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Events for Algebra and Logic

ICS calendar file for Algebra/Logic

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.

Tue, Feb. 3 1:25pm (online)	Sara Ugolini (IIIA-CSIC Barcelona) View Online:https://cuboulder.zoom.us/j/96896272260 X In this talk, we begin by considering the semiring of the natural numbers with truncated difference, N = (N, +, *, -, 0, 1). Its equational theory is not recursively axiomatizable, due to the fact that one can essentially encode in it the undecidability of Hilbert’s tenth problem. Our aim is to study finitely axiomatizable varieties of semirings with difference which include the one generated by N, and are as close to it as possible. To this end, we introduce the variety of almost natural semirings with difference, AN. We show that the subdirectly irreducible algebras in this variety coincide with the models of PA, a weak form of Peano Arithmetic without induction that is an axiomatic extension of Robinson Arithmetic. Models of PA are known to satisfy all Sigma_1 sentences true in N. This variety can be axiomatized by a few simple equations and enjoys several appealing universal-algebraic properties: it is connected to lattice-ordered rings, it is a discriminator variety, ideal determined and 0-regular; thus it admits an associated 0-assertional logic. Nevertheless, we will see that its connection to arithmetic still yields an undecidable equational theory. This talk is based on ongoing joint work with Guillermo Badia, Xavier Caicedo, and Carles Noguera. Almost natural semirings with difference
Tue, Feb. 10 1:25pm (online)	Claudia Muresan (University of Bucharest) View Online:https://cuboulder.zoom.us/j/96896272260 Abstracting congruence extensions through complete join–semilattice morphisms between commutator lattices
Tue, Feb. 24 1:25pm (online)	Zoltan Vidnyanszky (ELTE Budapest) View Online:https://cuboulder.zoom.us/j/96896272260 X Descriptive combinatorics is a field concerned with graph theoretic problems on nice (definable) infinite graphs. In this first half of the talk, I will introduce the field of descriptive combinatorics and discuss some of the basic results of the area. Then, I will turn to the descriptive version of complexity problems, in particular, the CSP Dichotomy: it turns out that the finitary complexity landscape is only partially reflected in the descriptive context. CSPs in the descriptive context
Tue, Mar. 3 2pm (online)	Ana Belen Avilez Garcia (Chapman University) View Online:https://cuboulder.zoom.us/j/96896272260 X Cozero elements of a frame play an important role in point-free topology. The set of cozero elements, Coz L, of a frame L is a sub -frame of L (that is, a sublattice closed under countable suprema and finite infima). Moreover, the lattice Coz L join-generates the frame L if and only if L is completely regular (a result analogous to the classical one for completely regular topological spaces). Within the setting of completely regular frames, we consider the Dedekind–MacNeille completion of the lattice of cozero elements, which in this context coincides with the Bruns–Lakser construction. The frame obtained through this process turns out to be a sublocale of the original frame, specifically, the smallest sublocale containing Coz L. A central aim of the talk is to compare this sublocale with the original frame and to present results and examples showing when the two coincide and when they differ. Viewing Coz L both as a join-generating sublattice and through its completion leads naturally to two related but distinct classes of frames: cozero frames and perfectly regular frames. We will examine the relationship between these notions and provide illustrative examples. This is an ongoing joint work with Guram Bezhanishvili and Joanne Walters-Wayland. Cozero frames and perfectly regular frames

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Events for Algebra and Logic