Carolina Vallejo Rodríguez

I am a profesora ayudante doctora (assistant professor) at the Universidad Autónoma de Madrid (UAM) and a member of the Instituto de Ciencias Matemáticas (ICMAT). My main interest are the so-called Counting Conjectures, which fit into the class of global/local problems in Group Representation Theory.

From September 2020 to June 2021 I was an assistant professor at the Universidad Carlos III de Madrid. Previously, I held different postdoc positions. I was a Juan de la Cierva postdoctoral researcher at the UAM, a Severo Ochoa fellow at the ICMAT and a postdoc associated with the Mathematical Science Research Institute (MSRI) research program Group Representation Theory and Applications.

I completed my Ph.D. (as well as my Degree and Master) at the University of Valencia, where I worked under the supervision of Gabriel Navarro. The main goal of my Ph.D. thesis was to find explicit bijections between character sets, so that fields of values of characters were preserved.


Together with Gabriel Navarro and Britta Späth I organize the workshop "Counting conjectures and beyond" within the scientific programme "Groups, representations and applications: new perspectives" of the Isaac Newton Institute (Cambridge). The purpose of the workshop is to gather relevant mathematicians working on counting conjectures and related global-local problems in order to discuss the state of the art and the new developments in the area. In particular, this meeting will celebrate the great influence of Gunter Malle on those developments.



  1. Height zero characters in principal blocks (with N. Hung and A. A. Schaeffer Fry).

  2. Published

  3. Sylow branching coefficients and a conjecture by Malle and Navarro (joint work with E. Giannelli, S. Law and J. Long), Bull. London Math. Soc. 54 (2022), 552-567.
  4. Principal blocks with 5 irreducible characters (joint work with N. Rizo and A. A. Schaeffer Fry), J. Algebra 585 (2021), 316-337.
  5. Characters of π '-degree and small cyclotomic fields (with E. Giannelli, N. Hung and A. A. Schaeffer Fry). Ann. Mat. Pura Appl. (4) 200 (2021), no. 3, 1055 - 1073.
  6. Characters and generation of Sylow 2-subgroups (with G. Navarro, N. Rizo and A. A. Schaeffer Fry), Represent. Theory 25 (2021), 142-165.
  7. A reduction theorem for the Galois-McKay conjecture (with G. Navarro and B. Späth), Trans. Amer. Math. Soc. 373 (2020), no. 9, 6157–6183.
  8. Galois action on the principal block and cyclic Sylow subgroups (with N. Rizo and A. A. Schaeffer Fry), Algebra Number Theory 14 (2020), no. 7, 1953–1979.
  9. Character correspondences in solvable groups with a self-normalizing Sylow subgroup, J. Algebra Appl. 19 (2020), no. 10, 2050190, 8 pp.
  10. Characters of π '-degree (with E. Giannelli and A. A. Schaeffer Fry), Proc. Amer. Math. Soc. 147 (2019), no. 11, 4697-4712.
  11. Brauer correspondent blocks with one simple module (with G. Navarro and P. H. Tiep), Trans. Amer. Math. Soc. 371 (2019), no. 2, 903-922.
  12. Even degree characters in the principal block (with E. Giannelli and G. Malle), J. Pure Appl. Algebra 223 (2019), no. 2, 900–907.
  13. 2-Brauer correspondent blocks with one simple module (with G. Navarro), J. Algebra 488 (2017), 230-243.
  14. Feit numbers and p'-degree characters, J. Group Theory 19 (2016), no. 6, 1129-1136.
  15. Brauer characters and coprime action (with B. Späth), J. Algebra 457 (2016), 278-311.
  16. Certain monomial characters and their subnormal constituents (with G. Navarro), Groups St. Andrews 2013, London Mathematical Society Lecture Note Series 442 (2015), 436–438.
  17. McKay natural correspondences of characters (with G. Navarro and P. H. Tiep), Algebra Number Theory 8 (2014), no. 8, 1839–1856.
  18. A criterium for monomiality, Rend. Sem. Mat. Univ. Pad., 131 (2014), 259–262.
  19. Certain monomial characters of p'-degree (with G. Navarro), Archiv Math. 99 (2012), no. 5, 407–411.

