Carolina Vallejo

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" last year.

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).

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). Transactions of the American Mathematical Society 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), Journal of Algebra, 488 (2017), 230-243.
• Feit numbers and p'-degree characters, Journal of Group Theory, 19 (2016), no. 6, 1129-1136.
• Coprime action and Brauer characters (joint work with B. Späth), Journal of 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 and 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 der Mathematik, 99 (2012), no. 5, 407–411.

Invited

• (Upcoming) "Groups, rings and associated structures 2019", Spa, Belgium. June 2019.
• 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.)