Andrea Solotar
Visiting Professor
Mathematics with Computer Science Program
Andrea Solotar will join the Department of Mathematics with Computer Science at GTIIT as a Visiting Professor in October 2020. Dr. Solotar received a Ph. D. in Mathematics from Universidad de Buenos Aires (UBA) in 1988 and later, in 2000, she obtained an Habilitation à diriger des recherches from Université Paris 7, She is a Full Professor at Facultad de Ciencias Exactas, Universidad de Buenos Aires and a Superior Researcher at IMAS (CONICET-Argentina). She has supervised eight PhD. thesis and is currently supervising one graduate student. She is also a Senior Associate Professor at the International Centre for Theoretical Physics (ICTP, Trieste, Italy). She has been a long term visiting professor at Université de Paris 11, Université de Paris 13 and visiting researcher at IHES (France).
The objectives of her research are placed at the intersection of three areas of algebra: Lie theory, homological algebra and rewriting methods. More precisely, her aim is to study several families of algebras having interesting – mainly physical – applications and their representations, using homological tools such as Hochschild homology and cohomology, which provide several homological invariants. The main families of algebras concerned in her work are: Brauer graph algebras, Yang-Mills algebras and their generalizations; string algebras, algebras related to quantum and classic flag varieties and quantum affine algebras, Weyl algebras, their generalizations and the subalgebras appearing as the elements fixed by the action of subgroups of their automorphism groups, down-up algebras, truncated quiver algebras and also truncated linear categories. Andrea focuses on some problems arising in this study such as the computation of bimodule resolutions of these algebras – taking into account the fact that a resolution of a given algebra is an object that coincides with it in the derived category, the construction of deformation algebras, and in particular of Poincaré-Birkhoff-Witt deformations, and the description of properties of Koszul algebras and their generalizations.
Dr. Solotar has authored/co-authored over 55 journal papers and 1 undergratuate teaching textbook.
Hochschild (co)homology
Papers
Representation theory of Yang-Mills algebras (Estanislao Herscovich and A. Solotar). Ann. Math. 173 (2), pp. 1043-1080, 2011.
Hochschild and cyclic homology of Yang-Mills algebras (Estanislao Herscovich and A. Solotar). J. reine angew. Mathematik 665, pp. 73-156, 2012.
On the Lie algebra structure of the first Hochschild cohomology of gentle algebras and Brauer graph algebras (Cristian Chaparro Acosta, Sibylle Schroll and A. Solotar). J. Algebra 558, pp. 293-326, 2020.
Weight modules of quantized Weyl algebras (Vyacheslav Futorny, Laurent Rigal and A. Solotar). To appear in Mathematical Research Letters. Accepted December 2019. arXiv:1812.02118
Split bounded extension algebras and Han’s conjecture (Claude Cibils, Marcelo Lanzilotta, Eduardo N. Marcos and A. Solotar). Pacific J. Math. 307 (1), pp. 63-77,2020.