Dr. Alejandro Tolcachier
Welcome! I'm an Argentinian mathematician. I finished my undergraduate studies in December 2018 and my PhD in December 2023.
I got my PhD at FAMAF (Facultad de Matemática, Astronomía y Física), under the supervision of Dr. Adrián Andrada.
Here is my Undergraduate thesis (in Spanish), called "Grupos de Bieberbach y holonomía de solvariedades planas".
Here is my PhD thesis (in Spanish), called "Propiedades geométricas de solvariedades y productos de variedades sasakianas".
My interests lie at the intersection of the study of differential geometry and Lie theory. More precisely, I am interested in investigating geometric structures on Lie groups and their compact quotients, with a particular focus on solvmanifolds. During my PhD thesis, I studied four distinct topics:
Complex solvmanifolds with holomorphically trivial canonical bundle.
Special Hermitian metrics on the product of two Sasakian manifolds.
Harmonic almost complex structures on almost abelian Lie solvmanifolds
G_2-structures on flat solvmanifolds.
Here is my CV.
I'm part of the Differential Geometry Group. I'm currently co-organizing the Differential Geometry Seminar at FAMAF, with Jorge Lauret and in 2023 with Marcos Origlia.
Preprints and Publications
On the canonical bundle of complex solvmanifolds and applications to hypercomplex geometry, (with Adrián Andrada). Preprint available at Arxiv.
Harmonic complex structures and special Hermitian metrics on products of Sasakian manifolds, (with Adrián Andrada). J. Geom. Anal. (2024). Article
Harmonic almost complex structures on almost abelian Lie groups and solvmanifolds, (with Adrián Andrada). Ann. Mat. Pura Appl. (2023). Article
G_2-structures on flat solvmanifolds. Abh. Math. Semin. Univ. Hambg. 92 (2022), 179-207. Article
Classification of 6-dimensional splittable flat solvmanifolds, Manuscripta Math. 170 (2022), 531-561. Article
Holonomy groups of compact flat solvmanifolds, Geom. Dedicata 209 (2020), 95--117. Article
Seminars and Invited Talks
Complex solvmanifolds with holomorphically trivial canonical bundle. Seminar at Geometry Webinar AmSur/AmSul, April 2024.
Special Hermitian metrics on products of Sasakian manifolds. Poster at Workshop: Special Holonomy and Geometric Structures on Complex Manifolds}, Rio de Janeiro, Brazil 2024.
Canonical bundle of complex solvmanifolds. Scientific communication at UMA 2023. Salta, Argentina. September 2023. (slides in spanish)
Harmonic almost complex structures on almost abelian solvmanifolds. Seminar at Geometry Seminar UNS. Bahía Blanca, Argentina. June 2023. (slides in spanish)
Special Hermitian structures on products of Sasakian manifolds. Seminar at Virtual seminar on geometry with symmetries. April 2023. (slides, video)
Complex solvmanifolds with invariantly and non-invariantly holomorphically trivial canonical bundle. Seminar at Differential Geometry Seminar, FAMAF, Córdoba, Argentina. October 2022. (slides and video in spanish)
Flat solvmanifolds and relations with G_2-geometry. Seminar at Research Seminar in Algebra and Topology at KU Leuven. Kortrijk, Belgium. October 2022. (slides)
Solvmanifolds with invariantly and non-invariantly holomorphically trivial canonical bundle. Seminar at Seminario di Geometría del Dini, Università di Firenze. Italy. October 2022. (slides)
Conjugacy classes of GL(n,Z) and the classification of flat solvmanifolds. Poster at 9th Heidelberg Laureate Forum, Heidelberg, Germany. September 2022. (poster)
