Research:
Publications (since 2000)  Preprints  Talks
Publications:

Okubo algebras with isotropic norm; in
NonAssociative Algebras and Related Topics. NAART 2020,
287301. Edited by H. Albuquerque, J. Brox, C. Martínez, and P. Saraiva. Springer Proceedings in Mathematics & Statistics, vol 427, Springer, Cham, 2023. (Preprint arXiv:2210.03456.)  Local derivations and automorphisms of Cayley algebras (with Shavkat Ayupov and Karimbergen Kudaybergenov); J. Pure Appl. Algebra (2023), 107277 (16 pages, doi 10.1016/j.jpaa.2022.107277). (Preprints arXiv:2105.08423 and arXiv:2205.06559.)
 Real simple symplectic triple systems (with Cristina Draper); Anal. Math. Phys. 12 (2022), paper no. 69, 46 pp. (Preprint arXiv:2107.05882.)
 Nongroup gradings on simple Lie algebras; Linear Algebra Appl. 640 (2022), 149161. (Preprint arXiv:2107.13791.)
 Gradings on associative algebras with involution and real forms of classical simple Lie algebras (with Mikhail Kochetov and Adrián RodrigoEscudero); J. Algebra 590 (2022), 61138. (Preprint arXiv:2105.13666.)
 Gradeddivision algebras and Galois extensions (with M. Kochetov); J. Pure Appl. Algebra 221 (2021), 106773. (Preprint arXiv:2008.06212.)
 Evolution algebras, automorphisms, and graphs (with A. Labra); Linear Multilinear Algebra 69 (2021), no. 2, 331342. (Preprint arXiv:1902.02191.)
 Gradeddivision algebras over arbitrary fields (with Y. Bahturin and M. Kochetov); J. Algebra Appl. 20 (2021), no. 1, 2140009, 28 pages. (Preprint arXiv:1912.11911.)
 Cross products, automorphisms, and gradings (with A. DazaGarcía and L. Tang); Linear Algebra Appl. 610 (2021), 227256. (Preprint arXiv:2006.10324.)

Composition algebras; in
Algebra and Applications I: Nonassociative Algebras and Categories
, Chapter 2, pp. 2757, edited by Abdenacer Makhlouf, SciencesMathematics, ISTEWiley, London 2021. (Preprint arXiv:1810.09979.)  Codes, Sstructures, and exceptional Lie algebras (with I. Cunha); Glasgow Math. J. 62 (2020), S14S27. (Preprint arXiv:1812.08439.)
 Reductive homogeneous spaces and nonassociative algebras; Commun. Math. 28 (2020), no. 2, 199229. (Preprint arXiv:1503.03227.)
 Gradedsimple algebras and cocycle twisted loop algebras; Proc. Amer. Math. Soc. 147 (2019), no. 7, 28212833. (Prepint arXiv:1807.01041.)
 On Kac's Jordan superalgebra (with A.S. CórdovaMartínez and Abbas Darehgazani); Linear Multilinear Algebra 67 (2019), no. 3, 490498. (Preprint arXiv:1701.06798.)
 Gradings on semisimple algebras (with Alejandra Sarina Córdova Martínez); Linear Algebra Appl. 559 (2018), 145171. (Preprint arXiv:1803.09959.)
 Gradings on the simple real Lie algebras of types G_{2} and D_{4} (with Mikhail Kochetov); J. Algebra 512 (2018), 382426. (Preprint arXiv:1803.10949.)
 Order 3 elements in G_{2} and idempotents in symmetric composition algebras; Canadian J. Math. 70 (2018), no. 5, 10381075. (Preprint arXiv:1705.01293.)
 Clifford algebras as twisted group algebras and the Arf invariant (with Adrián RodrigoEscudero); Adv. Appl. Clifford Algebras (2018), 28:41. (Preprint arXiv:1801.07002.)
 Cross products, invariants, and centralizers (with G. Benkart); J. Algebra 500 (2018), 69102. (Preprint arXiv:1606.07588.)
 Gradings on modules over Lie algebras of E types (with C. Draper and M. Kochetov); Algebras and Representation Theory 20 (2017), no. 5, 10851107. (Preprint arXiv:1609.02510.)
 Maximal finite abelian subgroups of E_{8} (with C. Draper); Proc. Royal Soc. Edinburgh 147A (2017), 9931008. (Preprint arXiv:1312.4326.)
