theseactivities by allowing SX to devote part time to them. Among the morerelevant duties and tasks, there were the training sessions for the people(many of them high school teachers) that would be guides for visiting groups,and also the preparation and publication of a suitable catalog, [76] (the sixthousand copies were soon sold out). Even though Imaginary started at theMathematisches Forschungsintitute Oberwolfach (MFO), the Spanish versionintroduced substantial innovations that were later reused by other similarexhibits in other countries, including Germany. A recognition of this factwas the invitation in 2013 to deliver the main lecture in the MFO ceremonyarranged for the taking office of the present director, Prof. Dr. GerhardHuisken, as successor of Prof. Dr. Gert-Martin-Greuel (see [84]).Further comments. The lecture at MFO was based in part in the paper [77].ArbolMat. Since its beginnings in 2010, SX has been director of El Arbol delas Matematicas: Galerıa RSME-Universia de Matematicas, Ciencia y Tec-nologıa (http://www.arbolmat.com/), with the permission of UPC to devotepart of the time to the project. So far, 39 profiles have been prepared anduploaded. Among them, four Professors from UPC (Xavier Cabre, FerranHurtado, Marc Noy and Mateo Valero) and two doctors honoris causaby UPC (Juan I. Cirac and S Verdu).Further comments. For a report about the 39 profiles up to 2014, see [93].

In some cases, the ArbolMat work led to a deeper involvement with thebiography and science of the person. One special case is Emilio Elizalde,whose life and work is presented in the paper [75] at the beginning of [74].Recent biographical works. Has been a member of the RSME team toprepare proposals for the FBBVA Prizes. In 2013, David Mumford and

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Ingrid Daubechies were awarded with the Science Prize for 2012, whichdistinguished Mathematics for the first time. On this occasion published [87]and an extensive analysis [88] of Mumford’s work (Fields Medal 1974).

In 2014 took the RSME suggestion to write an obituary of the Norwegianalgebraic geometer Stein Arild Strømme, which was published in the EMSNewsletter: [94].

In 2015 has been invited to write a paper on the life and work of J. M.Montesinos Amilibia (Emeritus Full Professor of Analytical Geometryand Topology of the UCM, and profiled in ArbolMat in 2014), a task finishedin July 2015. This will be the basis for the opening lecture at the UCM dayplanned for September 8 in Montesinos homage.Further comments. The paper [82] should have also been included in thisparagraph.

The lecture on Montesinos life and work was indeed delivered on Septem-ber 8, 2015, and the paper was published as [100].Teaching innovation. In addition to the activities related to WebALTand JEM already described, in the last two terms has developed a methodfor teaching mathematical disciplines to degrees in Engineering by the nameof Continuous Learning. See [91] for a summary. The method has beenimplemented for teaching the FIB senior course Data and Image Processingwith remarkable success.Further comments. A later dissemination of these ideas was the participationin an RSME panel in its 2013 Congress, [83], and the lecture [89] (for themost part based on findings connected to Data and Image Compression.AGACSE 2015. In the last months, has been chairing the organizing com-mittee of the 6th edition of the conference Applied Geometric Algebra inComputer Science and Engineering (AGACSE 2015) which will take place onJuly 29-31, 2015, at UPC. The conference is preceded by a Summer Schoolon Geometric Algebra (27 and 28 July) oriented to achieve that that theparticipants can get an optimal profit of the conference lectures. The Schoolfeatures four lab sessions designed with the continuous learning principles.The conference program includes 9 invited lectures, 32 talks selected fromamong the received submissions, and 10 posters. The conference is dedi-cated to David Hestenes, an undisputed leader for over fifty years in thefield of Geometric Algebra and Geometric Calculus, including applicationsin several fields, particularly in Mathematical Physics. He will deliver thekey-note lecture.The first GAT intensive courses. In March 2015 delivered an intensivecourse (10 hours) at the University of San Luis Potosı (Mexico) withe title

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Geometric Algebra Techniques in Mathematics and Physics (GAT: 1 Firststeps; 2 Grassmann-Clifford algebra; 3 Geometric Algebra; 4 Space-time Ge-ometric Algebra; 5 Real and complex geometric algebras). After the course,delivered two lectures on spinors (a topic in which the advantage of using ofGeometric Algebra is especially compelling) in two “Encuentros” (one in SanLuis Potosı and another in San Carlos, Guaymas, Sonora).Further comments. As mentioned earlier, the thread of GA was rediscoveredin connection with the lecture [71]. Then it was cultivated further, in greatpart as a preparation for AGACSE 2015, in the lecture [92] and the ensuingpaper [95]. As explained in [104], also contributed to make reality a secondedition of Hestenes’ Space-time algebra, which he reviewed in [97].