Harmonic almost complex structures on almost abelian Lie groups and solvmanifolds. Short talk at Workshop on Geometric Structures and Moduli Spaces, FAMAF. Córdoba, Argentina. (slides)
Holonomy groups of flat solvmanifolds and relations with G_2-geometry. Talk at Mini-encontro do Geometria no IMECC, UNICAMP, Brasil. April 2022. (slides)
Flat solvmanifolds: questions about holonomy and classification in low dimensions. Seminar at Differential Geometry Seminar, FAMAF, Córdoba, Argentina. June 2021. (slides, video)
Classification of splittable flat solvmanifolds in low dimensions. Scientific communication at VirtUMA 2021 (online event), Argentina. September 2021. (slides and video in spanish)
Classification of 6-dimensional almost abelian flat solvmanifolds. Short talk in the "Group actions in Differential Geometry" session at Mathematical Congress of the Americas 2021 (online event). July 2021. (slides, video)
Classification of 6-dimensional almost abelian flat solvmanifolds. Scientific communication at XVI Congreso Dr. Antonio Monteiro (online event), Bahía Blanca, Argentina. June 2021. (slides and video in spanish)
How to prove that a function has no primitive in elementary terms. Seminar at Graduate Students Seminar, FAMAF. Córdoba, Argentina. April 2021. (slides and video in spanish)
Holonomy groups of compact flat solvmanifolds. Poster at Virtual Heidelberg Laureate Forum 2020. Germany. September 2020. (poster)
Holonomy groups of compact flat solvmanifolds (in spanish). Scientific communication at SUMA 2019. Mendoza, Argentina. September 2019.
Finite abelian groups as holonomy groups of flat solvmanifolds (in spanish). Seminar at Graduate Students Seminar, FAMAF, Argentina. May 2019.
Teaching
(Graduate) Teaching assistant at FAMAF-Universidad Nacional de Córdoba. Since October 2020.
Subjects: Linear Algebra (2020), Linear Algebra, Discrete Mathematics (2021), Introductory Course, Linear Algebra, Calculus II (2022), Introductory Course, Multivariable Calculus, Linear Algebra (2023). Introductory Course, Multivariable Calculus (2024).(Undergraduate) Teaching assistant at FAMAF-Universidad Nacional de Córdoba. From June 2016 to March 2019.
Subjects: Calculus I, Calculus II (2016), Calculus I, Calculus II (2017), Introductory Course, Discrete Mathematics, Calculus I (2018), Introductory Course (2019).
Graduate
courses
Stability of Einstein homogeneous manifolds. FAMAF, Univ. Nac. de Córdoba, Argentina, 2022.
Symmetric spaces. FAMAF, Univ. Nac. de Córdoba, Argentina, 2022.
Lie algebras. FAMAF, Univ. Nac. de Córdoba, Argentina, 2021.
Compact Lie groups. Univ. Nac. del Sur, Argentina, 2021. Grade: 10/10.
Riemann surfaces. FAMAF, Univ. Nac. de Córdoba, Argentina, 2020.
Geometric evolution on homogeneous spaces. FAMAF, Univ. Nac. de Córdoba, Argentina, 2019.
Geometric structures on Lie groups. FAMAF, Univ. Nac. de Córdoba, Argentina, 2019. Grade: 10/10.
Introduction to Hermitian geometry. FAMAF, Univ. Nac. de Córdoba, Argentina, 2019. Grade: 10/10.
Undergraduate
courses
Introduction to connection theory. FAMAF, Univ. Nac. de Córdoba, Argentina, 2018.
Harmonic analysis on Lie groups. FAMAF, Univ. Nac. de Córdoba, Argentina, 2018.
Introduction to Riemannian geometry. FAMAF, Univ. Nac. de Córdoba, Argentina, 2017. Grade: 10/10.
Algebraic topology. FAMAF, Univ. Nac. de Córdoba, Argentina, 2017. Grade: 10/10.
Lie groups and Lie algebras. FAMAF, Univ. Nac. de Córdoba, Argentina, 2017. Grade: 10/10.
Research
visits
Short research visit at Departamento de Matemática Universidad Nacional del Sur, Bahía Blanca, Argentina. June 12-16 (2023). Invited by Prof. Dr. Emilio Lauret.