 Graded simple modules and loop modules (with M. Kochetov); in “Groups, Rings, Group Rings and Hopf Algebras”, dedicated to Don Passman. Contemporary Mathematics, volume 688 (2017), pp. 5385. (Preprint arXiv:1601.03008.)
 Gradings on algebras over algebraically closed fields; in NonAssociative and NonCommutative Algebra and Operator Theory. NANCAOT, Dakar, Senegal, May 2325, 2014: Workshop in Honor of Professor Amin Kaidi, Gueye, Cheikh Thiecoumbe, Molina, Mercedes Siles (Eds.), pp. 113121, Springer 2016. (Preprint arXiv:1407.0480.)
 An overview of fine gradings on simple Lie algebras (with C. Draper); Note Mat. 36 (2016), 1534. (Preprint arXiv:1603.09482.)
 On nilpotent evolution algebras (with A. Labra); Linear Algebra Appl. 505 (2016), 1131. (Preprint arXiv:1602.01590.)
 Some special features of Cayley algebras, and G_{2}, in low characteristics (with A. CastilloRamírez); J. Pure Appl. Algebra. 220 (2016), no. 3, 11881205. (Preprint arXiv:1503.05529.)

Okubo algebras:
automorphisms, derivations and idempotents;
Contemporary Mathematics, vol. 652, Amer. Math. Soc. Providence, RI, 2015, pp. 6173.
Proceedings of the BicoccaWorkshop on Lie Algebras 2013, in honor of Professor Helmut Strade on the occasion of his 70th birthday, Milano, May 22nd24th, 2013; Marina Avitabile, Joerg Feldvoss, and Thomas Weigel, eds.
(Preprint arXiv:1310.5455.)  Gradings on the Lie algebra D_{4} revisited (with M. Kochetov); J. Algebra 441 (2015), 441474. (Preprint arXiv:1412.5076.)
 Graded modules over classical simple Lie algebras with a grading (with M. Kochetov); Israel J. Math. 207 (2015), no. 1, 229280. (Preprint arXiv:1308.6089.)
 Evolution algebras and graphs (with A. Labra); J. Algebra Appl. 14 (2015), no. 7, 1550103 (10 pages). (Preprint arXiv:1312.4685.)
 Fine gradings and gradings by root systems on simple Lie algebras; Revista Matemática Iberoamericana 31 (2015), no. 1, 245266. (Preprint arXiv:1303.0651.)
 Fine gradings on the simple Lie algebras of type E (with C. Draper); Note Mat. 34 (2014), no. 1, 5388. (Preprint arXiv:1403.0514.)
 Left unital Kantor triple systems and structurable algebras (with N. Kamiya and S. Okubo); Linear and Multilinear Algebra 62 (2014), no. 10, 12931313. (Preprint arXiv:1205.2489.)
 Classification of quadratic Lie algebras of low dimension (with S. Benayadi); J. Math. Phys. 55 (2014), 081703. (Preprint arXiv:1404.5174.)
 A Z_{4}^{3}grading on a 56dimensional simple structurable algebra and related fine gradings on the simple Lie algebras of type E (with D. ArandaOrna and M. Kochetov); Comment. Math. Univ. Carolin. 55 (2014), no. 3, 285313. (Preprint arXiv:1312.1067.)
 Gradings on simple Lie algebras (with M. Kochetov), Mathematical Surveys and Monographs 189, American Mathematical Society, 2013.
 Algebraic Groups of Type D_{4}, Triality, and Composition Algebras (with V. Chernousov, M. Knus and J.P. Tignol); Documenta Math. 18 (2013), 413468.
 On some Jordan baric algebras (with A. Labra); J. Algebra Appl. 12 (2013), no. 5, 1250215 (12 pages). (Preprint arXiv:1205.2993.)
 Weyl groups of fine gradings on simple Lie algebras of types A, B, C and D (with M. Kochetov), Serdica Math. J. 38 (2012), 736. (Preprint arXiv:1109.3540.)
 Lie algebras with prescribed sl_{3} decomposition (with G. Benkart), Proc. Amer. Math. Soc. 140 (2012), no. 8, 26272638. (Preprint arXiv:1101.0489.)
