Month: March 2018

Mehmet Akif Erdal, Bilkent University.
Date: 21st of March, 2018, Wednesday. Time: 09:30 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: Abstract homotopy theory, also known as homotopical algebra, provides a framework that allows us to use tools from homotopy theory in various different settings, ranging from representation theory to mathematical physics. For short, it is the study of everything that is related with higher categories. This talk will be a motivational introduction to the subject. We will discuss some of the main purposes of abstract homotopy theory and state some basic definitions and examples. In particular, we will talk about definitions of categories with weak equivalences, homotopical categories and their homotopy category and we will discuss existence of the homotopy category. Later, if the time permits, we state some of the difficulties in the construction of homotopy categories and discuss why we need extra structures, such as model categories or (co)fibration categories.

Aslı Güçlükan İlhan, Dokuz Eylül University.
Date: 7th and 14th of March, 2018, Wednesday. Time: 09:30 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: In this series of talks, we will introduce the fundamental group
and discuss some of its applications including the proof of the
fundamental theorem of algebra. In this talk, we will prove that every
group can be realized as a fundamental group. We will also discuss
the theory of covering spaces for graphs. As a consequence, we show that
every subgroup of a free group is free. If time permutes, we give a quick
introduction to basic notions of homotopy theory such as cofibrations,
fibrations and weak equivalences.