Short research visit at Department of Mathematics at KU Leuven, Kortrijk, Belgium. October 10-14 (2022). Invited by Prof. Dr. Jonas Deré.
Short research visit at Dipartimento di Matematica e Informatica "Ulisse Dini", Università di Firenze, Italy. From September 26th to October 7th (2022). Invited by Prof. Dr. Daniele Angella.
Short research visit at Instituto de Matemática, Estatística e Computação Científica at UNICAMP, Brazil. From March 19th to April 2nd. Invited by Prof. Dr. Viviana del Barco.
Attendance to Conferences and Workshops
Attendee, of the UMA 2023 (annual meeting of Argentinian Mathematical Union), Salta, Argentina. September 19-22, 2023.
Attendee, of the 9th Heidelberg Laureate Forum, Heidelberg, Germany. Selected among other 200 young researchers in Mathematics and Computer Sciences. September 18-23, 2022.
(Virtual) Attendee, of the Workshop on Special Geometries on Riemannian Manifolds, Montreal. CRM and online event. October 11-15, 2021.
Attendee, of the Workshop on compact homogeneous Einstein manifolds. Virtual event. September 20th to October 1st, 2021.
Attendee, of the 8th HLF (Heidelberg Laureate Forum) 2021, Germany. Virtual event. 20-23 September, 2021. Selected among other 200 young researchers in Mathematics and Computer Sciences.
Attendee, of the virtUMA 2021, annual meeting of the Argentinian Mathematical Union (virtual event).
Attendee, of the CLAM VI 2021 (Congreso Latinoamericano de Matemáticos), Uruguay. Virtual event. 13-17 September, 2021.
Attendee, of the VII School and Workshop on Lie Theory. Universidade Federal de Juiz de Fora, Virtual event. 8-15 September, 2021.
Attendee, of the 6th Geometry-Topology Summer School, Turkey (Online).
Attendee, of the CIRM-ICTP virtual meeting: Complex Analysis and Geometry - XXV 25th edition.
Attendee, of The 6th Workshop “Complex Geometry and Lie groups”, originally expected to be held at Toki Messe, Niigata. Online event.
Attendee, of the 1st and 2nd “Geometry and TACoS” online sessions, First session on “Co-homology and Characteristic Classes of (almost) complex manifolds” and Second session on “Nilmanifold and solvmanifold techniques in complex geometry”.
Attendee, of the virtual Heidelberg Laureate Forum 2020. Selected among other 200 young researchers in Mathematics and Computer Sciences.
Attendee, of the virtUMA 2020, (virtual) annual meeting of the Argentinian Mathematical Union.
Attendee, of the EVAH 2020, virtual meeting on Homological Algebra. Argentina.
Attendee, of the (virtual) Workshop: Hopf algebras and tensor categories. Hamburg. 2020.
Attendee, of the SUMA 2019 (annual meeting of Argentinian Mathematical Union together with SOMACHI), Mendoza, Argentina.
Attendee, of the National Meeting of Algebra IX (elENA IX), La Falda, Córdoba.
Attendee, of the UMA 2018 (annual meeting of Argentinian Mathematical Union), La Plata, Argentina.
Attendee, of the RSME-UMA 2017 (annual meeting of Argentinian Mathematical Union together with Real Sociedad Matemática Española), Buenos Aires, Argentina.
Attendee, of the UMA 2016 (annual meeting of Argentinian Mathematical Union), Bahía Blanca, Argentina.
Attendee, of EGEO 2016 VI Workshop on Differential Geometry. La Falda, Córdoba.
Attendee, of the UMA 2015 (annual meeting of Argentinian Mathematical Union), Santa Fe, Argentina.
References
Prof. Dr. Adrián Andrada
Universidad Nacional de Córdoba
andrada@famaf.unc.edu.arProf. Dr. Jorge Lauret
Universidad Nacional de Córdoba
jorge.lauret@gmail.com