Academic Track

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

sebastia.xambo@upc.edu9 November 2018

Abstract

This document was presented in Spring 2018 to the Research and AcademicCommittees of the Universitat Politecnica de Catalunya (UPC)1 by the Fac-ulty of Mathematics and Statistics (FME), The Faculty of Informatics (FIB)and the Department of Mathematics (MAT) proposing an extension of SX’snomination as Emeritus Professor of Mathematics (2015-2018). The exten-sion was approved by the Governing Council of UPC on October 24, 2018,and by the Social Council of UPC on Novembre 5, 2018.

The document itself is an extension of the document presented in Spring2015 by the same institutions for the first nomination (November 2015) andupdated to the start of the second nomination.

The main productions in the terms 2015-16 to 2017-18 are the following:International appointments: [100], [106], [119], [120], [127], [129], [130]Books: [118] (coauthor); [123] (coeditor); [126] (author).Papers: [96], [97], [102], [103], [107], [108], [110], [111], [115], [117],[124], [125], [131], [132]Short Courses and Lectures: [98], [99], [101], [104], [109], [112], [113],[114], [116], [121], [122]Software: [105]

Some activities planned for 2018-19 to 2020-21:[128], [133], [134], [135], [136], [137], [138], [139], [140], [141], [142]

General justification of the proposal

SX fulfills the requirements to be nominated as Emeritus Professor of Mathe-matics of the UPC. His main responsibilities and achievements in the service

1To ease the reading, acronyms have been collected in Section 4, page 27. The firstoccurrence of an acronym is only occasionally preceeded by its definition.

of the University and of the mathematics community for 49-years, with em-phasis on the last 25 as a Full Professor of Information and Coding Theoriesat UPC, are described in the sections 2 to 4. For a more complete list of thepublished materials, see the References at the end added to this version in atime-line style. For a more structured view, see SX’s Web page.

1. Short CV

EducationPhD in Mathematics, UB (1981)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, codebased Post-Quantum Cryptography.Effective Methods for Computer Mathematics, Symbolic Computation.Mathematical Models in Physics and Engineering.Geometric Algebra and Geometric Calculus. Geometric Calculus basedDeep Learning.

2

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).Instituto de Matematica, Estatıstica e Computacao Cientıfica (Univer-sidade Estadual de Campinas, July 2018).

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).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. Academic record

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 axiomatic

3

foundations of projective geometry. Research initiation in Algebraic Geom-etry through the seminars run by Federico Gaeta at UPC (Summer 1975and Summar 1976).

The two volumes [2, 3], with well over 900 pages in all, had a substantialinfluence in several generations. They were concerned with applications inMathematics, like the foundations of the minimum squares method and oflinear programming, and in Physics, like the dynamics of rigid bodies orthe deduction of the Lorentz transformations without assuming that c is aconstant. The algorithmic and computational points of view were importantthreads.

The aim of the memoir[1], Fundamentos de Geometrıa Proyectiva, wasto provide a brief account of how the linear algebra structure emerges frompurely geometric axioms. A recent revision was included as the first partof [96]).

The Gaeta seminars paved the way for next stage.

Fulbright-Hays grantSpent the terms 1977-78 and 1978-79 at the University of Brandeis (Waltham,Massachusetts, USA) with a Fulbright-Hays grant and a leave of absencefrom the Balmes High School. Took 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.

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 (130 p;see [11]). In 1987 organizes, in collaboration with Eduard Casas, the inter-national conference Enumerative Geometry, again in Sitges, and edits thecorresponding proceedings as LNiM 1436 (303 p; see [17]).

4

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 [95] in memoriam of S. A. Strømme publishedin the September 2014 EMS Newsletter.

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.

For a condensed version of the PhD thesis, see [5]. See also the papers[6, 7]. Papers related to the book with Casas: [10, 13]. An offshoot ofthe 1981 memoir [4] was the paper [12] with Rossello, with whom alsopublished [15, 19]. The visits to Max-Planck and Copenhagen contributedsignificantly in making possible to win in the next year the competition fora 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.

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).

Continues a productive collaboration with Josep M. Miret focused onunderstanding and completing Schubert’s numbers about singular cubics:[16, 18, 20, 24]. The paper [20] appeared in the Proceedings of the 1989Zeuthen Symposium, attended by the authors, and also the paper [21] writtenin collaboration with Claudio Procesi. Another contribution to a conference(Cortona, Italy, 1992) was [25].