12. Academic project (2015)

In this section the main working lines that will develop are briefly described.AGACSE-2015. The Scientific Committee of AGACSE 2015 will select,among the presented talks, those that will be invited to present an extendedpaper for the final Proceedings. One of the tasks will be, as editor, to find anoptimal way of publishing them and to insure excellent quality of the finalversions. We would like that AGACSE 2015 were remembered not only forhaving paid homage to Hestenes, but also for having produced a good setof proceedigns.Further comments. The Proceedings of AGACSE 2015 were published early2017, [103]. The contents, and notes on the preparation, were collected in thePreface, [104]. As decided in Barcelona, the 7th AGACSE will take place inCampinas (Sao Paulo, Brazil) in July 2018, with Carlile Lavor as chairmanof the Organizing Committee. For that occasion, SX has accepted to chairthe Scientific Committee.Author/editor. a) To transform the books [22], [32] and [40] to a digitalformat, supporting computational aspects and interactivity, along the linesof ElectoLibris.Further comments. Since ElectoLibris closed shop, this project has to beredefined. One possibility is to use the Jupyter notebooks technology thatwas tested for the AGACSE 2015 Summer School labs and successfully usedever since in the projects that led to [111] and [110]. The latter contains adescription of the engine, which is programmed in Python (work in progressin collaboration with Sayols), and includes many examples that illustratethe good features of the technology.

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b) Similarly, with the notes of Mathematical Models of Physics, written asteaching materials of the subject, with the book Geometry, sold out long ago,and with Coding Theory. In the latter case, the published book [48] alreadyhad the sought after qualities, for it used Wiris as the computational engine,but the idea is to include a chapter on convolutional codes and extend thecomputational package to include this important class.c) To write in more detail the GAT notes and use the computational systemset up for the AGACSE 2015 Summer School labs to produce an environmentthat covers the mathematical and physics aspects, but also an effective wayto deal with the algorithmic aspects.Further comments. This has evolved differently than expected. The mainreasons are the intensive courses in Valladolid (Novembre 2015 and May 2016,with the title Geometric Algebra Techniques in Mathematics, Physics andEngineering, similar to the Mexican GAT, but with more mathematical detailand including Conformal Geometric Algebra); the second intensive coursein San Luis Potosı (June 2016, with the title Formalisms in MathematicalPhysics: Perspectives, Structures and Methods: 1 Elements of GA, 2 ClassicalMechanics with GA, 3 Spinor dynamics, 4 Special relativity, 5 Quantummechanics); the commitment to the Santalo 2016 Research School; and thelecture at the Barcelona CSASC (September 2016). For these activities, aset of slides was produced for each lecture, like [96], [98], [99] and [102]. Afterthe Santalo School, the RSME asked me to present some of the basic ideasof GA in the journal La Gaceta. The yield in this direction is, so far, [101]and [107]. On the other hand, the June visit of Carlile Lavor to Barcelonahas given rise to [109] and [113].d) The same as in c), but referred to the teaching materials for Data andimage processing. In this case, many algorithms are already programmedin Python, the lingua franca for the course, so that the task amounts tosystematize and optimize the materials and find a suitable way to publishthem.Further comments. In this case the Jupyter technology is the best choice, forit is straightforward to include the mathematical texts and make the Pythoncode available.e) To contribute in the edition and publication of the Conferences FME in astyle like that used in the terms 2003/04 to 2008/09.Further comments. This task was not pursuit when the new series of sixpersonalities started in the term 2009/10. SX had the impression that theteam that took the leadership of the FME in 2015 would relaunch the project,but this has not been the case. So this is no longer in the task list.

