ALGEBRA AND BEYOND

Course	Lectures	Teaching assistant	Exercise classes	OPAL
Algebra 1	Monday, 14:00–15:30, every week, MIB–1108	Dr. Maxime Gheysens	Friday, 11:30–13:00, every 2nd week, PRÜ–1103	link
Analysis on Groups	Monday, 9:30–11:00, every week, MIB–1113	Dr. Maxime Gheysens	Tuesday, 9:30–11:00, every week, MIB–1108	link
Automata Theory	Wednesday, 16:00–17:30, every week, RAM–1085	Maximilian Geißer, M.Sc.	Tuesday, 18:00–19:30, every 2nd week, PHY–0010	link

Summer 2021

• Algebra 2 (2+1; Course assistant: Dr. Maxime Gheysens)
• Topological Data Analysis (2+2; Course assistant: Dr. Maxime Gheysens)
• Coding Theory and Cryptography (2+1; Course assistant: Maximilian Geißer, M.Sc.)

Winter 2020/21

• Algebra 1 (2+1; Course assistant: Dr. Maxime Gheysens)
• Topology (2+2; Course assistant: Dr. Maxime Gheysens)
• Automata Theory (2+1; Course assistant: Maximilian Geißer, M.Sc.)

Topological groups and dynamics

• infinite-dimensional transformation groups
• fixed-point properties
• ergodic theory of continuous group actions

Asymptotic geometric analysis and functional analysis

• concentration phenomena
• metric measure geometry
• combinatorial aspects

Ring theory and general algebra

• structure theory and harmonic analysis of infinite rings
• automorphism groups of relational structures
• topological aspects of universal algebra

JOURNAL ARTICLES

Juschenko, K.; Schneider, F. M.:
Skew-amenability of topological groups.
To appear in Commentarii Mathematici Helvetici.
arXiv

Schneider, F. M.; Solecki, S.:
Concentration of measure, classification of submeasures, and dynamics of L₀.
Journal of Functional Analysis 280 (2021), no. 5, 108890.
doi arXiv

Hanika, T.; Schneider, F. M.; Stumme, G.:
Intrinsic dimension of geometric data sets.
To appear in Tohoku Mathematical Journal.
arXiv

Schneider, F. M.; Thom, A.:
The Liouville property and random walks on topological groups.
Commentarii Mathematici Helvetici 95 (2020), no. 3, pp. 483–513.
doi arXiv

Schneider, F. M.:
Equivariant dissipation in non-archimedean groups.
Israel Journal of Mathematics 234 (2019), no. 1, pp. 281–307.
doi arXiv

Schneider, F. M.; Zumbrägel, J.:
MacWilliams' extension theorem for infinite rings.
Proceedings of the American Mathematical Society 147 (2019), no. 3, pp. 947–961.
doi arXiv

Schneider, F. M.:
Equivariant concentration in topological groups.
Geometry & Topology 23 (2019), no. 2, pp. 925–956.
doi arXiv

Schneider, F. M.:
About von Neumann's problem for locally compact groups.
Journal of Noncommutative Geometry 12 (2018), no. 4, pp. 1531–1549.
doi arXiv

Schneider, F. M.; Thom, A.:
On Følner sets in topological groups.
Compositio Mathematica 154 (2018), no. 7, pp. 1333–1362.
doi arXiv

Pestov, V. G.; Schneider, F. M.:
On amenability and groups of measurable maps.
Journal of Functional Analysis 273 (2017), no. 12, pp. 3859–3874.
doi arXiv

Schneider, F. M.:
A uniform Birkhoff theorem.
Algebra Universalis 78 (2017), no. 3, pp. 337–354.
doi arXiv

Schneider, F. M.; Zumbrägel, J.:
Profinite algebras and affine boundedness.
Advances in Mathematics 305 (2017), pp. 661–681.
doi arXiv

Schneider, F. M.; Thom, A.:
Topological matchings and amenability.
Fundamenta Mathematicae 238 (2017), pp. 167–200.
doi arXiv

