UNCE / SCI / 022
Project seminar 27.June 2018, 13.oo
The seminar will take place in the seminar room of the
Dept. of Algebra (MFF, Sokolovska 83, 3rd fl.).
Program:
Lectures will be cca 30 min, with a generous break
before or after the third lecture.
Vita Kala:
Universal quadratic forms over number fields
A universal form is a positive definite quadratic form with integral
coefficients which represents all positive numbers - a classical example over
the integers is the sum of four squares x^2 + y^2 + z^2 + w^2. I shall discuss
some recent results concerning the number of variables required by a universal
form over a real quadratic field, and the (non-)existence of universal forms
with Z-coefficients.
Alexander Kazda:
Constraint Satisfaction Problem and friends
The Constraint Satisfaction Problem (CSP) is a very general
computational problem. In this talk, we will explain why universal
algebra is suitable for describing the complexity of CSP and how we can
transfer our tools from CSP to various similar problems: valued CSP
(VCSP), counting CSP (#CSP), and especially promise CSP (PCSP).
Andrew Moorhead (Vanderbilt University):
Supernilpotence in Universal Algebra
The commutator for groups can be seen as a special case of a
commutator theory for general algebraic systems. With such a
commutator it is possible to define analogues of abelianness,
solvability and nilpotence. This commutator theory has recently been
extended to something called higher commutator theory, from which one
can define a stronger type of nilpotence which is called
supernilpotence. In this talk we will discuss some of the reasons that
supernilpotence is a useful concept.
Benjamin Vejnar:
The complexity of the homeomorphism relation between compact spaces
We study the complexity of the homeomorphism relation of compact metric spaces
when restricted to some subclasses such as continua, regular
continua or regular
compacta. The complexity of an equivalence relation on a Polish space is
compared with some others using the notion of Borel reducibility.
Jonathan Verner:
Complexity of Ultrafilters
As is well known, constructing a non-trivial ultrafilter requires (some amount
of) the axiom of choice so these objects are inherently complicated. It is not
clear, however, whether they are all created equal or whether some are more
complex than others. In this talk I will introduce several different
"measures" of complexity of ultrafilters, give an overview of the known
results, and show that even after more than half a century of intensive
research, basic questions still remain unanswered.