Azza Gaysin

Research Assistant

University of Passau

About me

I am a research assistant at Chair of Mathematical Logic, Faculty of Computer science and Mathematics, University of Passau, Passau, Germany.

Research interests: Logic, Computational complexity theory, Proof complexity theory, Bounded arithmetic, Universal algebra.

Education

PhD in Mathematics, 2018 - 2023

Faculty of Mathematics and Physics,
Department of Algebra,
Charles University
Master's degree in Mathematics, 2014 - 2018

Faculty of Mathematics and Physics,
Department of Algebra,
Charles University
Master's degree in Mathematics, 2009 - 2011

Faculty of Mathematics and Mechanics,
Department of Algebra,
Ural State University

Contact

Universität Passau,
Lehrstuhl Mathematische Logik,
Dr.-Hans-Kapfinger Straße 30, 94032 Passau
Room: HK30 101
Email: azza.gaysin@uni-passau.de
ORCID: 0000-0001-6863-8156

Skills

Programming

Python, SQL, LaTeX, MatLab, SageMath

Microsoft SQL Server, Oracle SQL Developer, PL/SQL, Oracle Data Modeler, Aqua Data Studio, Bizagi Modeler, Service Desk (Change Manager, L2), SVN, VBA, Google Analytics, CMS, IDEF0, BPMN, ISO 20000, ITIL, The Basics of Cryptography.

Languages

English (C1), Russian (mother tongue), Czech (C1)

Teaching:

Summer semester 2024:

Computational Logic (4V +2Ü)

Assistant lecturer, Übungen on Thursday 14:00-16:00 and 16:00-18:00 im SR001

The course gives an introduction into mathematical logic with special focus on applications in computer science. It presents first propositional logic, then first-order logic and treats especially resolution as a formal proof system, a calculus that plays a central role in computer science. Additionally the course presents modal logic and their applications to formal verification, as well as the automata theoretic approach to their algorithmics.

Link

Advanced Model theory (2V +2Ü)

Assistant lecturer, Übungen on Wednesday 14:00-16:00 in HS12

Vector spaces over a given field are determined (up to isomorphism) by their dimension. Algebraically closed fields with a given characteristic are determined by their transcendence degree. In particular, these theories have exactly one model in each uncountable cardinality. What do these theories have in common that explains this similar behavior? The course gives an introduction to stability theory. In particular, it introduces a general notion of dimension. The central goal of the course is to prove Morley’s theorem: if a theory has exactly one model of some uncountable cardinality, then this holds for all uncountable cardinalities. The course is a continuation of last semster's course Model Theory. With some extra effort the course is accessible to students with only some good background in first-order logic

Link

Publications

Proof complexity of universal algebra in a CSP dichotomy proof

A. Gaysin, submitted

PDF

Lattices of Weighted clones

A. Gaysin, J. Vančura, in preparation

Proof complexity of CSP

A. Gaysin, submitted

PDF

H-colouring Dichotomy in Proof Complexity

A. Gaysin, Journal of Logic and Computation, 31(5):1206–1225

PDF

Block-groups and Hall relations

A. Gaysin, M. Volkov, Semigroups, Categories, and Partial Algebras, 25–32. Springer Singapore, (2021)

PDF

Theses

Proof Complexity of CSP

PhD Thesis, Charles University in Prague, Czech Republic, 2023

Supervisor: Jan Krajíček
Study Programme: Algebra, Theory of Numbers and Mathematical Logic

PDF

Lattices of Weighted Clones

Master's Thesis, Charles University in Prague, Czech Republic, 2017

Supervisor: Libor Barto
Study Programme: Mathematical structures

PDF

Semigroups of Hall relation and block-groups

Master's Thesis, Ural State University, Russia, 2011

Supervisor: Mikhail Volkov
Study Programme: Discrete Mathematics and Mathematical Logic (confirmed by Ostrava University, Applied Mathematics Study Program, Applied Mathematics)