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ArbolMat. To continue uploading profiles to ArbolMat. There is a long listof names chosen by an RSME Committee, and among them there is a goodrepresentation of UPC. Some of these profiles are already under preparationand hopefully will be able to devote more time to it when freed of the teachingduties.Further comments. In the years 2015 and 2016, 29 more profiles were added[105], making a total of 68. Among those 29, there are three from UPCAmadeu Delshams, Enrique Garcıa-Berro and Joan Sola-Morales.Before renegotiating the renewal of the projecct with Universia, some six toeight new profiles will be uploaded. If the project continues, the expectationis to add some 70 new profiles.Coaching. In favorable circumstances, would like to coach novel teachersand researchers, on an individual basis or in organized groups (as for examplevia the ICE); about matters of mathematics or physics ranging from concep-tual aspects to algorithmic and computational ones; or seminars on specifictopics, as for example programming in Python.Further comments. No formal arrangements have been made in that regard,but several informal tasks developed during the last two years would be easilyrecognized to fit into one or more of the above possibilities.ICIAM 2019. Member of the (early) Steering Committee of ICIAM 2019,and at present member of the public awareness committee.

Needed resourcesOffice, internet connection and email. Has a portable PC acquired with

funds from previous projects and it is adequate for the current needs.

13. Report on recent activities (2015-2017)

Many have already been reported in the preceding pages:GAT: Intensive courses in San Luis Potosı (Mexico) and Valladolid(Spain), and other related lectures, represented by [96], [98] and [102].Santalo 2016: Direction of the Santalo 2016 Research School, in whichhe delivered 4 lectures: [99].Papers on GA: [95], [97], [101], [108] and [107] (the latter two willappear in the Fall of 2017).ArbolMat: Addition of 29 profiles, [105]. Publication of [100].Edition of the AGACSE 2015 Proceedings in AACA (published 2017):[103], [104].Error-Correcting Codes: [111], [110], [112]. The symbolic compu-tational system is being developed in collaboration with Sayols and

15

briefly documented in [110] and online at PyCC. The developmentis done with Jupyter (extensive use of notebooks) and programed inPython.Geometry-Physics interface: [106]

14. Upadate of the academic project (2017)

The most pressing piece is preparing the ICCA lecture [114] on W. Ro-drigues jr life and work, which is to be delivered on 9 August, 2017. At-tending the conference is also a great opportunity.

Then comes the delivering of [109] (basically, translating from Spanish,adapting, and extending in various ways materials such as [101]) and [113](SX part is based on summarizing GA for use in the later chapters and totranslate from Spanish, adapt, and extend in various ways the paper [107]).This is a first step into a more ambitious road that conceivably leads to noveland interesting applications of GA.

Next, the commitment to contribute to the organization AGACSE 2018,and particularly to insure high quality of the scientific program, all as out-lined during Lavor’s visit to Barcelona in June 2017.

In coding theory, continue developing PyCC in three fronts: extend thefacilities so as to be able to deal (symbolically) with convolutional codes, usecyton (C code in a Pyton environment) so as to gain faster processing, anddevelop a system of “post-quantum” crytography based on binary classicalGoppa codes (we have a prototype based on McElice scheme that seemspromissing).

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15. Acronyms

3ecm 3rd European Congress of MathematiciansAGACSE Applications of Geometric Algebra

