Mallika Roy

Postdoctoral Fellow

University of the Basque Country UPV/EHU.

Research area: Combinatorial and Geometric Group Theory.

I am a Margarita Salas postdoctoral fellow in GTA research group at University of the Basque Country (UPV) from July, 2022. In UPV I am working with Prof. Montserrat Casals-Ruiz and Prof. Ilya Kazachkov.

I did my PhD as a BGSMath fellow (María de Maeztu) from the Universitat Politècnica de Catalunya under the supervision of Prof. Enric Ventura. After finishing my doctoral studies, I was a visiting researcher (March-June, 2020) in the department of Mathematics of the Universidad del País Vasco UPV/EHU working with Prof. Montserrat Casals-Ruiz. Then I was a visiting researcher (July-December, 2020) in LaBRI at Université Bordeaux I-CNRS working with Prof. Pascal Weil. From February 2021 until June 2022, I was a postdoctoral fellow at Chennai Mathematical Institute (CMI) working with Prof. Priyavrat Deshpande.

Research Interests

My research interest lies in the field of Combinatorial and Geometric Group Theory. Within this area I am interested (mainly but not only) in the study of partially commutative groups (a.k.a right-angled Artin groups), Artin groups, Baumslag-Solitar groups, Bestvina-Brady groups from different perspectives (algebraic, algorithmic, combinatorial and geometric) regarding the following topics:

Automorphisms of free groups and free-abelian times free groups; their fixed points and computation of auto-closure.
The lattice of subgroups of a free group (to some extent finitely presented groups) via graphs and automata.
Rank problem for the subgroups of free-abelian times free groups.
Subgroup intersection problem.
Conjugacy and twisted conjugacy problem.
Generic properties of subgroups of coherent RAAGs.

Publications and Preprints

Fixed subgroups and computation of auto-fixed closures in free-abelian times free groups, joint work with Enric Ventura ; Journal of Pure and Applied Algebra, Volume 224, Issue 4, April 2020. (journal link) (arXiv).
Degrees of compression and inertia for free-abelian times free groups, joint work with Enric Ventura ; Journal of Algebra, 568 (2021), 241-272. (journal link) (arXiv).
Intersection configurations in free and free times free-abelian groups, joint work with Jordi Delgado and Enric Ventura; Proceedings of the Royal Society of Edinburgh Section A: Mathematics. (journal link) (arXiv).
On the structure of finitely presented Bestvina-Brady groups, joint work with Priyavrat Deshpande; International Journal of Algebra and Computation, Vol. 34, No. 01, pp. 69-85. (journal link) (arXiv ).
The central tree property and algorithmic problems on subgroups of free groups, joint work with Enric Ventura and Pascal Weil; Journal of Group Theory. (journal link) (arxiv).
Computation of endo-fixed closures in free-abelian times free groups, joint work with Enric Ventura; submitted. (arxiv).
Quotient-saturated groups, joint work with Jordi Delgado and Enric Ventura; submitted. (arxiv).