Title: On groups with quadratic Dehn functions
Abstract: This is a joint work with A. Olshanskii. We construct a finitely presented group with quadratic Dehn function and undecidable conjugacy problem.
Title: Approximations of groups and equations over groups.
Abstract:
The talk is largely based on the paper which may be found here: https://authors.elsevier.com/a/1UN3b4~FOr6ze
Title: Old and New Results on Subgroup Growth in Pro-p Groups.
Abstract: I will survey our current knowledge about subgroup growth in pro-p growth. In particular I will present new solutions to long standing open problems in the area:
1. What is the minimal subgroup growth of non-$p$-adic analytic pro-$p$ groups? (Joint work with Benjamin Klopsch and Jan-Christoph Schlage-Puchta.)
2. What are the subgroup growths of the Grigorchuk group and the Gupta-Sidki groups? (Joint work with Jan-Christoph Schlage-Puchta.)
Title: Inp-minimal ordered groups.
Abstract. The main goal of the talk is to present the proof of the theorem stating that inp-minimal (left)-ordered groups are abelian. This generalizes a previous result of P. Simon for bi-ordered inp-minimal groups.
Title: Random integer matrices
Abstract: I will discuss various models of random integer matrices, and their (occasionally surprising) properties. Some of the work discussed is joint with E. Fuchs.
Title: A tale of three elliptic curves.
Abstract: We will show how the arithmetic of three elliptic curves answers three old questions in the Euclidean geometry.
Title: Fixed points of finite groups on modules
Abstract: Suppose G is a finite group, p is a prime, S is a Sylow p-subgroup of G, and V is a G-module over a field of characteristic p. In some situations, an easy calculation shows that the fixed points of G on V are the same as the fixed points of the normalizer
of S in G. Generalizations of this result have been obtained previously to study the structure of G for p odd. We plan to describe a new generalization for p = 2. (This is part of joint work with J. Lynd that removes the classification of finite simple groups
Title: Almost Congruence Extension Property for subgroups of free groups.
Abstract.
The talk essentially based on: https://arxiv.org/abs/1606.02345
Let G be a group and H
every normal subgroup N of H is an intersection of some normal subgroup of G with H. The CEP appears in group theory in different context.
The following question seems to be very difficult:
Which finitely generated subgroup of a free group has CEP?