in Computer Science and EngineeringAMS American Mathematical SocietyBBVA Banco de Bilbao-Vizcaya-ArgentariaCIMNE Centre Internacional de Metodes Numerics per a l’EnginyeriaCSASC Cech, Slovenian, Austrian, Slovac and Cantalan Societies (joint meeting)EMS European Mathematical SocietyEU European UnionFBBVA Foundation of the BBVAFIB Facultat d’Informatica de Barcelona (UPC)FM Facultat de Matematiques (UB)FME Facultat de Matematiques i Estadıstica (UPC)FP Framework Program (of the EU)FPGA Field Programmable Gate ArrayGAT Geometric Algebra TechniquesICCA International Conference on Clifford AlgebrasICM International Congress of MathematiciansIEEE Institute of Electric and Electronic EngineersIMUVA Instituto de Matematicas de la Universidad de ValladolidJEM Joining Educational MathematicsLNiM Lecture Notes in MathematicslPBP Linear Parallel Belief Propagation (algorithm for SV)M4M Maths for More (name of a company)MAT Departament de Matematiques (UPC)MFO Mathematisches Forschungsinstitut OberwolfachMIT Massachusetts Institute of TechnologyRSME Real Sociedad Matematica EspanolaSCM Societat Catalana de MatematiquesSBMA Sociedade Brasileira de Matematica AplicadaSX Sebastia Xambo-DescampsSV Stereoscopic VisionUAB Universitat Autonoma de BarcelonaUB Universitat de BarcelonaUCM Universidad Complutense de MadridUPC Universitat Politecnica de Catalunya / BarcelonaTechUIMP Universidad Internacional Menendez PelayoUIB Universitat de ses Illes BalearsWCCI World Congress of Computational IntelligenceWebALT Web Advanced Learning TechnologiesWMY World Mathematical Year

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References

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[4] 1981: Teorıa de Serre de multiplicidades. Notas del Seminario deAlgebra Conmutativa y Geometrıa Algebraica, no 2. Universidad deBarcelona, 1981.

[5] 1981: Variedades proyectivas de grado mınimo. UB, 1981. Condensedversion of the PhD thesis.

[6] 1981: On projective varieties of minimal degree. Collectanea Mathe-matica 32/2 (1981), 149-163.

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[17] 1990 (editor): Enumerative Geometry (Proceedings of a Conferenceheld in Sitges, Spain, June 1-6, 1987). Springer, LNiM 1436, 303 pp.

[18] 1990 (with Miret): On Schubert’s degenerations of cuspidal planecubics. In Enumerative geometry (Sitges, 1987), Springer LNiM 1436(1990), 189-214.

[19] 1991 (with Rossello): Chow groups and Borel-Moore schemes. An-nali di Matematica Pura ed Applicatta 160/4 (1991), 19-40.

[20] 1991 (with Miret): On the geometry of nodal plane cubics: the condi-tion p. Enumerative algebraic geometry (Copenhagen, 1989), Contem-porary Mathematics 123 (1991), 169-187, AMS.

[21] 1991 (with Procesi): On Halphen’s first formula. Enumerative alge-braic geometry (Copenhagen, 1989), Contemporary Mathematics 123(1991), 199-211, AMS. Original manuscript.

[22] 1992 (with Delgado and Fuertes): Introduccion al Algebra I. Edi-torial Complentense, 1992, ix + 252 pp.

[23] 1993: Geometria i Realitat. Opening lecture, September 30 1993, forthe academic year 1993/1994 of the FME (UPC).

[24] 1994 (with Miret): Rational equivalence on some families of planecurves. Annales de l’Institut Fourier (Grenoble) 44/2 (1994), 323-345.

[25] 1994: Francesco Severi and the principle of conservation of number.In Algebra e geometria (1860-1940): il contributo italiano (Cortona,Italy, 4-8 may 1992, edited by A. Brigaglia, C. Ciliberto, and

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[26] 1994: Sobre puntos y coordenadas. In Contribuciones matematicas:estudios en honor del profesor Jose Javier Etayo Miqueo. EditorialComplutense, 1994, 61-93.

[27] 1994: On Calabi–Yau manifolds: bridging enumerative geometry andstring theory. In Proceedings of the Fall Workshop on Differential Ge-ometry and its Applications. Barcelona’ 93 (edited by X. Gracia, M.C. Munoz, and N. Roman), 63-73. Original manuscript.

[28] 1996: Omega: Problem solving with the interpreter ω0. Proceedingsof the III International Congress of Project Engeneering, 1667-1704.Barcelona, 1996.

[29] 1996 (with Mola): Omega: Engineering a System for Effective Com-putations related to Block Error-Correcting Codes. Proceedings of theIII International Congress of Project Engeneering, Barcelona, 1996.

[30] Using intersection theory. Aportaciones Matematicas, Nivel Avanzado,7. Sociedad Matematica Mexicana, 1996, 122 pp.

[31] 1997: Geometria. Edicions UPC, 2001, x + 303 pp.

