Carolina Vallejo

Carolina Vallejo Rodríguez

I am a Rita Levi Montalcini researcher (ricercatrice tipo B) at the University of Florence (UNIFI), where I work as a member of the Algebra group. I am also a member of the GNSAGA of the Istituto di Alta Matematica "Francesco Severi" (INdaM).

My main interest are the so-called Counting Conjectures, which fit into the class of global/local problems in Group Representation Theory.

Between April 2019 and June 2021 I was an assistant professor in Madrid, first at at the Universidad Carlos III de Madrid (UC3M) and later at the Universidad Autónoma de Madrid (UAM). Prior to that, I have held different postdoc positions. I was a Juan de la Cierva postdoctoral researcher at the UAM, a Severo Ochoa fellow at the Instituto de Ciencias Matemáticas (ICMAT) and a postdoc at the Simons Laufer Mathematical Science Institute (UC Berkeley).

I completed my Ph.D. 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.

My research is currently funded by the Rita Levi-Montalcini Programme for Young Reseachers (Ministero dell'Università e della Ricerca di Italia). Previously, I was the PI of the Spanish I+D+i project "COCO" (Counting Conjectures, PID2020-118193GA-I00).

News

Together with Eugenio Giannelli, we are organising a conference in Florence next June 2025. You can find more information and register on the Group Representation Theory conference website.
Next August I will participate in the AGGITatE 2025: Groups, Representations and Cohomology conference in Essex.

Publications

Submitted

The continuity of p-rationality of characters and the principal block (joint work with G. Malle and J. M. Martínez).

In Press

On almost p-rational characters in principal blocks (joint work with A. Maróti, J. M. Martínez, A. A. Schaeffer Fry). To appear in Publicacions Matemàtiques.

Published

Characters and Sylow subgroup abelianization (joint work with E. Giannelli, N. Rizo and A. A. Schaeffer Fry), J. Algebra 667 (2025), 824-864.
Principal blocks with six irreducible characters (joint work with N. N. Hung and A. A. Schaeffer Fry), J. Algebra 655 (2024), 517-536. Special issue in memory of Georgia Benkart.
The fields of values of the 2-height zero characters (joint with G. Navarro, L. Ruhstorfer and P. H. Tiep), Adv. Math. 443 (2024), 109589.
A lower bound on the number of generators of a defect group , Vietnam J. Math. 51, 571–576 (2023). Special issue dedicated to Pham Huu Tiep on his 60th birthday.
Relative character conductors, Archiv Math. 120 (2023), 237-244.
Height zero characters in principal blocks (with N. Hung and A. A. Schaeffer Fry), J. Algebra 622 (2023), 197–219.
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.
La conjetura de pesos de Alperin, Gaceta Real Soc. Mat. Española 25 (2022) no. 1 , pp. 171-187.
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 AMS 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.
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

The fields of values of the 2-height zero characters. Oberwolfach Report 19 (2023). DOI: 10.14760/OWR-2023-19.
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.
Certain monomial characters and their subnormal constituents (with G. Navarro), Groups St. Andrews 2013, London Mathematical Society Lecture Note Series 442 (2015), 436–438.

Coauthors

Eugenio Giannelli, Nguyen Ngoc Hung, Stacey Law, Jason Long, Gunter Malle, Attila Maróti, J. Miquel Martínez, Gabriel Navarro, Noelia Rizo, Lucas Ruhstorfer, Mandi Schaeffer Fry, Britta Späth, Pham Huu Tiep.

Conferences

Some invited talks

Representations at the Villa Denis, Frankenstein (Germany), September 27-28, 2024. Characters and Sylow subgroup abelianization.
Symmetric groups and Lie-theoretic friends, University of Birmingham (UK), May 14-15, 2024. Fields of values of height zero characters.
Advances in Group Theory and Applications 2023 conference. Università del Salento (Italy), June 6-9, 2023. The McKay conjecture and its Galois refinement.
Oberwolfach workshop Representations of Finite Groups (Germany), April 17-21, 2023. The fields of values of the 2-height zero characters.
Finite groups in Valencia (Spain, online). February 26 - March 30, 2021. Problems on characters involving two primes.
3rd BYMAT Conference, Bringing Young Mathematicians Together (Spain, online). 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.
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, 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.

Seminar talks

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), Cambridge (UK), Firenze (Italy), Jena (Germany), Kaiserslautern (Germany), Lausanne (Switzerland), London (UK), Madrid (Spain), Málaga (Spain), Manchester (UK), Murcia (Spain), Roma (Italy), Santa Cruz (USA), Shenzhen (China) and Stuttgart (Germany).

Some beamer talks

Below you can find the slides of some of my beamer talks.

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

Conference organization

I have co-organized the following conferences.

Characters and Blocks of Finite Groups, celebrating Gabriel Navarro's 60th birthday. València, Spain. January 2025.
Group Theory in Florence IV, DIMAI, Florence (Italy). July 2024. Check out the photo gallery.
Counting Conjectures and Beyond, Isaac Newton Institute, Cambridge (UK). May 2022.
Groups in Madrid 2021, ICMAT, Madrid (Spain). November 2021.
V Congreso jóvenes investigadores de la RSME, Castellón (Spain). January 2020. (Member of the scientific committee.)
Groups in Madrid 2019, ICMAT, Madrid (Spain). November 2019.
Groups in Madrid 2018, ICMAT, Madrid (Spain). November 2018.

Research Visits

I visited the Southern University of Science and Technology of Shenzhen (SUSTech) in China between December 27, 2024 and January 13, 2025.

_{The Boguan bridge.}

I visited the University of Manchester in July 2024 funded by the Heilbronn Institute under a Focused Research Grant.

_{Manchester red brick.}

I visited the SLMath (formerly MSRI) in 2019 and 2023 as a member of their Summer Research program.

_{San Francisco Bay, mesmerising view from the MSRI.}

I visited the Isaac Newton Institute (Cambridge) during May 2022.

_{Cows taking a break nearby Darwin College.}

I visited the University of Florence during the spring semesters of 2019, 2020 and 2022.

_{Palazzo Vecchio al tramonto, Piazza della Signoria.}

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 while completing my PhD studies.

_{The Manchester Art Gallery.}

I visited twice the TU Kaiserslautern while completing my PhD studies (in 2014 and 2015).

_{Les feuilles mortes.}

Miscellanea

In January 2025, we celebrated the great influence an impact that Gabriel Navarro has had, and continues to have, on Finite Group Representation Theory.

_{On the right you can see a picture of Gabriel on a train to Mainz, while visiting B. Huppert, in 1988.}

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. The course was recorded and the videos are available on Youtube (through the ICMAT channel).

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 brother José Antonio is also a mathematician. He works at the UNED (Universidad Nacional de Educación a Distancia) in Spain.

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

The Spanish band Hidrogenesse made a beautiful album dedicated to Alan Turing in 2012: "Un dígito binario dudoso. Recital para Alan Turing".

The first song is called "El beso" and they say in it "This song is a kiss to wake Alan Turing up" ♥

How to contact me

Università degli studi di Firenze
Dipartimento di Matematica e Informatica ‘Ulisse Dini’ (DIMAI)
Viale Morgagni 67/a,
50134 Firenze (IT).

You may contact me at one of the following email addresses.

carolina . vallejo rodriguez at unifi . it
carolina . vallejo at uv . es

https://orcid.org/0000-0003-3363-3376