Jan Jurka

I am currently a PhD student in mathematics at Masaryk University. I also did my bachelor's and master's in mathematics at Masaryk University.

Email address: jurka@math.muni.cz

Research interests: Category theory (e.g. locally presentable categories, enriched categories, and the small object argument), universal algebra, and order theory. I also enjoy thinking about effect algebras, semigroup theory, and theoretical computer science.

Publications

• Algebraic Reasoning over Relational Structures. With Stefan Milius and Henning Urbat. Proc. 40th Conference on Mathematical Foundations of Programming Semantics (MFPS 2024). To appear. (arXiv version: arXiv:2401.08445)


• Are Chain-Complete Posets Co-wellpowered? With Jiří Rosický. Order 39, 71–76 (2022). doi:10.1007/s11083-021-09567-2. (Corrected version: arXiv:2007.02255)

Preprints

• An Enriched Small Object Argument Over a Cofibrantly Generated Base. arXiv:2401.05974.


• Constructing spectra using cone injectivity. With Tomáš Perutka and Lukáš Vokřínek. arXiv:2201.03516.

Talks

• CT 2024 - An Enriched Small Object Argument Over a Cofibrantly Generated Base (slides)


• MFPS 2024 - Algebraic Reasoning over Relational Structures (slides, video)

Notes

Here you can find notes from most of the courses that I took. The notes are in czech unless stated otherwise, [CZ/EN] means that some parts are in czech and some are in english, [EN] means that the notes are either completely or almost completely in english. Some notes can also be found on Ondřej Darmovzal's website.

Bachelor's

• M1100 - Mathematical Analysis I
• M1110 - Linear Algebra and Geometry I
• M1120 - Discrete Mathematics
• M1130 - Mathematics Seminar I
• M5140 - Graph Theory
• M6520 - Elementary Number Theory
• M7400 - Problem Solving Seminar

• M2100 - Mathematical Analysis II
• M2110 - Linear Algebra and Geometry II
• M2120 - Financial Mathematics
• M2130 - Mathematics Seminar II
• M2150 - Algebra I
• M4155 - Set Theory
• M7400 - Problem Solving Seminar

• M1160 - Introduction to Programming I
• M3100 - Mathematical Analysis III
• M3121 - Probability and Statistics I
• M3150 - Algebra II
• M7150 and M7151 - Category Theory [CZ/EN]
• M7400 - Problem Solving Seminar
• MA007 - Mathematical Logic

• M4122 - Probability and Statistics II
• M4170 - Measure and Integral
• M4180 - Numerical Methods I
• M4190 - Differential Geometry of Curves and Surfaces [CZ/EN]
• M6140 - Topology [CZ/EN]
• M7400 - Problem Solving Seminar
• M8195 - Number Theory Seminar

• M3130 - Linear Algebra and Geometry III
• M5110 - Rings and Modules [CZ/EN]
• M5130 - Global Analysis [CZ/EN]
• M5170 - Mathematical Programming
• M7400 - Problem Solving Seminar [EN]
• M9260 - Model Theory [EN]

• M6150 - Functional Analysis I
• M6170 - Complex Analysis
• M8250 - Topics in Category Theory [EN]
• IB005 - Formal Languages and Automata

Master's

• MD134 - Ordered Algebraic Structures
• MD136 - Homological Algebra [CZ/EN]
• M7110 - Differential Geometry [EN]
• M7120 - Spectral Analysis I
• IB107 - Computability and Complexity
• MA017 - Geometric Algorithms [EN]

• MD131 - Representation Theory [EN]
• MD140 - Singularity Theory [EN]
• M7190 - Game Theory
• M7230 - Galois Theory
• M8130 - Algebraic Topology [CZ/EN]
• M8250 - Topics in Category Theory [EN]
• IV003 - Algorithms and Data Structures II
• INNOLEC - Polynomial and Rational Convexity in Complex Geometry [EN]

• MD107 - Simplicial Sets [CZ/EN]
• M7180 - Functional Analysis II
• M7250 - Semigroups & Formal Languages
• M7270 - Complex Analysis II [EN]
• M9130 - Lattice Theory [EN]