Speaker: Kostas Beros (U. North Texas)

Title: Normal numbers and a completeness result in the difference hierarchy

Abstract: In this talk I consider a natural set of real numbers, arising in ergodic theory, and show that it is Wadge-complete for the class of differences of $F_{\sigma\delta}$ sets. I will recall basic definitions and motivate my result with a discussion of related theorems from the past twenty years.

Logic seminar

Keller Hall 401

Achilles Beros will
speak on “Algorithmic learning and the arithmetic hierarchy”

Summary:

I will present a theorem from my thesis that establishes the arithmetic
complexity of a well-known learning criterion. Two other papers have
been published since then that continue the line of research. I will
discuss the newer papers as well as broader connections between
recursion theory and learning theory.

Keller Hall 303

This week the Sporadic Logic Seminar will be Mushfeq Khan speaking on
“Turing degrees and Muchnik degrees of recursively
bounded DNR functions”.

Summary:

This talk is based on a forthcoming paper by Steve Simpson. It contains
some results that shed light on a part of the Muchnik lattice that remains
poorly understood: the various degrees of recursively bounded DNR functions
obtained by varying the recursive bound.

Keller 303