Carolina Vallejo

Carolina Vallejo Rodríguez

I am a Juan de la Cierva (JCF) postdoctoral researcher at the UAM. I am part of the research team of Andrei Jaikin. 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 Severo Ochoa postdoc at the ICMAT and an MSRI postdoc associated with the 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. 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.

The UAM/ICMAT group theory seminar is organized by Yago Antolín, so you can contact him if you are willing to give a talk. Here you can find a list of talks for the current academic year. I co-organized the third edition of "Groups in Madrid" in 2018.

News

Together with Mandi Schaeffer Fry and Noelia Rizo, I will be part of the "Summer Research for Women in Mathematics" program of the MSRI (July 2019).

I co-organize the workshop "Counting conjectures and beyond" within the scientific programme "Groups, representations and applications: new perspectives" to be held at the Isaacs Newton Institute for Mathematical Science (Spring semester 2020).

Together with Olivier Dudas and Mandi Schaeffer Fry, we are planning to organize a Summer School on Representations of Finite Groups in Castro Urdiales, Spain. More information to come! The expected dates are September 7-12, 2020.

Research

Preprints

A reduction theorem for the Galois-McKay conjecture (joint work with G. Navarro and B. Späth).

Submitted

Character correspondences in solvable groups with self-normalizing Sylow subgroups.

In press

Characters of π '-degree (joint work with E. Giannelli and A. Schaeffer Fry). To appear in Proc. Amer. Math. Soc.

Published

Brauer correspondent blocks with one simple module (joint work with G. Navarro and P. H. Tiep). Trans. Amer. Math. Soc. 371 (2019), no. 2, 903-922.
Even degree characters in the principal block (joint work with E. Giannelli and G. Malle). J. Pure Appl. Algebra 223 (2019), no. 2, 900–907.
2-Brauer correspondent blocks with one simple module (joint work with G. Navarro), J. Algebra, 488 (2017), 230-243.
Feit numbers and p'-degree characters, J. Group Theory, 19 (2016), no. 6, 1129-1136.
Coprime action and Brauer characters (joint work with B. Späth), J. Algebra, 457 (2016), 278-311.
Certain monomial characters and their subnormal constituents (joint work with G. Navarro), Groups St. Andrews 2013, London Mathematical Society Lecture Note Series 442 (2015), 436–438.
McKay natural correspondences of characters (joint work with G. Navarro and P. H. Tiep), Algebra Number Theory, 8 (2014), no. 8, 1839–1856.
A criterium for monomiality, Rend. Sem. Mat. Univ. Pad., 131 (2014), 259–262.
Certain monomial characters of p'-degree (joint work with G. Navarro), Archiv Math., 99 (2012), no. 5, 407–411.

Some Talks

Invited

(Upcoming) "Gruppen und topologische Gruppen", Milano, Italy. June 2019.
(Upcoming) "Groups, rings and associated structures 2019", Spa, Belgium. June 2019. Characters of degree not divisible by two primes.
InSeGTo , Universidad de Málaga, Spain. May 22, 2019. The McKay conjecture and fields of values of characters
Seminario di Algebra, Universitá degli Studi di Firenze. February 20, 2019. The McKay conjecture and fields of values of characters.
"Congreso Bienal de la RSME 2019", Group Theory Special Session, Santander, Spain. February 2019. On character degrees of finite groups.
"Representations of Finite and Algebraic Groups", MSRI, USA. Simons Auditorium, April 2018. The McKay conjecture and fields of values of characters.
"Connections for Women: Group Representation Theory and Applications", MSRI, USA, Simons Auditorium, February 2018. Sylow normalizers and Galois action on characters.
"IV Congreso jóvenes investigadores de la RSME", Universitat de València, Spain. September 2017. On Feit numbers.
"Representation Theory in Kaiserslautern", TU Kaiserslautern, Germany. July 2017. On Brauer correspondent blocks.
"Triangle meeting", University of Birmingham, UK. January 2017. Detecting local properties in the character table.
Seminar during the semester "Local representation theory and simple groups". CIB (EPFL), Lausanne, Switzerland. October 2016. Detecting local properties in the character table.
"Second joint Conference of the Belgian, Royal Spanish and Luxembourg Mathematical Societies". Riojaforum and Faculty of Science and Technology of Logroño, Spain. June 2016. The self-normalizing case of the McKay conjecture.
"Global/Local Conjectures in Representation Theory of Finite Groups", Banff, Canada. March 2014. McKay natural correspondences of characters.

Contributed

"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.

Some beamer talks

I have only used beamer in my first three talks. I don't really like giving beamer talks (mainly because I'm not good at it). You can find the slides below.

McKay natural correspondences, Lausanne (2014).
McKay natural correspondences , Banff (2014).
Certain monomial characters and their subnormal constituents, St. Andrews (2013). (This was my first talk at conference.)

Miscellanea

I visited the Universitá Degli Studi di Firenze (DIMAI) in February 2019.

_{David, Galleria dell'Accademia di Firenze.}

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».

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 the EHU/UPV in Bilbao during May 2017.

_{The Guggenheim museum.}

I visited the Centre Interfacultaire Bernoulli at the EPFL as a guest of the semester "Local representation theory and simple groups" in October 2016.

_{The Rolex learning center.}

I visited the University of Manchester in April 2016.

_{The Manchester Art Gallery.}

I visited twice the TU Kaiserslautern while completing my PhD studies.

_{The forest is especially beautiful in autumn.}

How to contact me

Universidad Autónoma de Madrid
Departamento de Matemáticas
Facultad de Ciencias
28049, Madrid (ES)

You may contact me by e-mail (in inverse order of preference)

carolina . vallejo at uam . es
carolina . vallejo at icmat . es
carolina . vallejo at uv . es