 Weyl groups of fine gradings on matrix algebras, octonions and the Albert algebra (with M. Kochetov), J. Algebra 366 (2012), no. 1, 165186. (Preprint arXiv:1009.1462.)
 Gradings on the exceptional Lie algebras F_{4} and G_{2} revisited (with M. Kochetov), Rev. Mat. Iberoamericana 28 (2012), no. 3, 775815. (Preprint arXiv:1009.1218.)
 A class of Locally Nilpotent Commutative Algebras (with A. Behn and A. Labra), Internat. J. Algebra Comput. 21 (2011), no. 5, 763774. (Preprint arXiv:0907.3569.)
 Fine gradings on exceptional simple Lie superalgebras (with C. Draper and C. MartínGonzález), International Journal of Mathematics 22 (2011), no. 12, 18231855. (Preprint arXiv:1101.5470.)
 Special FreudenthalKantor triple systems and Lie algebras with dicyclic symmetry (with S. Okubo), Proc. Royal Soc. Edinburgh 141A (2011), no. 6, 12251262. (Preprint arXiv:1004.1125.)
 Tits construction of the exceptional simple Lie algebras, Pure and Applied Mathematics Quarterly 7 (2011), no. 3 (Special Issue: In honor of Jacques Tits), 559586. (Preprint arXiv:0907.3789.)
 Derivations of the ChengKac Jordan superalgebras (with E. Barreiro and C. Martínez), J. Algebra 338 (2011), no. 1, 144156. (Preprint arXiv:1101.0485.)
 Irreducible LieYamaguti algebras of generic type (with P. Benito and F. MartínHerce), J. Pure Applied Algebra 215 (2011), 108130. (Preprint arXiv:0907.3622.)
 Fine gradings on simple classical Lie algebras, J. Algebra 324 (2010), no. 12, 35323571. (Preprint arXiv:0906.0655.)
 Gradings on symmetric composition algebras, J. Algebra 322 (2009), no. 10, 35423579. (Preprint arXiv:0809.1922.)
 Jordan gradings on the exceptional simple Lie algebras, Proc. Amer. Math. Soc. 137 (2009), no. 12, 40074017. (Preprint arXiv:0810.2737.)
 More non semigroup Lie gradings, Linear Algebra Appl. 431 (2009), no. 9, 16031606. (Preprint arXiv:0809.4547.)
 The Supermagic Square in characteristic 3 and Jordan superalgebras (with Isabel Cunha), Algebras, Representations and Applications. Proceedings of a Conference in Honour of Ivan Shestakov's 60th Birthday (Maresias, Brazil 2007). Contemporary Mathematics 483 (2009), 91106. (Preprint arXiv:0802.3271)
 Lie algebras with S_{3} or S_{4}action and generalized Malcev algebras (with Susumu Okubo), Proc. Royal Soc. Edinburgh 139A (2009), 321357. (Preprint arXiv:0801.2481)
 Irreducible LieYamaguti algebras (with Pilar Benito and Fabián MartínHerce), J. Pure Applied Algebra 213 (2009), 795808. (Preprint arXiv:0810.0440)
 Models of some simple modular Lie superalgebras, Pacific J. Math. 240 (2009), no. 1, 4983. (Preprint arXiv:0805.1304)
 The Tits construction and some simple Lie superalgebras in characteristic 3, J. Lie Theory 18 (2008), no. 3, 601615. (Preprint arXiv:math.RA/0703784. A review of this paper appears in the Excerpts from Zentralblatt MATH. Special Issue ICM 2010, Hyderabad)
 Maximal subalgebras of Jordan superalgebras (with Jesús Laliena and Sara Sacristán), J. Pure Appl. Algebra 212 (2008), no. 11, 24612478. (Preprint arXiv:math.RA/0606017)
 S_{4}symmetry on the Tits construction of exceptional Lie algebras and superalgebras (with Susumu Okubo), Publ. Mat. 52 (2008), no. 2, 315346. (Preprint arXiv:math.RA/0611303)
 Wedderburn quasialgebras (with Helena Albuquerque and José María PérezIzquierdo), Portugal Math. (N.S.) 65 (2008), no. 2, 275283.
 On the classification of commutative right nilalgebras of nilindex 5 and dimension 4 (with Alicia Labra), Commun. Algebra 36 (2008), 17041716. (Preprint of the 'Seminario García Galdeano'.)