[32] 1998 (with Delgado and Fuertes): Introduccion al Algebra II: Anil-los, factorizacion y teorıa de cuerpos. Publicaciones de la Universidadde Valladolid, 1998, 273 pp.

[33] 1998 (with Marques): Mathematical symbolic systems and func-tional languages. In Proceedings of the �IV Journees Catalanesde Mathematiques Appliquees� (Tarragona, 11-13 February 1998;edited by C. Garcia, C. Olive and M. Sanroma). Departamentd’Enginyeria Informatica, Universitat Rovira i Virgili (1998), 175-192.

[34] 1998 (with Conte): Fernando Serrano (1957-1997): A biographicalsketch and appreciation of his scientific work. Collectanea Mathematica49/2-3 (1998), 135-148.

[35] 1999: Omega: a system for the effective construction, coding and de-coding of block error-correcting codes. Contributions to Science, 1/2(1999), 199-224. Author’s copy.

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[36] 1999: Using Omega for the effective construction, coding and decodingof block error-correcting codes. Proceedings of EACA-1999, Universi-dad de La Laguna, Santa Cruz de Tenerife, 1999, 67-122.

[37] 1999 (editor, with Jou): Physics and Geometry. Proceedings of theColloquium held at the IEC as the “2es Jornades Cientıfiques de l’IEC,Seccio de Ciencies i Tecnologia, 1996”. Institut d’Estudis Catalans,1999. 198 pp.

[38] 1999: 10 anotacions sobre el sistema metric decimal. Speech on theoccasion of celebrating the bicentenial of Decimal Metric System, CityHall, Barcelona, 1999.

[39] 1999: La Societat Catalana de Matematiques a les portes del segle XXI.In Ciencia i Cultura al llindar del segle xxi, IEC (1999), 175-180.

[40] 2000 (with Delgado and Fuertes): Introduccion al Algebra III:Soluciones de los problemas. Publicaciones de la Universidad de Val-ladolid, 2000, 198 pp.

[41] 2000 (with Bras): Omega decoders for Goppa codes. In EACA-2000(Barcelona 6-8 September 2000): Actas del vi Encuentro de AlgebraComputacional y Aplicaciones (edited by Antonio Montes), 129-142.Barcelona, UPC, Departament de Matematica Aplicada II, 2000.

[42] 2000: El desarrollo de la sociedad y las Matematicas en la Universi-dad. Jornada Matematica. Publicaciones del Congreso de los Diputa-dos, 2000.

[43] 2000: Paraules de cloenda. In Commemoracio de l’any mundial de lesmatematiques, Publicacions del Parlament de Catalunya (2002), 137-142.

[44] 2001 (editor, with Miro, Casacuberta and Verdera): Proceed-ings of the Third European Congress of Mathematics (Barcelona, 2000).Birhauser, Basel 2001, 582 + 640 pp. (2 volumes).

[45] 2001 (editor, with Miro, Casacuberta and Ortega): Mathemat-ical glimpses into the XXI Century. Proceedings of the Round TableProgram of the Third European Congress of Mathematics (Barcelona,2000). CIMNE and SCM, 2001, 203 pp.

[46] 2002 (with Eixarch and Marques): WIRIS: An Internet platform forthe teaching and learning of mathematics in large educational commu-nities. Contributions to Science, 2/2 (2002), 269-276. Author’s copy.

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[47] 2002: Hipermatematiques: Noves Tecnologies en la Docencia i Apre-nentatge de les Matematiques. In Reptes i problemes: l’impacte de lasocietat de la informacio, Fundacio Catalana per a la Recerca (2002),81-86.

[48] 2003: Block error-correcting codes. A computational primer. Universi-text, Springer-Verlag, Berlin, 2003, vi + 265 pp.

[49] 2003 (with Miret and Hernandez): Completing Hermann Schu-bert’s work on the enumerative geometry of cuspidal cubics in P3.Communications in Algebra 31/8 (2003), 4037-4068. Special issue inhonor of Steven L. Kleiman.

[50] 2004: Recreacions computacionals de la teoria de codis correctorsd’errors. In Matematiques del segle XXI: dels fonaments a la tecnologia,Edicions Fundacio Caixa de Sabadell (2004), 41-71.