Schneider, F. M.; Zumbrägel, J.:
Every simple compact semiring is finite.
Topology and its Applications 206 (2016), pp. 305–310.
doi arXiv

Borchmann, D.; Schneider, F. M.:
Topological entropy of formal languages.
Semigroup Forum 94 (2017), no. 3, pp. 556–581.
doi arXiv

Bodirsky, M; Schneider, F. M.:
A topological characterisation of endomorphism monoids of countable structures.
Algebra Universalis 77 (2017), no. 3, pp. 251–269.
doi arXiv

Schneider, F. M.; Kerkhoff, S.; Pöschel, R.; Behrisch, M.; Siegmund, S.:
Dynamical systems in categories.
Applied Categorical Structures 25 (2017), no. 1, pp. 29–57.
doi

Kerkhoff, S.; Schneider, F. M.:
Dualities induced by topological semirings.
Applied Categorical Structures 24 (2016), no. 4, pp. 315–329.
doi

Kerkhoff, S.; Schneider, F. M.:
Clones of (continuous) partial cofunctions.
Journal of Multiple-Valued Logic and Soft Computing 28 (2017), no. 1, pp. 59–79.
doi

Schneider, F. M.; Kerkhoff, S.; Behrisch, M.; Siegmund, S.:
Chaotic actions of topological semigroups.
Semigroup Forum 87 (2013), no. 3, pp. 590–598.
doi

Schneider, F. M.; Kerkhoff, S.; Behrisch, M.; Siegmund, S.:
Locally compact groups admitting faithful strongly chaotic actions on Hausdorff spaces.
International Journal of Bifurcation and Chaos 23 (2013), no. 9, pp. 135–158.
doi

Schneider, F. M.:
Weak homomorphisms between functorial algebras.
Demonstratio Mathematica 44 (2011), no. 4, pp. 801–818.
doi

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ARTICLES IN PEER-REVIEWED CONFERENCE PROCEEDINGS

Kerkhoff, S.; Schneider, F. M.:
Directed tree decompositions.
In: Formal Concept Analysis: 12th International Conference, ICFCA 2014 Proceedings.
Lecture Notes in Computer Science (2014), vol. 8478, pp. 80–95.

Schneider, F. M.:
Chaotic actions of locally compact Hausdorff topological groups.
Proc. Workshop on Algebra, Coalgebra and Topology (WACT 2013),
Electronic Notes Theoretical Computer Science (2014), vol. 303, pp. 181–195.

Kerkhoff, S.; Pöschel, R.; Schneider, F. M.:
A short introduction to clones.
Proc. Workshop on Algebra, Coalgebra and Topology (WACT 2013),
Electronic Notes Theoretical Computer Science (2014), vol. 303, pp. 107–120.

Kerkhoff, S.; Schneider, F. M.:
Clones of partial cofunctions.
Proceedings of the 43rd IEEE International Symposium on Multiple-Valued Logic,
IEEE Computer Society 2013, pp. 186–191.

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EXTENDED ABSTRACTS

Schneider, F. M.:
On Følner sets in topological groups.
Oberwolfach Report No. 41/2016, pp. 26–27.

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PHD THESIS

Schneider, F. M.:
A relational localisation theory for topological algebras.
TU Dresden, 2012, 192 pages.

DIPLOMA THESIS

Schneider, F. M.:
A foundation for a relational localisation theory for topological algebras.
TU Dresden, 2011, 49 pages.

Meeting	Venue	Link
Unifying Themes in Ramsey Theory, November 2018	Banff International Research Station (BIRS)	video
Mean Dimension and Sofic Entropy Meet Dynamical Systems, Geometric Analysis and Information Theory, July 2017	Banff International Research Station (BIRS)	video
Structure and Geometry of Polish Groups, June 2017	BIRS-affiliated Casa Matemática Oaxaca (BIRS-CMO)	video