 The existence of superinvolutions (with Oliver Villa), J. Algebra 319 (2008), 43384359. (Preprint arXiv:0704.3127)
 Symplectic and orthogonal triple systems, and a Freudenthal Magic Supersquare, Proceedings of the "XVI Coloquio Latinoamericano de álgebra" (Colonia de Sacramento, Uruguay, 2005), Biblioteca de la Revista Matemática Iberoamericana (2007), 253270. (Preprint of the 'Seminario García Galdeano'.)
 The S_{4}action on the Tetrahedron Algebra, Proc. Royal Soc. Edinburgh 137A (2007), 12271248. (Preprint arXiv:math.RA/0604218)
 Some new simple modular Lie superalgebras, Pacific J. Math. 231 (2007), no. 2, 337359. (Preprint arXiv:math.RA/0512654)
 An extended Freudenthal Magic Square in characteristic 3 (with Isabel Cunha), J. Algebra 317 (2007), 471509. (Preprint arXiv:math.RA/0605379)
 The Kac Jordan superalgebra: automorphisms and maximal subalgebras (with Jesús Laliena and Sara Sacristán), Proc. Amer. Math. Soc.135 (2007), no. 12, 38053813. (Preprint arXiv:math.RA/0509040)
 The extended Freudenhtal Magic Square and Jordan algebras (with Isabel Cunha), manuscripta math. 123 (2007), no. 3, 325351. (Preprint arXiv:math.RA/0608191)
 The magic square and symmetric compositions II; Rev. Mat. Iberoamericana 23 (2007), 5784.(Preprint arxiv:math.RT/0507282)
 On the classification of commutative rightnilalgebras of dimension at most four (with Alicia Labra); Commun. Algebra 35 (2007), no. 2, 577588. (Preprint of the 'Seminario García Galdeano'.)
 Lie algebras with S_{4}action and structurable algebras (with Susumu Okubo), J. Algebra 307 (2007), 864890. (Preprint arXiv:math.RA/0508558)
 Freudenthal's magic supersquare in characteristic 3 (with Isabel Cunha); From Lie Algebras to Quantum Groups (H. Albuquerque, S. Lopes and J. Teles eds.), Centro Internacional de Matemática, Coimbra (Portugal) 2006, pp. 1725. (Preprint of the 'Seminario García Galdeano'.)
 A Lie grading which is not a semigroup grading; Linear Algebra and Appl. 418 (2006), 312314. (Preprint arXiv:math.RA/0512618)
 A new look at Freudenthal's magic square, in Non Associative Algebra and Its Applications, (L. Sabinin, L. Sbitneva and I.P. Shestakov, eds.); Lecture Notes in Pure and Applied Mathematics, vol. 246, pp. 149165. Chapman and Hall, Boca Raton 2006. (Preprint of the 'Seminario García Galdeano'.)
 New simple Lie superalgebras in characteristic 3; J. Algebra 296 (2006), 196233. (Preprint arXiv:math.RA/0412395)
 (1,1)balanced Freudenthal Kantor triple systems and noncommutative Jordan algebras (with Noriaki Kamiya and Susumu Okubo); J. Algebra 294 (2005), 1940. (Preprint arXiv:math.RA/0404550)
 LieYamaguti algebras related to g_{2} (with Pilar Benito and Cristina Draper); J. Pure Appl. Algebra 202 (2005), 2254.
 A Note on the Linkage of Hurwitz Algebras (with Oliver Villa); manuscripta math. 117 (2005), 15110. (Preprint of the 'Seminario García Galdeano'.)
 Symmetric Composition Algebras and Freudenthal's Magic Square; Resenhas IMEUSP 6 (2004), no. 2/3, 165176.
 A(n,n)graded Lie superalgebras (with Georgia Benkart and Consuelo Martínez); J. Reine Angew. Math. 573 (2004), 139156. (Preprint arXiv:math.RT/0309395)
 The magic square and symmetric compositions; Revista Mat. Iberoamericana 20 (2004), no. 2, 475491. (Preprint Jordan Theory Preprint Archives 130, June 2002)
 A modified Brauer algebra as centralizer algebra of the unitary group; Trans. Amer. Math. Soc. 356 (2004), no. 10, 39633983. (Preprint arXiv:math.RT/0305429)
 Maximal subalgebras of associative superalgebras (with J. Laliena and S. Sacristán); J. Algebra 275 (2004), 4058.
