Carolina Vallejo

I am a Severo Ochoa postdoctoral researcher at the ICMAT. 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 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 superb 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.

Preprints

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

In press

• Even degree characters in the principal block (joint work with E. Giannelli and G. Malle). To appear in Journal of Pure and Applied Algebra.
• Brauer correspondent blocks with one simple module (joint work with G. Navarro and P. H. Tiep). To appear in Transactions of the American Mathematical Society.

Published

• 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

• "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.
• Algebra and Number Theory Seminar of the UCSC, USA. January 26, 2018. Sylow normalizers and Galois action on characters.
• "IV Congreso jóvenes investigadores de la Real Sociedad Matemática Española", Universitat de València, Spain. September 2017. On Feit numbers.
• "Representation Theory in Kaiserslautern", TU Kaiserslautern, Germany. July 2017. On Brauer correspondent blocks.
• Algebra seminar, UPV/EHU, Spain. May 2017. Detecting local properties in the character table of a group.
• Algebra seminar, University of Murcia, Spain. March 2017. Detecting local properties in the character table of a group.
• "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.
• Algebra seminar, University of Birmingham, UK. May 2016. Coprime action and Brauer characters.
• Algebra seminar, University of Manchester, UK. April 2016. Coprime action and Brauer characters.
• Oberseminar Algebra, Universitaet Stuttgart, Germany. May 2015. p-Rational characters and p-decomposable Sylow normalizers.
• Oberseminar Algebra/Zahlentheorie, Universitaet Jena, Germany. May 2015. Coprime action and Brauer characters.
• Seminar Gruppen und Darstellungen: Sommersemester 2015, TU Kaiserslautern, Germany. April 2015. Coprime action and Brauer characters.
• "Global/Local Conjectures in Representation Theory of Finite Groups", Banff, Canada. March 2014. McKay natural correspondences of characters.

Contributed

• 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. 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.)