Other Publications

  • La conjetura de pesos de Alperin. Gaceta de la Real Sociedad Matemática Española 25 (2022) no. 1 , pp. 171-187.
  • Characters of finite groups. TEMat monográficos 2 (2021): Proceedings of the 3rd BYMAT Conference, pp. 1-6.
  • Restriction of characters and Sylow subgroups. Oberwolfach Report 9 (2020). DOI: 10.4171/OWR/2020/9.


Eugenio Giannelli, Nguyen Ngoc Hung, Stacey Law, Jason Long, Gunter Malle, Gabriel Navarro, Noelia Rizo, Mandi Schaeffer Fry, Britta Späth, Pham Huu Tiep.

Some Talks



  • "Group Theory in Florence II", Italy. September 2018. Even degree characters in principal blocks.
  • "XI Encuentro en Teoría de Grupos", Barcelona, Spain. September 2016. La tabla de caracteres de un grupo y sus propiedades locales.
  • "Darstellungstheorie-Tage 2014", TU Kaiserslautern, Germany. November 2014. p-Rational characters and p-decomposable p-Sylow normalizers.
  • "X Encuentro en Teoría de Grupos", Sevilla, Spain. October 2014. El caso autonormalizante de la conjetura de McKay.
  • "Young Algebraists’ Conference 2014", EPFL Lausanne, Switzerland. June 2014. McKay Natural Correspondences.
  • "Groups St. Andrews 2013", St. Andrews, UK. August 2013. Certain monomial characters and their subnormal constituents.


Apart from talks at conferences, I've given a number of seminar talks. I'm very grateful for each of these invitations, so that I had the opportunity to visit (in alphabetical order): Bilbao (Spain), Birmingham (UK), Firenze (Italy), Jena (Germany), Kaiserslautern (Germany), Lausanne (Switzerland), London (UK), Madrid (Spain), Málaga (Spain), Manchester (UK), Murcia (Spain), Santa Cruz (USA) and Stuttgart (Germany).

Some beamer talks

Below you can find the slides of some beamer talks.

Research Visits

I visited the University of Florence during the spring semesters of 2020 and 2022.

Palazzo Vecchio al tramonto, Piazza della Signoria.

I visited the MSRI last July 2019 as part of the SWiM program 2019.

San Francisco Bay, mesmerising view from the MSRI.

I spent a week visiting the Algebra group of the University of Florence in February 2019.

David, Galleria dell'Accademia di Firenze.

I spent a week in Paris visiting the Institut de Mathématiques de Jussieu-Paris Rive Gauche in June 2018.

La coucher du soleil from the outside of the Hôtel Lauzun, sur la rive nord de l'île Saint-Louisin, Paris.

I visited the TU Kaiserslautern during July 2017.

Wild raspberries in the Palatinate forest.

I visited twice the TU Kaiserslautern while completing my PhD studies (in 2014 and 2015).

The forest is especially beautiful in autumn.


I was awarded a Vicent Caselles Award in 2018. (A video made for this edition can be found here and you can see a picture of the ceremony on the right.)

The Vicent Caselles awards are given by the Royal Spanish Mathematical Society and the BBVA Foundation and their aim is to «celebrate knowledge through Mathematics».

My PhD. thesis received a and a special mention in the Reinhold Baer Prize 2017 edition (whose winner was Urban Jezernik). The Baer Prize is given by the association AGTA that aims to «promote and disseminate the scientific culture and the research in group theory and its applications».

My brother, José Antonio, is also a mathematician. He is a research professor at the Universidad Autónoma de San Luis de Potosí, México. Check out his webpage!

On the right you can see a picture of him delivering a talk at the ICMAT.

How to contact me

Universidad Autónoma de Madrid
Departamento de Matemáticas
Ciudad Universitaria de Cantoblanco,
28049, Madrid (ES)

Nicolás Cabrera, 13-15
Campus Cantoblanco,
28049, Madrid (ES)

You may contact me at one of the following email addresses.
  • carolina . vallejo at uam . es
  • carolina . vallejo at icmat . es
  • carolina . vallejo at uv . es