Carolina Vallejo

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.

News

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.

Publications

Submitted

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

Published

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.
Principal blocks with 5 irreducible characters (joint work with N. Rizo and A. A. Schaeffer Fry), J. Algebra 585 (2021), 316-337.
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.
Characters and generation of Sylow 2-subgroups (with G. Navarro, N. Rizo and A. A. Schaeffer Fry), Represent. Theory 25 (2021), 142-165.
A reduction theorem for the Galois-McKay conjecture (with G. Navarro and B. Späth), Trans. Amer. Math. Soc. 373 (2020), no. 9, 6157–6183.
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.
Character correspondences in solvable groups with a self-normalizing Sylow subgroup, J. Algebra Appl. 19 (2020), no. 10, 2050190, 8 pp.
Characters of π '-degree (with E. Giannelli and A. A. Schaeffer Fry), Proc. Amer. Math. Soc. 147 (2019), no. 11, 4697-4712.
Brauer correspondent blocks with one simple module (with G. Navarro and P. H. Tiep), Trans. Amer. Math. Soc. 371 (2019), no. 2, 903-922.
Even degree characters in the principal block (with E. Giannelli and G. Malle), J. Pure Appl. Algebra 223 (2019), no. 2, 900–907.
2-Brauer correspondent blocks with one simple module (with G. Navarro), J. Algebra 488 (2017), 230-243.
Feit numbers and p'-degree characters, J. Group Theory 19 (2016), no. 6, 1129-1136.
Brauer characters and coprime action (with B. Späth), J. Algebra 457 (2016), 278-311.
Certain monomial characters and their subnormal constituents (with G. Navarro), Groups St. Andrews 2013, London Mathematical Society Lecture Note Series 442 (2015), 436–438.
McKay natural correspondences of characters (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 (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.

Coauthors

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

Invited

Finite groups in Valencia. February 26 - March 30, 2021. Problems on characters involving two primes.
3rd BYMAT Conference. This is the 3rd edition, and the 1st one online, of the Bringing Young Mathematicians Together Conference. December 1-3, 2020. Characters of Finite Groups.
MFO Mini-Workshop: Kronecker, Plethysm, and Sylow Branching Coefficients and their Applications to Complexity Theory, Oberwolfach, Germany. February 2020. Restriction of characters and Sylow subgroups.
"V Congreso jóvenes investigadores de la RSME" (Group Theory Special Session), Universitat de Castelló, Spain. January 2020. Natural correspondences for the McKay conjecture.
"ARTS in Rome", University of Rome Tor Vergata, Italy. November 2019. Galois action on the principal block.
"Gruppen und topologische Gruppen", Milano, Italy. June 2019. Characters of degree not divisible by two primes.
"Groups, rings and associated structures 2019", Spa, Belgium. June 2019. Characters of degree not divisible by two primes.
"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" (Group Theory Special Session), 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.
"Second joint Conference of the Belgian, Royal Spanish and Luxembourg Mathematical Societies" (Algebra Special Session). 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.

Seminars

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.

Character Tables and Sylow 2-Generation, London Algebra Colloquium (2021).
Problems on characters involving two primes, Manchester Algebra Seminar (2021).
Characters of finite groups, BYMAT Conference (2020). (This was my first online talk at a conference.)
McKay natural correspondences , BIRS (2014).
Certain monomial characters and their subnormal constituents, Groups St. Andrews (2013). (This was my first talk at a conference.)

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 the University of the Basque Country in Bilbao during May 2017.

_{The Guggenheim museum.}

I visited the Centre 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 (in 2014 and 2015).

_{The forest is especially beautiful in autumn.}

Miscellanea

I taught a course on the Burnside p^aq^b theorem (in Spanish) as part of the Escuela JAE de Matemáticas 2021 at the ICMAT.

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.