5

At the end of this period, was invited by Sevın Recillas to teach anintensive course on intersection theory in Mexico (Morelia and 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 [95] gives an account of the evolution of these ideas up to ourdays.

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].

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 cubicas

6

cuspidales (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.

• 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.

On the first term at the FME, was invited to deliver the opening 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 mostdynamic interactions between these two fields”. Among the speakers wereA. Ashtekar, A. Connes, G. F. R. Ellis, and B. B. Mandelbrot.

The reflections with Rue on the mathematical structure of quantum com-puting 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.

Coeditor of the 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.

Being the president of a society such as SCM, and the more so with allthe fireworks concomitant to the 3ecm organization and the WMY, entailsthat one has to speak and write in unsuspected places. Here is a sample:[38], [39], [42], [43], [47], and [50] (the latter belongs to the same series, butwith some sort of retarded effect).

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.

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 volumes

8

collecting 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 includedthem 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]).

The collaboration with Miret continued, now also with his students,and the main contributions in this regard are the papers [49], [61], [70]. Allalong, worked in an Omega implementation of the Katz-Strømme Schubertpackage (in Maple) for computations in intersection theory. A report onthese efforts was the lecture [67]. See also [95] for another perspective on theapproach.

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

The rather long paper [69] is a scientific biography of M. Atiyah 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 this field was the lecture [71].

9

3. European projects

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

Here are two papers written in the context of JEM: [58] and [59]. Arelated work 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.

The main work in this project was in collaboration with J. Saludes. Thecore techniques that were developed are presented in [78], while [79, 80, 81]envision some application scenarios.

4. 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 (now

10

ACCIO), 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 IEEEWorld 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 at the MFO ceremonyorganized for the inauguration of the present director, Prof. Dr. GerhardHuisken, as successor of Prof. Dr. Gert-Martin Greuel (see [84]). Thelecture at MFO was based, in part, in the paper [77].ArbolMat. Since its beginnings in 2010, SX has been director of El Arbolde las Matematicas: Galerıa RSME-Universia de Matematicas, Ciencia yTecnologıa (ArbolMat), with the permission of UPC to devote part of thetime to the project. So far, 68 profiles have been prepared and uploaded.

For a report about the 39 profiles up to 2014, see [94]. Similarly, [108]accounts for the profiles published in the two-year period 2015-1016.

11

In some cases, the ArbolMat work led to a deeper involvement with thebiography and science of the person: Emilio Elizalde, whose life and workis presented in the paper [75] at the beginning of [74]; Jose M. MontesinosAmilibia in [102];2 and Antonio Campillo, in the paper [125] (with F.Montserrat) included in [123] (see also [124] for the context in which thiswork was produced).Other biographical works. The paper [82], in memoriam of F. Hirze-bruch, was an attempt to trace his enormous scientific and institutionalinfluence, particularly in relation to Spain.

Was a member of the RSME team to prepare proposals for the FBBVAPrizes. In 2013, David Mumford and Ingrid Daubechies were awarded theScience Prize for 2012, which distinguished Mathematics for the first time.On this occasion published [87] and an extensive analysis [88] of Mumford’swork (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, [95].Teaching innovation. In addition to the activities related to WebALTand JEM already described, in the terms 2013-14 and 2014-15 developed amethod for teaching mathematical disciplines to degrees in Engineering bythe name of Continuous Learning. See [91] for a summary. The methodwas implemented in the teaching of the FIB senior course Data and ImageProcessing with remarkable success.

Additional dissemination of these ideas was the participation in an RSMEpanel in its 2013 Congress, [83], and the lecture [89] (for the most part basedon findings connected to Data and Image Compression).GAT intensive courses, I. In March 2015 delivered an intensive course (10hours) at the University of San Luis Potosı (Mexico) with the title Geomet-ric Algebra Techniques in Mathematics and Physics (GAT: 1 First steps; 2Grassmann-Clifford algebra; 3 Geometric Algebra; 4 Space-time GeometricAlgebra; 5 Real and complex geometric algebras). After the course, deliveredtwo lectures on spinors (a topic in which the advantage of using of Geomet-ric Algebra is especially compelling) in two “Encuentros” (one in San LuisPotosı and another in San Carlos, Guaymas, Sonora).

