הרצאה ראשונה
מרצה: ג׳ורג׳ פטרזייל

Title: Approximating equivalence classes with finite equivalence classes
Abstract: Suppose you have a nice equivalence relation on the real line such that every class is countable. A standard question in descriptive set theory is the following: when can this equivalence relation be written as an increasing union of subequivalence relations on the real line which have finite classes, and each of them is also nice? We will show that if one is willing to remove a topologically small set, the answer for this question is always yes; every such equivalence relation, restricted to a large set, can be written as an increasing union of equivalence relations with finite classes. The proof demonstrates a useful tool which can often replace Fubini's theorem in topological settings.

----------------------------------------------------------------------------------------------------------

הרצאה שנייה
מרצה: צור פלוטניקוב

Title: Automorphism towers of groups
Abstract: Given a group , we will look at the group of automorphisms of  (namely, ), and look further at the group of automorphisms of that group (namely, ), and so forth, forming the so-called automorphism tower of .

A very interesting question about this construction is whether the automorphism tower stabilizes at some point. 
In this talk we will try to understand this construction, and discuss some results related to the question above. Also, we will look at some open problems

The talk should be understandable to anybody with knowledge of the "Mivnim 1" course material.