Carolina Vallejo Rodríguez

I am a Profesora Ayudante Doctora at the Universidad Carlos III de Madrid (UC3M) 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.

Previously, I was a Juan de la Cierva postdoctoral researcher at the Universidad Autónoma de Madrid, a Severo Ochoa fellow at the ICMAT and a postdoc associated with the MSRI research program Group Representation Theory and Applications at the UC Berkeley.

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.


Olivier Dudas, Mandi Schaeffer Fry and I are organizing a a Summer School in Representation Theory in beautiful Castro Urdiales, Spain. The event will take place at the CIEM during June 21-26, 2021. Check out the webpage for further information!

Most of the activities related to the GRA programme at the Isaac Newton Institute (Cambridge) were cancelled due to the COVID19 global crisis, including the "Counting conjectures and beyond" workshop. We hope to celebrate it in May 2022. For a modularised conference picture you can click here .



  1. Sylow branching coefficients and a conjecture by Malle and Navarro (joint work with E. Giannelli, S. Law and J. Long).
  2. Principal blocks with 5 irreducible characters (joint work with N. Rizo and A. A. Schaeffer Fry).

  3. In press

  4. Characters and generation of Sylow 2-subgroups (with G. Navarro, N. Rizo and A. A. Schaeffer Fry). To appear in Rep. Theory.
  5. Characters of π '-degree and small cyclotomic fields (with E. Giannelli, N. Hung and A. A. Schaeffer Fry). To appear in Ann. Mat. Pura Appl.

  6. Published

  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, no. 11, (2019), 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

  • Restriction of characters and Sylow subgroups. Oberwolfach Report 9 (2020). DOI: 10.4171/OWR/2020/9.

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), Madrid (Spain), Málaga (Spain), Manchester (UK), Murcia (Spain), Santa Cruz (USA) and Stuttgart (Germany).

Some beamer talks

Below you can find the slides of my beamer talks (without repetitions).

Research Visits

I visited the University of Florence between March and July 2020.

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 visited the Algebra group of the University of Florence in February 2019.

David, Galleria dell'Accademia di Firenze.

I visited 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.


My brother, José Antonio, is also a mathematician. He is a Research Professor at the UASLP, México. Check out his webpage!

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

My PhD. thesis has received a Vicent Caselles Award 2018 edition (a video made for this edition can be found here) and a special mention in the Reinhold Baer Prize 2017 edition (whose winner was Urban Jezernik).

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».
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».

How to contact me

Universidad Carlos III de Madrid
Departamento de Matemáticas
Edificio Sabatini
Avenida Universidad 30, 28911, Leganés. Madrid (ES)

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

You may contact me at one of the following email addresses

  • carolina . vallejo at uc3m . es
  • carolina . vallejo at icmat . es
  • carolina . vallejo at uv . es