Gabriel Navarro Ortega

Gabriel Navarro Ortega (born in Sueca, Valencia) is a Spanish mathematician specializing in group theory, and representation theory of finite groups. Currently he is a full professor at the Universitat de València.

Career

G. Navarro at Oberwolfach, 2015

Navarro received his PhD at the Universitat de València in 1989. He held a Fulbright post doctoral position at MSRI and at the University of Wisconsin-Madison under the supervision of I. M. Isaacs. He is fellow of the American Mathematical Society^[1] and Distinguished Speaker of the European Mathematical Society.^[2]

In 2024 together with G. Malle, A. Schaeffer-Fry and P. H. Tiep, he completed the proof of Brauer's Height Zero Conjecture.^[3] He also extended the McKay Conjecture (with congruences of degrees modulo p with I. M. Isaacs,^[4] and with Galois automorphisms: the Galois-McKay conjecture^[5]). Together with I. M. Isaacs and G. Malle, he reduced the McKay conjecture to a question of finite simple groups^[6] establishing the path for its final solution by M. Cabanes and B. Späth in 2024. This reduction inspired several other reductions, such as the Alperin Weight Conjecture^[7] (with P. H. Tiep) or the Alperin-McKay conjecture^[8] (by B. Späth).

with G. Malle, A. Schaeffer-Fry, P. H. Tiep: Brauer's Height Zero Conjecture, Ann. of Math. 200 (2024), 557–608. doi:10.4007/annals.2024.200.2.4
with P. H. Tiep: The fields of values of characters of degree not divisible by p. Forum Math. Pi 9 (2021), vol 9, 1-28. doi:10.1017/fmp.2021.1
Character theory and the McKay conjecture. Cambridge Studies in Advanced Mathematics, 175. Cambridge University Press, Cambridge, 2018. doi:10.1017/9781108552790
with Britta Spath: On Brauer's Height Zero Conjecture, J. Eur. Math. Soc. 16, 695-747 (2014). doi:10.4171/JEMS/444
with P. H. Tiep: Characters of relative p'-degree with respect to a normal subgroup, Ann. of Math.178 (3) (2013), 1135–1171. doi:10.4007/annals.2013.178.3.7
with P. H. Tiep: A reduction theorem for the Alperin weight conjecture. Invent. Math. 184 (2011), no. 3, 529–565. doi:10.1007/s00222-010-0295-2
with I. M. Isaacs and G. Malle: A reduction theorem for the McKay conjecture. Invent. Math. 170 (2007), no. 1, 33–101. doi:10.1007/s00222-007-0057-y
The McKay conjecture and Galois automorphisms. Ann. of Math. (2) 160 (2004), no. 3, 1129–1140. doi:10.4007/annals.2004.160.1129
with I. M. Isaacs: New refinements of the McKay conjecture for arbitrary finite groups. Ann. of Math. (2) 156 (2002), no. 1, 333–344. doi:10.2307/3597192
Characters and blocks of finite groups. London Mathematical Society Lecture Note Series, 250. Cambridge University Press, Cambridge, 1998. doi:10.1017/CBO9780511526015

^ "List of Fellows of the American Mathematical Society". American Mathematical Society.
^ "EMS Distinguished Speakers". European Mathematical Society.
^ Malle, Gunter; Navarro, Gabriel; Schaeffer Fry, Amanda; Tiep, Pham (30 August 2024). "Brauer's Height Zero Conjecture". Annals of Mathematics. 200 (2): 557–608. arXiv:2209.04736. doi:10.4007/annals.2024.200.2.4.
^ Isaacs, I. Martin; Navarro, Gabriel (July 2002). "New Refinements of the McKay Conjecture for Arbitrary Finite Groups". Annals of Mathematics. 156: 333–344. arXiv:math/0411171. doi:10.2307/3597192.
^ Navarro, Gabriel (November 2004). "The McKay conjecture and Galois automorphisms". Annals of Mathematics. 160: 1129–1140. doi:10.4007/annals.2004.160.1129.
^ Isaacs, I. Martin; Malle, Gunter; Navarro, Gabriel (31 May 2007). "A reduction theorem for the McKay conjecture". Inventiones mathematicae. 170: 33–101. doi:10.1007/s00222-007-0057-y.
^ Navarro, Gabriel; Tiep, Pham Huu (3 November 2010). "A reduction theorem for the Alperin weight conjecture". Inventiones mathematicae. 184: 529–565. doi:10.1007/s00222-010-0295-2.
^ Späth, Britta (29 March 2012). "A reduction theorem for the Alperin–McKay conjecture". Journal für die reine und angewandte Mathematik (Crelle's Journal). 680: 153–189. doi:10.1515/crelle.2012.035.