 Composition algebras satisfying the flexible law (with Hyo Chul Myung); Commun. Algebra 32(5) (2004), 19972013.
 Quaternions, octonions and the forms of the exceptional simple classical Lie superalgebras; Comment. Math. Helv. 79 (2004), no. 1, 208228.
 Nonassociative systems and irreducible homogeneous spaces (with Pilar Benito and Fabián Martín Herce); in "Recent Advances In Geometry and Topology". The 6th International Workshop on Differential Geometry and Topology and The 3rd GermanRomanian Seminar on Geometry. ClujNapoca, September 16 2003, pp. 6576. (Preprint of the 'Seminario García Galdeano'.)
 Lie superalgebras graded by the root system A(m,n) (with Georgia Benkart); J. Lie Theory 13 (2003), 387400. (Preprint arXiv:math.RA/0202284)
 Lie superalgebras graded by the root system B(m,n) (with Georgia Benkart); Selecta math., New ser. 9 (2003), 313360.
 Simple (1,1) balanced Freudenthal Kantor triple systems (with Noriaki Kamiya and Susumu Okubo); Glasgow Math. J. 45 (2003), 353372.
 Models of the octonions and G_{2} (with M.P. Benito and C. Draper), Linear Algebra Appl. 371 (2003), 333359.
 The Tits construction and the exceptional simple classical Lie superalgebras (with Georgia Benkart), Quartely J. Math. 54 (2003), 123137.
 Lie superalgebras graded by the root systems C(n), D(m,n), D(2,1;a), F(4), and G(3) (with Georgia Benkart), Canadian Math. Bull. 45 (4) (2002), 509524.
 Composition superalgebras (with Susumu Okubo), Commun. Algebra 30 (2002), no. 11, 54475471.
 A new construction of the Kac Jordan superalgebra (with Georgia Benkart), Proc. Amer. Math. Soc. 130 (2002), no.11, 32093217.
 Composition of quadratic forms and the HurwitzRadon function in characteristic 2, Linear Algebra Appl. 348 (2002), 87103.
 Z_{2}quasialgebras (with H. Albuquerque and J.M. PérezIzquierdo), Commun. Algebra 30(5) (2002), 21612174.
 On the Cartan Jacobson theorem (with P. Alberca Bjerregaard, C. Martín González and F.J. Navarro Márquez), J. Algebra 250 (2002), 397407.
 Local triality and some related algebras (with S. Okubo), J. Algebra 244 (2001), 828844.
 Alternative Quasialgebras (with H. Albuquerque and J.M.PérezIzquierdo), Bull. Australian Math. Soc. 63 (2001), 257268.
 Invariant projectively flat affine connections on Lie groups, Hokkaido Math. J. 30 (2001), 231239.
 A note on triality and symmetric compositions, Abh. Math. Sem. Univ. Hamburg 70 (2000), 125135. (http://dx.doi.org/10.1007/BF02940909)
 Power associative composition algebras (with J.A. Cuenca and J.M. PérezIzquierdo), manuscripta math. 103 (2000), 7590.
 On algebras satisfying x^{2}x^{2}=N(x)x (with S. Okubo), Math. Z. 235 (2000), no. 2, 275314.
 Triality and automorphisms and derivations of composition algebras, Linear Algebra Appl. 314 (2000), 4974.
 Octonions and affine connections on spheres (with H.C. Myung), Nonassociative Algebra and Its Applications (R. Costa, H. Guzzo Jr., A. Grichkov and L.A. Peresi, eds.), Lecture notes in pure and applied mathematics 211, 4354. MarcelDekker, Nueva York 2000.
 Invariant connections on symmetric spaces (with C. Draper and M.P. Benito), Nonassociative Algebra and Its Applications (R. Costa, H. Guzzo Jr., A. Grichkov and L.A. Peresi, eds.), Lecture notes in pure and applied mathematics 211, 2133. MarcelDekker, Nueva York 2000.
 The Reductive Pair (B_{4},B_{3}) and Affine Connections on S^{15} (with H.C. Myung), J. Algebra 227 (2000), 504531.
 Pseudocomposition superalgebras (with S. Okubo), J. Algebra 227 (2000), 125.
