Month: February 2018

Aslı Güçlükan İlhan, Dokuz Eylül University.
Date: 28th of February, 2018, Wednesday. Time: 09:30 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: A small cover is a smooth closed manifold which admits a
locally standard (Z/2)^n-action whose orbit space is a simple
convex polytope. The notion of a small cover is introduced by Davis and
Januszkiewicz as a generalization of real toric manifolds. In this talk,
we first discuss the small covers over cubes whose complete
characterization is given by Choi-Masuda-Oum. Using this classification,
they also show that small covers over cubes satisfy the cohomological
rigidity problem. We also discuss the recent results obtained by
Altunbulak-Güçlükan İlhan about the number of small covers over product of
simplices.

Aslı Güçlükan İlhan, Dokuz Eylül University.
Date: 21st of February, 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 calculate the
fundamental group of a circle and give some of its applications. We also
discuss the van Kampen theorem which allows us to compute the fundamental
group of a space from the simpler ones. Then we prove that every group
can be realized as a fundamental group.

Müge Kanuni, Düzce University.
Date: 14th of February, 2018, Wednesday. Time: 09:30 – 12:00.
Place: Dokuz Eylül Univ., Tınaztepe Campus, Faculty of Science, Department of Mathematics, Room B206.
Abstract: A ring R is said to have Invariant Basis Number property, or more simply IBN, in case no two free left R-modules of different rank are isomorphic. W. G. Leavitt constructed some non-IBN algebras — what we now call Leavitt algebras — in the 1960’s. The Leavitt path algebra of a quiver with one vertex and m loops turns out to be Leavitt algebra R of type (1,m), that is a non-IBN algebra where R is isomorphic to m-copies of R as a left module and not isomorphic to n-copies of R for any 1 < n < m. On the other hand, there is an abundance of examples of Leavitt path algebras which have IBN. Moreover, we give an algorithm to decide whether a Leavitt path algebra has IBN or not. If time permits, we discuss the ideal structure of Leavitt path algebras.

Aslı Güçlükan İlhan, Dokuz Eylül University.
Date: 7th of February, 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 the first talk, after a quick
discussion of what algebraic topology is, we will give the definition and
some properties of the fundamental group. We will also discuss the picture
hanging problem as a motivation.