Libor Barto
 HOME COCOSYM RESEARCH FOR STUDENTS

ARCHIV 19/20 zimni semestr

[Zpet]

UNIVERSAL ALGEBRA (NMAG405)

Lecture: Wed 11:30 - 13:00 K12
Practicals run by M. Kompatscher: Tue 11:30 - 13:00 K8

• Practicals ("Z: Zapocet"): homeworks (60% from 4 best scores out of 5 homeworks)
• Lecture ("Zk: Zkouska"): 15% homeworks, 85% written test + possible oral examination

Literature:

 topics recommended reading homework 2.10. Motivation. Algebra (signature, type). Examples. Ex.: Lattices vs. lattice ordered sets Bergman 1.1, 1.2 9.10. Lattices, complete lattices, closure operators. Ex.: Isomorphism Bergman 2.1, 2.2, 2.3 16.10. Algebraic lattices and closure operators. Galois correspondences. Ex.: Distributive and modular lattices. The lattice of equivalence relations. Bergman 2.4, 2.5 Homework 1 due 29 Oct 23.10. Subalgebras, products, quotients. Ex.: Complete lattices, closure operators, Galois correspondences. Bergman 1.3, 1.4, 1.5 30.10. H,S,P operators, variety. Homomorphisms. Ex.: Subalgebras, congruences. Bergman 1.1, 1.3, 3.1, 3.5 Homework 2 due 12 Nov 6.11. Direct and subdirect decomposition Ex.: Homomorphisms. Finite algebras generate locally finite varieties. Bergman 3.2, 3.3 13.11. --- Ex.: ---. 20.11. Subdirect decomoposition, SIs in congruence distributive vaieties Ex.: Direct and subdirect decomposition. Bergman 3.4, 3.5, (5.2) Homework 3 due 3 Dec 27.11. Terms, identities, free algebras. Ex.: SIs in monnounary algebras. Bergman 4.3, 4.4 4.12. The syntax-semantics Galois correspondence, Birkhoff's theorem. Ex.: Free algebras. Bergman 4.4, (4.6) Homework 4 due 17 Dec 11.12. Clones. Free algebras as clones of term operations. Ex.: Equational bases. Bergman 4.1 18.12. The operations-relations Galois correspondence. Ex.: Clones. Bergman 4.2 Homework 5 due 7 Jan 8.11. Mal'cev conditions: Mal'cev, majority. Ex.: Algebraic and relational clones. Bergman 4.7 (part)

INTRODUCTION TO COMPLEXITY OF CSP (NMAG563)

Run by Antoine Mottet: Thr 9:00 seminar room of the Department of Algebra

References:

• short survey (Barto): here (see complexity column)
• longer survey (Barto, Krokhin, Willard): here
• 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

Wed 15:40 seminar room of KA web

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