This file can be used to add scheduled events to your calendar, however every program is unique. Below you will find what information is available, but if nothing else works try creating a new calendar in your program and using
http://math.colorado.edu/seminars/ics/allo.ics
as the source.
Thunderbird
The Algebra and Logic seminar is a research and learning seminar organized by the algebra and logic research group of the Department of Mathematics at the University of Colorado at Boulder. The scope of the seminar includes all topics with links to algebra, logic, or their applications, like general algebra, logic, model theory, category theory, set theory, set-theoretic topology, or theoretical computer science. If you have questions regarding this seminar, please contact Keith Kearnes or Peter Mayr.
We want to study the class of all finite structures together with the preorder given by primitive positive constructions as it plays an important role in the theory of constraint satisfaction problems. It is also equivalent to the homomorphism poset of the polymorphism minion of the structure, which is the right generalization of endomorphism monoid/ring in this context. It turns out that the first two layers of this order consist of a single equivalence class each, while the third layer consists of infinitely many points, represented by the transitive tournament on three vertices and structures in one-to-one correspondence with all finite simple groups.
Finite simple groups in the primitive positive constructability poset
Given a finite set of oriented graphs F, the F-free orientation problem is the following decision problem. Given a finite input graph, is there an orientation of its edges such that the resulting directed graph omits every member of F. If the set F consists of tournaments (i.e. complete oriented graphs), Bodirsky and Guzmán-Pro have recently established that this computational problem exhibits a complexity dichotomy: it is either solvable in polynomial time or NP-complete. I will explain how the F-free orientation problem can be viewed as the constraint satisfaction problem (CSP) of an omega-categorical template, making it amenable to universal algebraic methods. In particular I will demonstrate how the recently developed technique of "smooth approximations", provides a shorter algebraic proof of the complexity dichotomy for the graph orientation problem.
Graph orientation problems with forbidden tournaments
The notion of half-homomorphism between two groups is trivial, but it is an interesting subject when we drop the associativity law. In this talk, we will discuss some properties of half-homomorphism between two loops, paying special attention to some Bol loops and code loops.
Introduced in the 1960's, BCK-algebras are the algebraic semantics of BCK-logic. Like with many algebraic structures, there is a natural way to associate a topological space to a BCK-algebra; we call this space the spectrum. In this talk I'll recall what is known about spectra of commutative BCK-algebras before asking: what happens when we drop the assumption of commutativity? The discussion will close with a conjecture about spectra of finite BCK-algebras.
A variety is Hobby-McKenzie if it satisfies an idempotent Mal’tsev condition that fails in semilattices. Such varieties form a Mal’tsev class which resembles that of Taylor varieties: the idempotent condition can be chosen to be a set of linear identities in two variables. For locally finite varieties, this class contains precisely the varieties omitting TCT types 1 and 5. In this talk, we provide a characterization of general (not necessarily locally finite or idempotent) Hobby-McKenzie varieties based on their compatible 3-ary relations. As a consequence, we prove that these varieties form a prime filter in the interpretability lattice of varieties. We also propose a nice characterization that depends instead on the compatible digraphs of the variety, but which is only proven to be correct in the locally finite case. Joint work with B. Bodor, M. Maróti and L. Zádori
We classify the possible types of minimal operations above an arbitrary permutation group. Above the trivial group, a theorem of Rosenberg says that there are five types of minimal operations. We show that above any non-trivial permutation group there are at most four such types. Indeed, except above Boolean groups acting freely on a set, there are only three. In particular, this is the case for oligomorphic permutation groups, for which we improve a result of Bodirsky and Chen. Building on these results, we answer some questions of Bodirsky related to infinite-domain constraint satisfaction problems (CSPs). This is joint work with Michael Pinsker.
An algebra is called minimal Taylor if its clone satisfies a non-trivial minor condition, but no proper subclone does so. Recently, Barto, Brady, Bulatov, Kozik and Zhuk initiated the systematic study of minimal Taylor algebras, intending to build a unified theory to understand the complexity of constraint satisfaction problems. They conjecture that every minimal Taylor algebra is finitely related, which we disprove by giving a counterexample.
This result can be interpreted as follows: there is an infinite sequence of tractable finite domain CSPs, such that every CSP harder than all problems in the sequence, is already NP-complete.
Finite simple groups in the primitive positive constructability poset