Preprints:
 Almost fine gradings on algebras and classification of gradings up to isomorphism (with Mikhail Kochetov); arXiv:2308.07230.
 Short (SL_{2}xSL_{2})structures on Lie algebras (with Patricia D. Beites, Alejandra S. CórdovaMartínez and Isabe Cunha); arXiv:2303.17993. To appear in Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM.
 From octonions to composition superalgebras via tensor categories (with Alberto DazaGarcía and Umut Sayin); arXiv:2205.06559. To appear in Rev. Mat. Iberoam.
Talks:
 The extended Freudenthal magic square via tensor categories. Symmetric Tensor Categories and Representation Theory (IPAM, January 812, 2024).
 Gradings and Sstructures on Lie algebras. VI International Workshop on NonAssociative Algebras (Madrid, Spain, June 1923, 2023) and Groups, Rings, Lie and Hopf Algebras. V (Memorial University of Newfoundland, Harlow campus, UK, August 2125, 2023).

Tensor categories, algebras, and superalgebras.
European NonAssociative Algebra Seminar
(January 9, 2023); Virtual conferenceRepresentations of Lie Superalgebras and Related Topics
, School of Mathematics, IPMIsfahan (Iran; August 31  September 1, 2023); SeminarLie and Jordan Algebras and their Representations
, Universidade de Sao Paulo (Brasil; August 18, 2022); NonAssociative Algebras and Related Topics II (NAART II, July 1822, 2022); and Universidad de Málaga (June 21, 2022).
(Here you may get the slides of the talk.)  Quaternions and octonions. Seminar of the School of Mathematical Sciences of Harbin Normal University (China, December 13, 2022).

Gradings on simple Lie algebras.
Online seminar
Quadratic forms, Linear algebraic groups and Beyond
, January 26, 2022; and Tianyuan Mathematical Center in Southeast China, February 28, 2020.
(Here you may get the slides of the talk.) 
Nongroup gradings on simple Lie algebras.
International Conference
Trends in Combinatorial Ring Theory
(Dedicated to the 70th anniversary of Vesselin Drensky). Sofia (Bulgaria, September 2024, 2021), and RSME2022 (Congreso bienal de la Real Sociedad Matemática Española
, Ciudad Real, Spain, January 1722, 2022) 
Composition algebras.
Online minicourse (5 lectures) at the CIMPA School
Nonassociative algebras and their Applications
August 30 to September 11, 2021. University of Antananarivo (Madagascar).
(Here you may get the slides of the course.) 
Gradeddivision algebras
and Galois extensions.
International Conference on ring Theory, dedicated to the 100th
anniversay of A.I. Shirshov (19211981). Novosibirsk (Russia, August 1621).
(Here you may get the slides of the talk.)  Gradings and affine group schemes. Online minicourse (4 lectures) at the University of Isfahan (Iran, JuneJuly 2021).

Gradedsimple algebras and twisted loop algebras.
Online seminar
Lie and Jordan Algebras and their Representations
. Universidade de Sao Paulo (Brasil; October 8, 2020).
(Here you may get the slides of the talk.)  Codes, Sstructures, and exceptional Lie algebras, III International Workshop on NonAssociative Algebras. Universidad de Málaga (Spain; February 37, 2020).
 Triality, Workshop on Differential Geometry and Nonassociative Algebras. CIRM Luminy (France; November 1215, 2019).
 Clifford algebras as twisted group algebras and the Arf invariant, Dia de Álgebra, dedicado a Helena Albuquerque, por ocasião do seu aniversário. Universidade de Coimbra (Portugal; September 27, 2019).
 Gradedsimple algebras and loop algebras, International Workshop on NonAssociative Algebras in Porto (Portugal; April 29  May 3, 2019), and International Workshop on Nonassociative Algebras and Geometry, Bonne Bay Marine Station, Memorial University of Newfoundland (Canada, August 1216, 2019).
 Gradings on semisimple algebras, Workshop on NonAssociative Algebras and Applications, Lancaster University (UK; July 913, 2018).