[51] 2005 (editor): Conferencies FME, I : Curs Poincare (2003-2004). FME,UPC, 2005. 180 pp.

[52] 2005 (editor): Conferencies FME, II : Curs Einstein (2004-2005). FME,UPC, 2005. 316 pp.

[53] 2006 (editor): Conferencies FME, III : Curs Gauss (2005-2006). FME,UPC, 2006. 383 pp.

[54] 2006 (with Koubychine): Sobre la sorprenent efectivitat de lesMatematiques en la Fısica. In [53], 315-330.

[55] 2006 (editor, with Seppala and Caprotti): Proceedings of the 1stWebALT Conference (Technical University Eindhoven, January 2006).WebALT Inc., Helsinki, 2006, 169 pp.

[56] 2006 (with Bass, Bolanos, Seiler, and Seppala): E-Learningmathemtics. International Congress of Mathematicians, Vol. III, 1743-1768. EMS, 2006.

[57] 2006 (with Estela): Teaching and Learning Mathematics usingMapleTA and Wiris technology in a Moodle environment. Conferencepaper at the “12th International Conference on Technology SupportedLearning & Training”, Online Educa Berlin, 2006.

[58] 2006 (with Seppala and Caprotti): Using web technologies to teachmathematics. In Proceedings of Site-2006, Universite de Montreal,2006.

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[59] 2007 (with Caprotti and Seppala): Novel aspects of the use of ICTin Mathematics Education. In Innovations in E-learning, Instructiontechnology, Assessment and Engineering Education, Springer, 2007,295-300. Proceedings of CISSE-2006.

[60] 2007 (editor): Conferencies FME, IV : Curs Euler (2006-2007). FME,UPC, 2007. 232 pp.

[61] 2007 (with Hernandez and Miret): Computing the characteristicnumbers of the variety of nodal plane cubics in P3. Journal of SymbolicComputations 42/1-2 (2007), 192-202.

[62] 2008 (editor): Conferencies FME, V : Curs Riemann (2007-2008).FME, UPC, 2008. 248 pp.

[63] 2008: Euler and the dynamics of rigid bodies. In “Proceedings of theInternational Symposium on Leonhard Euler (1707-1783)”, Quadernsd’historia de l’enginyeria, vol. ix (2008), 279-303. Original manuscript.

[64] 2008: Laudatio of Professor Sir Michael F. Atiyah on the occasion ofhis honorary doctoral degree by the UPC (25 April, 2008). pdf (9 pp).

[65] 2008: The Life and Work of Professor Sir Michael Atiyah. in 8 posters.Posters 1-8 were also displayed at the University of Edinburgh on theoccasion of the “Atiyah80 Conference on Geometry and Physics” (April20-22, 2009).

[66] 2008 (with Tarrago, Perarnau, Luna, and Lisa): AlgorismeLPBP per a la visio estereoscopica. Final report of the VISIO Project.115 pp.

[67] 2009: A Structured and Comprehensive Package for Computations inIntersection Theory. Lecture at the Special Session on Computationaland Analytic Geometry of the 2009 AMS/JMM in Washington DC (5-8January, 2009) Slides

[68] 2009 (editor): Conferencies FME, VI : Curs E. Noether (2008-2009).FME, UPC, 2009. 203 pp.

[69] 2009: Sir Michael Atiyay. Vida i obra. Butlletı de la SCM 24/2 (2009),137-207.

[70] 2009 (with Miret, Pujolas, Saurav): Computing some fundamen-tal numbers of the variety of nodal cubics in P3. Journal of SymbolicComputation 44/10 (2009), 1425-1447.

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[71] 2009: A Clifford perspective on Klein’s geometry. Lecture at the Di-dactics of Mathematics as a Mathematical Discipline. Universidade daMadeira, Funchal, Portugal (1-4 October, 2009). Slides.

[72] 2009: A mathematical view of quantum computation. Lecture atthe “Quantum Computation and Information Seminar”, Security andQuantum Information Group, Technical University of Lisbon (9 Octo-ber 2009). Slides.