2This paper on the life and work of J. M. Montesinos Amilibia (Emeritus FullProfessor of Analytical Geometry and Topology of the UCM, and profiled in ArbolMat in2014) was written at the request of Jose M. Rodrıguez Sanjurjo. It was the basis forthe opening lecture delivered at the UCM meeting on September 8, 2015, to pay homageto Montesinos on the occasion of his academic jubilee.

12

As mentioned earlier, the thread of GA was rediscovered in connectionwith the lecture [71]. Then it was cultivated further, in great part as apreparation for AGACSE 2015, in the lecture [92] and the ensuing paper [96].AGACSE 2015. Chaired the Organizing Committee of the 6th edition ofthe conference Applied Geometric Algebra in Computer Science and Engi-neering (AGACSE 2015) which took place on July 29-31, 2015, at UPC.

The conference was preceded by a Summer School on Geometric Algebra(27 and 28 July) oriented to achieve that the participants could get an opti-mal profit of the conference lectures. The School featured four lab sessionsdesigned with the continuous learning principles.

The conference program included 9 invited lectures, 32 talks selectedfrom among the received submissions, and 10 posters. The conference wasdedicated 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. Hestenes deliveredthe key-note lecture.

After the conference, was the Editor in Chief of the Proceedings, [106].As explained in [107], also contributed to make reality a second edition ofHestenes’ masterpiece Space-time algebra, which he reviewed in [97].GAT intensive courses, II. Two intensive courses in Valladolid (November2015 and May 2016, with the title Geometric Algebra Techniques in Math-ematics, Physics and Engineering, similar to the earlier Mexican GAT, butwith more mathematical detail and including Conformal Geometric Algebra).See [98] and [99].

Second intensive course in San Luis Potosı (June 2016, with the titleFormalisms in Mathematical Physics: Perspectives, Structures and Methods:1 Elements of GA, 2 Classical Mechanics with GA, 3 Spinor dynamics, 4Special relativity, 5 Quantum mechanics).

Director of Santalo 2016 Research School, contributing with four lecturesto the program, [101].

Lecture at the Barcelona CSASC (September 2016), [104].After the Santalo School, the RSME asked SX to present some of the

basic ideas of GA in the journal La Gaceta. The yield in this direction is,so far, [103] and [110]. On the other hand, the June 2017 visit of C. Lavorto Barcelona gave rise to [118] and this provided inspiration for [126].Agacse 2018. Has chaired the Scientific Committee of AGACSE 2018 (23-27 July, 2018, Campinas, Sao Paulo, Brazil). The main contributions of thatcommittment are represented in [120] and [119]. The event was accepted asa Satellite Conference of ICM-2018 (1-9 August, 2018, Rio de Janeiro) and

13

of ICIAM-2019 (15-19 July, 2019, Valencia, Spain).The conference was dedicated to the memory of Waldyr A. Rodrigues

(1946-2017) and SX contributed by giving the plenary lectures [121] (a follow-up of [114]) and [122].

References

[1] 1974: Fundamentos de Geometrıa Proyectiva. UB, 1974, 33 pp.

[2] 1977: Algebra Lineal y Geometrıas Lineales, Vol. I. Barcelona, Eunibar,1977, xxxii + 430 pp.

[3] 1978: Algebra Lineal y Geometrıas Lineales, Vol. II. Barcelona, Euni-bar, 1978, xx + 451 pp.

[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.

[7] 1981: Scrolls and quartics. Collectanea Mathematica 33/1 (1982), 89-101.

[8] 1983: Geometria no euclıdea: d’Euclides a Gauss. Butlletı de la SeccioMatematica de la Societat Catalana de Ciencies Fısiques, Quımiques iMatematiques 14 (1983), 64-97.

[9] 1985 (editor, in collaboration with Casas and Welters): AlgebraicGeometry (Proceedings of a Conference held in Sitges, Spain, October5-12, 1983.

[10] 1985 (with Casas): Enumerative theory of conics in Pn. Proceedingsof the tenth Spanish-Portuguese conference on mathematics (Murcia,1985), 117-128, Univ. Murcia, Murcia, 1985.