 Quaternions
and Octonions, International Workshop
Combinatorics of Group Actions and its Applications
, Memorial University of Newfoundland (Canada; August 28 to September 1, 2017), andFourth International Colloquium on Representations of Algebras and its Applications; Alexander Zavadskij
(National University of Colombia; November 46, 2020).  Order 3 elements in G_{2} and idempotents in symmetric compostion algebras, "Lie Theory, Cohomology, and Geometry in Wildrose Country", a workshop in honour of Vladimir Chernousov and Arturo Pianzola; University of Alberta (Edmonton, Canada; August 21 to 25, 2017); and II Joint Meeting SpainBrazil in Mathematics (Cádiz, Spain; December 11 to 15, 2018).
 Cross products, invariants, and centralizers, Universidad de Málaga, (Spain; July 17, 2017), and the International Workshop "Combinatorics of Group Actions and its Applications", Memorial University of Newfoundland (Canada; August 28 to September 1, 2017).
 Triality, Congreso Bienal de la Real Sociedad Matemática Española, Universidad de Zaragoza, (Spain; January 30 to February 3, 2017).
 Graded simple algebras and modules, Workshop on NonAssociative Algebras and Other Structures, Universidad de Málaga, (Spain; December 14 and 15, 2016).
 Okubo algebras, Conference in honor of Ernst Dieterich and KarlHeinz Fieseler, Uppsala University, (Sweden; September 15, 2016).
 Graded modules over simple Lie algebras, International Conference "Groups and Rings  Theory and Applications" (GRiTA2016), Sofia (Bulgaria; July 1115, 2016).

Gradings on simple
Lie algebras,
Jilin University, November 13, 2020;
Algebra Seminar,
Chalmers University of Technology and the University of Gothenburg, March 10, 2016; and
“Workshop on Graded Algebra, Geometry and Related Topics” (Honoring the 60th birthday of
O. Adolfo SánchezValenzuela), Mérida (México, November 1518, 2016).
Here is a video of this last talk.  Octonions in low characteristics, First joint meeting BrazilSpain in Mathematics, Fortaleza (December 710, 2015); XXI Coloquio Latinoamericano de Álgebra, Buenos Aires (July 2429, 2016); and “Les Deuxièmes Journées de Géometrie, et Algèbre Non Associative”, Meknès (October 68, 2016).
 Octonions, Combinatorics Seminar, University of Wisconsin, November 9, 2015; Colloquium Talk, Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, March 11, 2016; and Colloquium Talk, Department of Mathematics, Uppsala University, September 16, 2016.
 Gradings on simple Lie algebras, (a threehours minicourse). Advances in Group Theory and Applications AGTA2015, Porto Cesareo (June 1619, 2015).
 Triality, composition algebras, and gradings on D_{4}. Minisymposium “Algebras and Algebraic Groups”, Uppsala (May 22, 2015); and “Lie and Jordan Algebras VI. Dedicated to Efim Zelmanov's 60th birthday”, Bento Gonçalves (Brazil; December 1319, 2015).
 Reductive homogeneous spaces and nonassociative algebras. Notes for a minicourse at the CIMPA research school “Géométrie différentielle et algèbres non associatives”, Marrakech (April 1324, 2015).

Otros números (Spanish);
Cincuentenario de la Olimpiada Matemática Española, Universidad Complutense de Madrid.
November 21, 2014.
An English version, under the title Octonions, was delivered at the “Universidad Internacional Menéndez Pelayo” (Santander, July 9, 2015).  Graded modules over classical simple Lie algebras; XII Jornadas de Álgebra No Conmutativa, Málaga, April 2014, and Enveloping Algebras and Representation Theory, St. John's (Canada), AugustSeptember 2014.
 Fine gradings and gradings by root systems on simple Lie algebras; Third Mile High Conference on Nonassociative Mathematics, August 2013 (University of Denver, USA), Groups, Nonassociative Algebras and Combinatorics, SeptemberOctober 2013 (CIRM, Luminy, France), and Infinite Dimensional Lie Superalgebras and Their Representations, May 2016 (IPM Isfahan, Iran).
 Some simple modular Lie superalgebras; Bicocca  Workshop on Lie Algebras 2013 (in honor of Professor Helmut Strade on the occasion of his 70th birthday). May 2013 (Milan, Italy).
 Symmetric composition algebras and exceptional simple Lie algebras; Colloquium Talk (Uppsala Universitet, Sweden). December 2012.
 A FreudenthalTits Supermagic Square; DAG days: "The FreudenthalTits Magic Square" (University of Ghent, Belgium), and Centro de Matemática da Universidade da Beira Interior (Covilhã, Portugal). October 2012.
