Gabriel Navarro Ortega Explained

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^[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).

Selected publications

• with G. Malle, A. Schaeffer-Fry, P. H. Tiep: Brauer's Height Zero Conjecture, Ann. of Math. 200 (2024), 557–608.
• 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.
• Character theory and the McKay conjecture. Cambridge Studies in Advanced Mathematics, 175. Cambridge University Press, Cambridge, 2018.
• with Britta Spath: On Brauer's Height Zero Conjecture, J. Eur. Math. Soc. 16, 695-747 (2014).
• with P. H. Tiep: Characters of relative p'-degree with respect to a normal subgroup, Ann. of Math.178 (3) (2013), 1135–1171.
• with P. H. Tiep: A reduction theorem for the Alperin weight conjecture. Invent. Math. 184 (2011), no. 3, 529–565.
• with I. M. Isaacs and G. Malle: A reduction theorem for the McKay conjecture. Invent. Math. 170 (2007), no. 1, 33–101.
• The McKay conjecture and Galois automorphisms. Ann. of Math. (2) 160 (2004), no. 3, 1129–1140.
• with I. M. Isaacs: New refinements of the McKay conjecture for arbitrary finite groups. Ann. of Math. (2) 156 (2002), no. 1, 333–344.
• Characters and blocks of finite groups. London Mathematical Society Lecture Note Series, 250. Cambridge University Press, Cambridge, 1998.

Notes and References

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