[11] 1986 (with Casas): The enumerative theory of conics after Halphen.LNiM 1196, Springer-Verlag, x + 129 pp., 1986.

14

[12] 1986 (with Rossello i Llompart): Remarks on multiplicities. Pro-ceedings of the tenth Spanish-Portuguese conference on mathematics(Murcia, 1985), 110-116, Univ. Murcia, Murcia, 1985.

[13] 1987 (with Casas): Halphen’s enumerative theory of conics and itsextension to higher order conditions. In Geometrie algebrique et appli-cations, II (Proceedings of the 2nd La Rabida International Conferenceof Algebraic Geometry, 1984), 55-73, Travaux en Cours, 23, Hermann,Paris, 1987.

[14] 1987 (with Kleiman and Strømme): Sketch of a verification of Schu-bert’s number 5819539783680 of twisted cubics. LNiM 1266, pp. 156-180.

[15] 1988 (with Rossello):7 Computing Chow groups. In Algebraic geom-etry (Sundance, UT, 1986), LNiM 1311, 220-234, Springer, 1988.

[16] 1989 (with Miret): Geometry of complete cuspidal plane cubics. In Al-gebraic curves and projective geometry (Trento, 1988), Springer LNiM1389 (1989), 195-234.

[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).

15

[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, andE. Sernesi). Supplemento dei Rendiconti del Circolo Matematico dePalermo, ii Serie 36 (1984), 255-277. Original manuscript.

[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.

16

[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.

[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.

17

[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.

[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. See also [139] .

[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.

18

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

[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.

19

[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.

[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].

20

[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.

[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] 2013: Realities of Imaginary. Lecture at the MFO on the occasion ofDirector Prof. 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] 2014: Optimizacion del Aprendizaje Continuo. Note published in Edu-caweb’s issue “Maestros excelentes”, March 2014. Link.

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

21

[93] 2014: L’esfera i la llum des d’Arquimedes a Einstein (CAT). Slides(CAT). Talk to a bachelor’s degree in Physical Engineering. This willbe taken as an outline for [141].

[94] 2014 (with annexes by A. Bermudez de Castro, M. A. Herrero,A. Linan, and J. Bonet): “El Arbol de las Matematicas” (ES). LaGaceta de la RSME, 17/4 (2014), 649-665.

[95] 2014: “Stein Arild Strømme (1951-2014): in memoriam”. EMSNewsletter 93 (2014), 37-45.

[96] 2015: “Escondidas sendas de la geometrıa proyectiva a los formalismoscuanticos”. In El legado matematico de Juan Bautista Sancho Guimera(ed. by D. Hernandez-Ruiperez y A. Campillo), Real SociedadMatematica Espanola y Ediciones Universidad de Salamanca, 2015,233–274. pdf.

[97] 2015: “Review of Hestenes’ Space-Time Algebra (second edition)”.EMS Newsletter 98 (2015), 63-66.

[98] 2015: Geometric Algebra Techniques in Mathematics, Physics and En-gineering, A: Intensive course at the IMUVA: 1 Firsts steps, 2 Grass-mann and Clifford algebras, 3 Geometric Algebra, and 4 Space-timealgebra.

[99] 2016: Geometric Algebra Techniques in Mathematics, Physics and En-gineering, B: Intensive course at the IMUVA: 5 Classical Mechanics, 6Quantum Esperanto and Pauli spinors, 7 Conformal Geometric Alge-bra 8. Classifications.

[100] 2016: Director of the “17th Lluıs Santalo Research Summer School”devoted to Geometric Algebra and Geometric Calculus, with Applica-tions in Mathematics, Physics and Engineering. N. Sayols was theSecretary of the School and the speakers, other than the Director, wereD. Hestenes, J. Lasenby, L. Dorst, and A. Lasenby. For moredetails, see LLuıs Santalo 2016.

[101] 2016: “Lectures” at the 17th “Lluıs Santalo” Research Summer School(see [100]): 1. Algebra and geometry in current curricula, 2. On axiomsystems for GA, 3. A view of F. Klein Erlangen Program through GAand 4. Enriching Abstract Algebra with GA.

[102] 2016: “Jose Marıa Montesinos Amilibia: biographical sketches”. InA mathematical tribute to Professor Jose Marıa Montesinos Amilibia,

22

33-62. Departamento de Geometrıa y Topologıa, Facultad de CienciasMatematicas, UCM, 2016.