[73] 2010 (editor, with Aranda): Plenary and Invited Lectures, 2010 IEEEWORLD CONGRESS ON COMPUTATIONAL INTELLIGENCE(WCCI 2010, July 18-23, Barcelona, Spain). Institute of Electrical andElectronics Engineering, Inc., 2010, x + 261 pp.

[74] 2011 (editor, with Odintsov and Saez): Cosmology, Quantum Vac-uum and Zeta Functions. Proceedings of the Conference to celebrateEmili Elizalde’s 60th birthday (Mars 8-10, 2010). Proceedings ofPhysics, Springer-Verlag, 2011. xii + 382 pp.

[75] 2011: Emili Elizalde. Perspectives on his Life and Work. In [74], 1-20.

[76] 2011: Imaginary, una mirada matematica. Catalog for the exhibit Imag-inary, RSME, 2011.

[77] 2012: Realidades de Imaginary. La Gaceta de la RSME, 15/3 (2012),423-426. pdf.

[78] 2012 (with Saludes): The GF Mathematics Library. In ProceedingsTHedu’11 (edited by Quaresma and Back). EPTCS 79 (2012), 102-110. arXiv.

[79] 2012 (with Saludes): Toward Multilingual Mechanized MathematicsAssistants. In Proceedings EACA-2012 (edited by Sendra and Vil-larino). Universidad de Alcala, 2012, 163-166. pdf

[80] 2012: Toward Multilingual Mechanized Mathematics Assistants. EACA2012: XIII Encuentro de Algebra Computacional y Aplicaciones, 13-15June 2012, Alcala de Henares. Slides, based on [79].

[81] 2012 (with Saludes): Multilingual Sage. Tbilisi Mathematical Journal5/2 (2012), 121-132 (special issue on “Symbolic computation with Sagein mathematical education and research”). pdf

[82] 2012: Friedrich Hirzebruch (1927-2012): Trazos de su influjo, in memo-riam. La Gaceta de la RSME, 15/4 (2012), 637-650.

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[83] 2013: Expectativas y experiencias. Ponencia para la mesa redondaMatematicas y Universidad, retos en tiempos de crisis, Congreso RSME21-25 de enero de 2013, Universidad de Santiago de Compostela. Slides.

[84] Realities of Imaginary. Lecture at the MFO on the occasion of DirectorProf. Dr. Gerhard Huisken taking office as successor of Prof. Dr. Gert-Martin Greuel. April 5, 2013. Slides. Related notes.

[85] 2013 (with Rue): Mathematical Essentials of Quantum Computing.Rue-Xambo-2013 (50 pp). Summarized in Rue-Xambo-2013-poster.

[86] 2013 (with Rue): Introduccio matematica a la computacio quantica.Butlletı de la Societat Catalana de Matematiques, 28/2 (2013), 183-231. This is essentially a Catalan version of [85]. Rue-Xambo-2013-Cat.

[87] 2013: Ingrid y David. O un extraordinario encuentro de dos personali-dades singulares. La Gaceta de la RSME, 16/3 (2013), 413-416.

[88] 2013: David Mumford: dialogo y semblanza. La Gaceta de la RSME,16/4 (2013), 643-668.

[89] 2013 (with Roma): Procesamiento de Patrones en Python. Lectureat the Conference PyConEs-2013, Universidad Politecnica de Madrid(23-24 November 2013). Slides

[90] 2013 (with Rue): El abece de la computacion cuantica. Ateneo Lectureat the “Instituto de Investigacion en Matematicas”, Universidad deValladolid (24 November 2013). Slides. Associated manuscript = [85].

[91] Optimizacion del Aprendizaje Continuo. Note published in Educaweb’sissue “Maestros excelentes”, March 2014. Link.

[92] 2014: Escondidas sendas de la geometrıa proyectiva a la fısica cuantica.Lecture in the “Simposio en Memoria de Juan Bautista SanchoGuimera” (4 April 2014, Salamanca). Slides.

[93] 2014 (with annexes by Bermudez de Castro, Herrero, Linan,and Bonet): El Arbol de las Matematicas. La Gaceta de la RSME,17/4 (2014), 649-665.

[94] 2014: Stein Arild Strømme (1951-2014): in memoriam. EMS Newslet-ter 93 (2014), 37-45.

