Gabriel Navarro Ortega

Gabriel Navarro Ortega
Gabriel Navarro Ortega
	G. Navarro at Oberwolfach, 2015
Born	Sueca, Valencia, Spain
Education	Universitat de València
Known for	Group theory, representation theory of finite groups, Brauer's Height Zero Conjecture, McKay Conjecture
Awards	Fellow of the American Mathematical Society, Distinguished Speaker of the European Mathematical Society
	Scientific career
Fields	Mathematics
Workplaces	Universitat de València
Doctoral advisor	I. M. Isaacs

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

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 and Distinguished Speaker of the European Mathematical Society.

In 2024 together with G. Malle, A. Schaeffer-Fry and P. H. Tiep, he completed the proof of Brauer's Height Zero Conjecture. He also extended the McKay Conjecture (with congruences of degrees modulo p with I. M. Isaacs, and with Galois automorphisms: the Galois-McKay conjecture). Together with I. M. Isaacs and G. Malle, he reduced the McKay conjecture to a question of finite simple groups 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 (with P. H. Tiep) or the Alperin-McKay conjecture (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.