[103] 2016: “Algebra Geometrica y Geometrıas Orgogonales”. La Gacetade la RSME, 19/3 (2016), 559-588. pdf An extended and adapted ver-sion in English will appear in chapters 2-4 of [126] (with permission).

[104] 2016: “Dirac’s equation seen in the Geometric Algebra light”. Lectureat the Differential geometry and Mathematical Physics special sessionof the CSASC joint meeting (20-23 September 2016). Slides.

[105] 2016— (with N. Sayols): Development of Python-coded environ-ments for specific symbolic computations, including Error-CorrectingCoding (PyECC) and Intersection Theory and Enumerative Geome-try (PyWit). See PyECC and PyWit for details. Its development anddissemination is enhanced by the use of Jupyter notebooks. Here aresome works that illustrate its usage: [111], [112], [117], [113], [116], and[131].

[106] 2017 (Editor in Chief): Proceedings of the AGACSE 2015 Conference(Barcelona, July 27-31, 2015), Special issue of Advances of AppliedClifford Algebras 27/1 (2017), 550 pp.

[107] 2017 (with M. Parra-Serra): “Preface” of [106], 345-349.

[108] 2017: “El Arbol de las Matematicas: 2015 y 2016”. La Gaceta dela RSME, 20/1 (2017), 1-12. pdf (a report on the publication at theArbolMat portal of 29 profiles elaborated in the years 2015 and 2016).

[109] 2017: Two-way bridges between Geometric Topology and MathematicalPhysics. Lecture at the special session on Geometric Topology (30.1-03.2, 2017) in honor of Marıa Teresa Lozano Imızcoz. Slides

[110] 2017: “Geometrıa y Fısica del espacio-tiempo”. La Gaceta de laRSME, 20/3 (2017), 24 pp. This material will be adapted and enlargedfor Chapter 3 of [118] (with permission).

[111] 2017 (with S. Molina and N. Sayols): “A bootstrap for the numberof 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

23

[113] 2017 (with N. Sayols): “Alternant codes and the McEliece cryptosys-tem”. Jornada de Teoria de Nombres, Universitat de Lleida, 7/10/2017.Slides

[114] 2017: Waldyr Rodrigues Jr.: Sketches on his Life and Work. Invitedplenary lecture at ICCA11 (Ghent, 9 August 2017). Later it will beexpanded into a fuller biographical work with special attention to hiscontributions at Mathematics/Physics interface. See [142].

[115] 2018: “From Leibniz’ characteristica geometrica to contemporary Geo-metric Algebra”. Quaderns d’Historia de l’Enginyeria, 16 (2017/2018),Special issue dedicated to commemorate Leibniz (1646-1716). Pages103-134.

[116] 2018 (with N. Sayols): “Computer algebra tales on Goppa codes andMcEliece cryptography”. Presented at the special session Computer Al-gebra in Coding Theory and Cryptography included in the 24th Con-ference on Applications of Computer Algebra (Santiago de Compostela,June 18-22, 2018). Slides

[117] 2018 (with Sayols and Farre): “On the PGZ decoding algorithm foralternant codes”. Computational and Applied Mathematics. In press.arXiv.

[118] 2018 (with C. Lavor and I. Zaplana): A Geometric Algebra In-vitation to Space-Time Physics, Robotics, and Molecular Geometry.Springer Briefs, x + 128 pages.

[119] 2018 (Editor in Chief): Early Proceedings of AGACSE 2018 .

[120] 2018 (as Chair of the SC of AGACSE 2018): Full Program. Containslinks to most of the slide presentations at the conference, and also tothe Early Proceedings (see [119]).

[121] 2018 (with C. Lavor and S. Wainer): Waldyr Alves Rodrigues Jr.:Annotations about his life track. Plenary lecture at AGACSE 2018 (July23, 2018). Slides.

[122] 2018 (with S. Wainer): Waldyr Alves Rodrigues Jr.: Fruits of a uni-fying philosophy. Plenary lecture at AGACSE 2018 (July 23, 2018).Slides.

[123] 2018 (with G.-M. Greuel, L. Narvaez (eds.)): Singularities, Alge-braic Geometry, Commutative Algebra, and Related Topics. Festschrift

24

for Antonio Campillo on the Occasion of his 65th Birthday. Springer,2018 (27 papers, xvi + 604 pages).

