Buonasera,

nel mese di novembre Giovanni Paolini (Caltech) terrà un mini-corso di 5
lezioni dal titolo

    Combinatorial topology and group theory

(vedere sotto per  maggiori dettagli).
Il corso sarà tenuto online. La riunione preliminare sarà

    il 4 novembre 2021,  ore 17 – 18,

su Google Meet: https://meet.google.com/fgj-yduu-kpf

Giovanni Alberti


==============

Titolo:
Combinatorial topology and group theory

Abstract:
In this course, we will cover combinatorial techniques to study topological
spaces and groups. On the topological side, we are going to see how
discrete Morse theory can be used to prove homotopical and homological
statements through the language of partially ordered sets (posets). On the
group-theoretic side, we are going to introduce Garside theory and apply it
to the study of symmetric groups and braid groups (as well as their
generalizations, Coxeter and Artin groups). Using discrete Morse theory, we
will prove one of the main results of Garside theory, namely the
construction of a classifying space (or K(π,1)) for an arbitrary Garside
group. We will also mention algorithmic aspects in discrete Morse theory
(related to collapsibility) and in Garside theory (the word problem). If
time permits, we will also touch on current research directions in the
theory of Garside groups, Coxeter groups, and Artin groups.

Prerequisiti:
Basic algebraic topology and homological algebra (e.g., the UniPi courses
"Elementi di topologia algebrica" and "Istituzioni di algebra"). Emanuele
Delucchi's course on "Combinatorial methods in topology" (Spring 2021) is
not a requirement but will be useful.

Programma provvisorio in 5 lezioni:
1. Partially ordered sets and relevant examples
2. Topological discrete Morse theory, applications and algorithms
3. Algebraic discrete Morse theory
4. Combinatorial Garside structures, the word problem, and examples
(symmetric groups and braid groups)
5. Classifying spaces of Garside groups and consequences


--
________________________________________________________
Prof. Giovanni ALBERTI
     coordinatore del dottorato in Matematica
     Università di Pisa

     director of the graduate program in Mathematics
     University of Pisa

     e-mail: coord_mat@dm.unipi.it
     phone: +39 050 2213 239
     virtual office: https://meet.google.com/rmt-jyke-iyw
     webpage: http://www.dm.unipi.it/webnew/dottorato/phd
________________________________________________________

_______________________________________________
Utenti mailing list
Utenti@fields.dm.unipi.it
https://fields.dm.unipi.it/listinfo/utenti