Libor Barto Studenti

Libor Barto

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UNIVERSAL ALGEBRA (NMAG405)

Lecture: Thr 15:40 - 17:10 K5
Practicals run by Filippo Spaggiari: Thr 17:20 - 18:50 K5

Grading:

Practicals ("Z: Zapocet"): homeworks (60% from the sum of 4 best scores out of 5 homeworks)
Lecture ("Zk: Zkouska"): written test + possible oral examination

Literature:

Clifford Bergman: Universal Algebra: Fundamentals and Selected Topics
Burris, Sankappanavar: A Course in Universal Algebra (an alternative source of examples and exercises)
Stanovsky: Exercises in algebra (in Czech) - chapter V

topics (future topics may change) recommended reading lecture notes homework

29.9. Motivation. Algebra (signature, type). Examples.
Pr.: Lattices vs. lattice ordered sets Bergman 1.1, 1.2 lecture 1 practicals 1

6.10. Lattices, complete lattices, closure operators.
Pr.: Distributive and modular lattices. The lattice of equivalence relations. Bergman 2.1, 2.2, 2.3 lecture 2 practicals 2

13.10. Algebraic lattices and closure operators. Galois correspondences.
Pr.: Complete lattices, closure operators, Galois correspondences. Bergman 2.4, 2.5 lecture 3 practicals 3 Homework 1
due 27.10. 17:20

20.10. Subalgebras, products, quotients.
Pr.: Subalgebras, congruences. Bergman 1.3, 1.4, 1.5 lecture 4 practicals 4
corrected (lower quality)

27.10. H,S,P operators, variety. Homomorphisms.
Pr.: Homomorphisms. Finite algebras generate locally finite varieties. Bergman 1.1, 1.3, 3.1, 3.5 lecture 5 practicals 5 Homework 2
due 10.11. 17:20

3.11. Direct and subdirect decomposition
Pr.: Direct and subdirect decomposition. Bergman 3.2, 3.3 lecture 6 practicals 6

10.11. Subdirect decomoposition, SIs in congruence distributive vaieties
Pr.: SIs in monounary algebras. Bergman 3.4, 3.5, (5.2) lecture 7 practicals 7 Homework 3
due 24.11. 17:20

17.11. ---
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24.11. Terms, identities, free algebras.
Pr.: Free algebras. Bergman 4.3, 4.4 lecture 8 practicals 8

1.12. The syntax-semantics Galois correspondence, Birkhoff's theorem.
Pr.: Equational bases. Bergman 4.4, (4.6) lecture 9 practicals 9 Homework 4
due 15.12. 17:20

8.12. Clones. Free algebras as clones of term operations.
Pr.: Clones. Bergman 4.1 lecture 10 practicals 10

15.12. The operations-relations Galois correspondence.
Pr.: Algebraic and relational clones. Bergman 4.2 lecture 11 practicals 11 Homework 5
due 5.1. 17:20

22.12. Mal'cev conditions: Mal'cev, majority.
Pr.: Mal'cev conditions Bergman 4.7 (part) lecture 12 practicals 12

5.1. Tame Congruence Theory
Pr.: Tame Congruence Theory practicals 13

INTRODUCTION TO COMPLEXITY OF CSP (NMAG563)

Fri 10:40 K12

Problems

References (contain a lot of spoilers):

survey (Barto, Krokhin, Willard): here
shorter survey (Barto): here (see the complexity column)
Krokhin's tutorial: available here
Another Krokhin's tutorial, a bit different topics: available here
My tutorial: PDF
Paper Bulatov, Jeavons, Krokhin: Classifying the Complexity of Constraints Using Finite Algebras PDF

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