[124] 2018 (with G.-M. Greuel, L. Narvaez): Preface to [123], v-vi.

[125] 2018 (with F. Monserrat): “Antonio Campillo. A Portrayal of hisLife and Work”. First paper in [123], 1-36.

[126] 2018: Real Spinorial Groups: A Short Mathematical Introduction.Springer Briefs, 2018. x + 140 pages.

[127] 2018-19 (Editor in Chief): Proceedings of AGACSE 2018, to appear asa Thematic Collection in Advances in Applied Clifford Algebras.

[128] 2018 (Researcher, with P. Vasik (coordinator), S. Vitabile, E. U.Moya, et al.): Advanced Applications of Geometric Calculus. Applica-tion for an European Twinning Project to be submitted on 15 Novem-ber 2018.

[129] 2018 (President): Scientific Board of [128].

[130] 2018 (with S. Vitabile): Clifford algebra based applications for med-ical image processing and their hardware/software implementations.Letter of Intention, following an initiative of Prof. Ing. SalvatoreVitabile (Dipartimento di Biopatologia e Beiotechnologie Mediche,Universita degli Studi di Palermo), signed by the UPC/BarcelonaTechVicerector for Research Policy on 10 January 2018, “to establish a re-search consortium” between the two academic institutions, and which“authorizes Prof. Sebastia Xambo-Descamps to participate in the ini-tiative”. See [128] and [136] for research activities in which both re-searchers take part.

[131] 2018 (with N. Sayols): “Codis correctors d’errors i criptografia post-quantica”. Butlletı de la SCM. In press. An enlarged and adpatedversion will be included as Chapter 5 of [139] (with permission).

[132] 2018 (with E. U. Moya, S. Salazar, U. Cortes): “A Bio-inspiredMonogenic CNN Layer”. Preprint, November 2018.

[133] 2018-2021: Elaboration of 60 new profiles for publication in ArbolMat.

[134] 2019 (with N. Sayols): A cloud Python package for the computa-tional treatment of error-correcting codes. Talk at the special session“Computacion Simbolica: nuevos retos en Algebra y Geometrıa y sus

25

aplicaciones” of the Biannual Congress of the RSME to be held inSantander, 4-8 February, 2019.

[135] 2019: Geometric and Topological Aspects of Light. Invited plenary lec-ture in honor of E. Corbacho and E. Martın Peinador on theoccasion of their Jubilee. Vigo, 19-22 June, 2019. Based on materialsto be included in [141].

[136] 2019 (Chair): Systems, patterns and data engineering with geometriccalculi, a 2-Part mini-symposium included in ICIAM 2019. The speak-ers, other than SX (first and eigth lectures, see [137] and [138]), are I.Zaplana, C. Lavor, P. Colapinto, S. Lazendic, S. Vitabile,E. U. Moya. See the web Minisymposium for a detailed description.

[137] 2019: Geometric calculus techniques in science and engineering,Keynote lecture for the Minisymposium [136].

[138] 2019: Geometric Calculus meets Deep Learning, Closing lecture (theeighth) of the Minisymposium [136].

[139] 2019 (with the collaboration of N. Sayols): Error-Correcting Codes—A Computational Primer. Second edition of the book [48], correctedand expanded with three additional chapters. See CC2 for details. Thecomputational support is based on [105].

[140] 2019 (with the collaboration of J. M. Miret and N. Sayols): Inter-section Theory and Enumerative Geometry—A Computational Primer.In practical terms, this book is meant to include [30] (with permission),with corrections and extensions, together with material that ought tohave amounted to a second part, plus a computational environmentfreely accessible through the web. For details, see ITEG. The compu-tational support is based on PyWit (see [105]).

[141] 2019: Spheres and Lights. Springer for the English version and Ini-ciativa Digital UPC for the Catalan and Spanish versions. Reflectionson the interrelation between Geometry and Physics based on teaching,lectures, and current research.

[142] 2020 (with S. Wainer): Waldyr A. Rodrigues Jr.: Life and ScientificWorks. Springer, 2019-2020. This book will systematize and enlarge thematerials presented in [114], [121] and [122].

26

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

27