Department of Mathematical Sciences Florida Atlantic University Friday, 9 January, 4:00, S&E 215

FAU Algebra / Logic Seminar

Spring 2015

## Growth of Subgroups and Subalgebras

Yuri Bahturin In this talk I would like to discuss various aspects of the growth of subgroups in groups and subalgebras in algebras. The talks will be based on some recent joint papers with Alexander Olshanskii. In these papers we studied the growth of actions, the distortion and the relative growth of subgroups and subalgebras.

Friday, 23 January, 4:00, S&E 215## Feedback Computability

Robert Lubarsky Many notions of computability allow for an oracle, which can be thought of as an external database accessible during a computation. One natural oracle is the set of algorithms which converge (i.e. end eventually, as opposed to, say, looping forever). Normally the way that's taken is that the programs that are running are different from those in the oracle -- the ones running can access an oracle, and the ones in the oracle can't. But what if the computations running and those in the oracle are the same?

Friday, 13 February, 4:00, S&E 215 ## Complexity of Intersections of Real Quadrics and Discriminant Varieties

Antonio Lerario In this talk I will focus on the problem of understanding the topology of an intersection X of real quadrics. I will introduce a new notion of algebro-geometric complexity (inspired by fewnomials and related considerations), using the discriminant in the space of quadratic forms. This leads to a "duality" between X and the set of singular quadrics in the linear system defining it. This approach is reminiscent of stratified Morse theory - topology and singularities interact in a controlled way, and in the case of intersections of three quadrics, we will see that the dual problem entails the first part of Hilbert's Sixteenth Problem.

Last modified: December 4, 2014, by Robert Lubarsky.