 Gradings on the Octonions, the Albert algebra, and exceptional simple Lie algebras; Groups, Rings, Lie and Hopf Algebras III (Memorial University of Newfoundland, Bonne Bay, NL, Canada). August 2012.
 Gradings on the Octonions and the Albert algebra; Workshop on Exceptional Algebras and Groups (Ottawa, Canada). April 2012.
 The Albert algebra as a twisted group algebra; International Conference on Ring Theory (dedicated to the 90th anniversary of A.I.Shirshov; Sobolev Institute of Mathematics, Novosibirsk, Russia), July 2011, and Nonassociative Algebra in Action: Past, Present, and Future Perspectives (in honor of Kevin McCrimmon; University of Virginia, USA), September 2011.
 Gradings on simple Lie algebras; Minicourse given at the Conference "NonAssociative Algebras and Related Topics" (Coimbra, Portugal). July 2011.
 Flexible composition algebras; International Conference in Memory of Hyo Chul Myung (KIAS, Seoul, Korea). April 2011.
 Gradings on simple Lie algebras; University of Lund (Sweden) and First Joint Meeting of the American Mathematical Society and Sociedad de Matemática de Chile (Pucón, Chile). December 2010.

Composition algebras and their gradings; Universidad de Málaga
(2010).
(This minicourse expands the one given in St. John's in 2009 under the same title.)  Jordan gradings on exceptional simple Lie algebras; Conference Algebras, Representations and Applications (Lie and Jordan Algebras, their Representations and Applications IV; Manaus, Brazil, 2009).) (Click here to see a picture.)
 Composition algebras and their gradings; Atlantic Algebra Center minicourse, Memorial University of Newfoundland (St. John's, 2009).
 Simple modular Lie superalgebras; Encuentro Matemático HispanoMarroquí (Casablanca, 2008).
 Números excepcionales; Seminario Vidal Abascal, Universidad de Santiago de Compostela (2008). (French version: Nombres exceptionnels, delivered at the Université de Pau et des Pays de l'Adour in 2008. English version: Exceptional Numbers, delivered at the Memorial University of Newfoundland in 2009.)
 Gradings on composition algebras; Memorial University of Newfoundland (St. John's, 2008).
 A Freudenthal Supermagic Square; University of California Lie Theory Workshop. A conference in honor of Professor Georgia Benkart (San Diego, 2008).
 Tits construction, Freudenthal Magic Square, and modular simple Lie superalgebras; Lie Algebras and their Applications (Seoul, 2007).
 Symmetry of the Tits construction of the exceptional simple Lie algebras; Primer Congreso HispanoFrancés de Matemáticas  Premier Congrès FrancoEspagnol de Mathématiques (Zaragoza, 2007).
 An extended Freudenthal Magic Square in characteristic 3; From Lie Algebras to Quantum Groups (Coimbra, 2006).
 Algunos objetos excepcionales; discurso de ingreso en la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza (February 23, 2006). (You may download the presentation too.)
 New simple Lie superalgebras in characteristic 3; CIMMA (Almería, 2005).
 Lie algebras with S_{4} action and structurable algebras; Workshop on Nonassociative Algebras (Fields Institute, Toronto, 2005)
 Otros números; Festividad de San Alberto Magno, Facultad de Ciencias de la Universidad de Zaragoza, (November 15, 2004). (You can check here how formal I am while lecturing.)
 Symmetric composition algebras and Freudenthal's Magic Square; Lie and Jordan algebras, their representations and applications II (Guarujá, Brazil, 2004).
 Productos vectoriales (Vector cross products); Seminario Rubio de Francia (Universidad de Zaragoza, 2004).
 Tits construction and Freudenthal's Magic Square; Lie Algebras and Related Topics (KIAS, Seoul, Korea, 2003).
 Nonassociative systems and irreducible homogeneous spaces; The Sixth International Workshop on Differential Geometry and Its Applications and The Third GermanRomanian Seminar on Geometry (ClujNapoca, Romania, 2003).
 A modified signed Brauer algebra as centralizer algebra of the unitary group; 2002 AMS Fall Central Section Meeting (Madison, WI, USA, 2002).
 Exceptional Lie superalgebras; Lie and Jordan algebras; their representations and applications (Guarujá, Brazil, 2002).
Last update: February 23, 2024