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[95] 2015: Escondidas sendas de la geometrıa proyectiva a los formal-ismos cuanticos. In El legado matematico de Juan Bautista SanchoGuimera (ed. by D. Hernandez-Ruiperez y A. Campillo), Real SociedadMatematica Espanola y Ediciones Universidad de Salamanca, 2015,233–274. pdf.

[96] 2015: Geometric Algebra Techniques in Mathematics, Physics and En-gineering, A: Intensive 2015 course at the IMUVA: 1 Firsts steps, 2Grassmann and Clifford algebras, 3 Geometric Algebra, and 4 Space-time algebra.

[97] 2015: Review of Hestenes’ space-time algebra (second edition). EMSNewsletter 98 (2015), 63-66.

[98] 2016: Geometric Algebra Techniques in Mathematics, Physics and En-gineering, B: Intensive 2016 course at the IMUVA: 5 Classical Mechan-ics, 6 Quantum Esperanto and Pauli spinors, 7 Conformal GeometricAlgebra Classifications.

[99] 2016: Lectures at the 17th “Lluıs Santalo” Research School: Algebraand geometry in current curricula, On axiom system for GA, A viewof F. Klein Erlangen Program through GA and Enriching AbstractAlgebra with GA.

[100] 2016: Jose Marıa Montesinos Amilibia: biographical sketches. In Amathematical tribute to Professor Jose Marıa Montesinos Amilibia,33-62. Departamento de Geometrıa y Topologıa, Facultad de CienciasMatematicas, UCM, 2016.

[101] 2016: Algebra Geometrica y Geometrıas Orgogonales. La Gaceta dela RSME, 19/3 (2016), 559-588. pdf An extended and adapted versionin English will appear as [109].

[102] 2016: Dirac’s equation seen in the GA light. Lecture at the Differentialgeometry and Mathematical Physics special session of the CSASC jointmeeting (20-23 September 2016). Slides.

[103] 2017 (editor, with Parra-Serra): Proceedings of the AGACSE 2015Conference (Barcelona, July 27-31, 2015), Special issue of Advances ofApplied Clifford Algebras 27/1 (2017), 550 pp.

[104] 2017 (with Parra-Serra): Preface. In Proceedings of the AGACSE2015 Conference (Barcelona, July 27-31, 2015), Special issue of Ad-vances of Applied Clifford Algebras 27/1 (2017), 345-349.

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[105] 2017: El Arbol de las Matematicas: 2015 y 2016. La Gaceta de laRSME, 20/1 (2017), 1-12.

[106] 2017: Two-way bridges between Geometric Topology and MathematicalPhysics. Lecture at the special session on Geometric Topology of theCongreso Bienal de la Real Sociedad Matematica Espanola (30.1-03.2,2017) in honor of Marıa Teresa Lozano Imızcoz. Slides

[107] 2017: Geometrıa y Fısica del espacio-tiempo. La Gaceta de la RSME,20/3 (2017), 24 pp.

[108] 2017: From Leibniz’ characteristica geometrica to contemporary Ge-ometric Algebra. Quaderns d’Historia de l’Enginyeria, 16, 2017/2018(25 pages, in press). Special issue dedicated to commemorate Leibniz(1646-1716).

[109] 2017: Real Spinorial Groups: A Short Mathematical Introduction.SBMA, Springerbrief, 2017. 80 pp.

[110] 2017 (with Sayols and Farre): On the PGZ decoding algorithm foralternant codes. arXiv.

[111] 2017 (with Molina and Sayols): A bootstrap for the number of Fqm-rational points on a curve over Fq. arXiv.

[112] 2017: Error-correcting codes: mathematics and computations. Alge-braic Geometry Seminar UB-UAB-UPC (5 May 2017). Slides

[113] 2017 (with Lavor and Zaplana: A Geometric Algebra Invitationto Space-Time Physics, Robotics and Molecular Geometry. SBMA,Springerbrief, 2017. 120 pp.

[114] 2017 (with Lavor): Waldyr Rodrigues Jr.: Sketches on his Life andWork. Invited lecture at ICCA11 (Ghent, 9 August 2017). Later it willbe expanded into a fuller biographical paper with special attention tohis mathematics.

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