Algorithm and classification in groups

• Grant number: 16/12196-5
• Support Opportunities: Research Grants - Young Investigators Grants
• Start date: November 01, 2016
• End date: November 30, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Francesco Matucci
• Grantee: Francesco Matucci
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated scholarship(s): 17/24373-1 - Co-context-free groups, BP.MS

Abstract

We will deal with questions in Asymptotic, Combinatorial and Geometric Group Theory. This project can be considered a natural continuation of my lines of research which have been published in international journals. In particular, my research regarding finiteness properties and simplicity, classification and embedding in Thompson groups and growth in groups. In this project we intend to work on several directions: (1) Dynamics in the higher dimensional Thompson group2V, with James Belk (Bard College, USA), Conchita Martínez-Pérez (Zaragoza, Spain) and Brita Nucinkis (Royal Holloway, UK). (2) Simplicity criterions in groups of homeomorphisms, with James Belk (Bard College, USA). (3) Embedding of groups in Thompson's group V, with Collin Bleak (St. Andrews, Reino Unido) and Ewa Biniecka (St. Andrews, Reino Unido). (4) Completions of self-similar groups}, with Pedro Silva (Porto, Portugal). (5) Rational groups of homeomorphisms, with James Belk (Bard College, USA) and Collin Bleak (St. Andrews, UK).(6) Intersection growth in groups}, with Ian Biringer (Boston College, USA), Khalid Bou-Rabee (CUNY, USA),Martin Kassabov (Cornell University, USA) and Ilir Snopche (UFRJ, Brazil). (7) Integrals of finite groups, with João Araujo (Universidade Aberta, Portugal) and Peter Cameron (St. Andrews, UK). During this project I will collaborate with James Belk (Bard, USA), Collin Bleak (St. Andrews, UK), Martin Kassabov (Cornell University, USA), Pedro Silva (Porto, Portugal) and Ilir Snopche (UFRJ, Brasil) and so I willask for funding to visit them or have some of them visit me at UNICAMP. (AU)

Scientific publications

(4)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

MATUCCI, FRANCESCO; SILVA, V, PEDRO. Extensions of automorphisms of self-similar groups. Journal of Group Theory, v. 24, n. 5, p. 857-897, SEP 2021. (16/12196-5)

BELK, JAMES; HYDE, JAMES; MATUCCI, FRANCESCO. On the asynchronous rational group. Groups Geometry and Dynamics, v. 13, n. 4, p. 1271-1284, 2019. (16/12196-5)

MATUCCI, FRANCESCO; DE OLIVEIRA-TOSTI, ALTAIR SANTOS. Conjugacy and centralizers in groups of piecewise projective homeomorphisms. Groups Geometry and Dynamics, v. 16, n. 1, p. 28-pg., 2022-01-01. (16/12196-5)

BELK, JAMES; BLEAK, COLLIN; MATUCCI, FRANCESCO. Rational embeddings of hyperbolic groups. JOURNAL OF COMBINATORIAL ALGEBRA, v. 5, n. 2, p. 123-183, 2021. (16/12196-5)