Who am I?I am a mathematician. My research interests include universal algebra and interactions with model theory, theoretical computer science, and Ramsey theory. At the Vienna University of Technology, I am the head of the research unit Algebra. Moreover, I am a principal investigator of the Synergy Grant POCOCOP (Polynomialtime Computation: Opening the Blackboxes in Constraint Problems) of the European Research Council (ERC) (03/2023  02/2029, jointly with Libor Barto and Manuel Bodirsky). I am also the principal investigator of the projects Identities in polymorphism algebras of infinite structures of the Austrian Science Fund (FWF) (05/2019  04/2023) and Constraint Satisfaction Problems: beyond the finite case of the Austrian Science Fund (FWF) and the Polish Science Center (NCN) (10/2022  09/2026, jointly with Marcin Kozik). Currently working in my research unit: Gerhard Dorfer, Mike Behrisch, and Peter Holy (faculty); Piotr Kawalek, Paolo Marimon, and Jakub Rydval (postdocs); Johanna Brunar, Moritz Schöbi, Roman Feller (PhD students); Tomas Nagy (visiting researcher); Christoph Spiess (MA student); Aahana Jain (visiting student). I am an associate editor of the journal Algebra Universalis, published by Springer. We welcome submissions through the journal's editorial system. I am a member of the steering committees of the Workshops on General Algebra and the CWC. I am an organizer of the yearly Early Student Award meetings of the Austrian Mathematical Society. Here you can find my academic family, including my former doctoral advisor Martin Goldstern and my former PhD students Clemens Schindler, Tomas Nagy, and Michael Kompatscher. 




NewsERC Synergy Grant POCOCOP: Together with Libor Barto (Charles University Prague) and Manuel Bodirsky (TU Dresden) we have been awarded a Synergy Grant by the European Research Council (ERC) for our project POCOCOP (Polynomialtime Computation: Opening the Blackboxes in Constraint Problems). The project started in 03/2023 for a duration of 6 years. [TU Wien Press release (German)] [ERC press release] Jobs: Informal inquiries about future postdoc or Ph.D. positions are welcome! Students:
Please contact me if you are interested in writing a thesis (at any level) or seminar work on a topic at least remotely connected to my research interests! Recent and future events:
All slides / videos of all scientific talks ever can be found further down the page. 
Publications
Preprints of most publications can also be downloaded from the arXiv.org archive. 
Past scientific talks and conference participation
2022/09  Universal algebra: the Sudoku revolution, Austrian Mathematical Society Early Student Awards Meeting, Admont. (organizer) 
2022/09  CWC: Fourth CSP World Congress, Molveno (organizer). 
2022/08  Smooth approximations and CSPs over finitely bounded homogeneous structures, ThirtySeventh Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), Haifa. [slides] 
2022/07  49th International Colloquium on Automata, Languages and Programming (ICALP), Paris (PC member). 
2022/05  Universal algebra: the Sudoku revolution, Austrian Mathematical Society Early Student Awards Meeting, Strobl. (organizer) 
2022/05  Surprises in infinitedomain Constraint Satisfaction, or: an order out of nothing The Constraint Satisfaction Problem: Complexity and Approximability, Schloss Dagstuhl. [slides] 
2022/05  Current challenges in infinitedomain Constraint Satisfaction Problems, IEEE International Symposium on MultipleValued Logic, Dallas (online). [slides] 
2021/10  Uniqueness of Polish topologies on endomorphism monoids of countable structures, Panglobal Algebra and Logic Seminar, online / University of Colorado. [pdf] 
2021/09  Second CSP world congress (CWC), Kranjska Gora (organiser). 
2021/07  Mathematics of Constraint Satisfaction, Durham University (postponed from 2020, then cancelled). 
2021/06  Uniqueness of Polish topologies on endomorphism monoids of countably categorical structures, Seminari di logica TorinoUdine. [pdf] 
2021/05  Smooth approxmations, CSPs online seminar. [pdf] 
2021/04  Algebraic, logical, and combinatorial methods for Constraint Satisfaction Problems, Pure Mathematics Colloquium, University of Waterloo. [pdf] 
2021/03  The infinite CSP dichotomy conjecture, Ulam Seminar "in" Boulder, Colorado. [pdf] 
2021/02  Smooth approximations, 100th Arbeitstagung Allgemeine Algebra, Jagiellonian University, Kraków. [pdf] 
2021/01  Oligomorphic clones I, Homogeneous Structures: Model Theory meets Universal Algebra, Mathematisches Forschungsinstitut Oberwolfach (I was also an organiser). [pdf] 
2020/09  Second CSP World Congress, Völs am Schlern (organizer). 
2020/07  Hrushovski's encoding and omegacategorical CSP monsters, ICALP, The Cloud, Saarbrücken. [video] 
2019/09  Topology: relevant or irrelevant? 57th Summer School on General Algebra and Ordered Sets in Karolinka, Czech Republic. [slides] 
2019/06  What is symmetry?, CSP World Congress (CWC) 2019, Simon Fraser University, Vancouver. 
2019/06  Topology is relevant (delivered by A. Mottet), ThirtyFourth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) in Vancouver. 
2019/03  (organizer), 97. Arbeitstagung Allgemeine Algebra (97th Workshop on General Algebra) at TU Wien. 
2018/11  Canonical functions and the Ramsey property, revisited, Unifying Themes in Ramsey Theory at the Banff International Research Station (BIRS). [video] 
2018/08  (no talk), Workshop on Logical Aspects of Quantum Information at the Lorentz center, Leiden. 
2018/06  Loop conditions, The Constraint Satisfaction Problem: Complexity and Approximability, Dagstuhl. [slides] 
2018/04  Reconstructing structures from their clones, Set Theory, Model Theory and Applications, Eilat. [slides] 
2018/01  Equations in algebras induced by beautiful firstorder structures, Prague Gathering of Logicians/Beauty of Logic 2018, Prague. [slides] 
2018/01  Canonical functions and the Ramsey property, revisited, AMSASL Special Session on Set Theory, Logic and Ramsey Theory at the JMM 2018, San Diego. [slides] 
2017/07  Oligomorphic clones (tutorial), Tianfu Universal Algebra workshop, SWUFE Chengdu, China. 
2017/06  The two dichotomy conjectures for infinite domain CSPs are equivalent, LICS 2017, Reykjavik. [slides] 
2017/05  Equations in algebras from omegacategorical structures, Algebra seminar, TU Wien. 
2017/03  Double shrinking PseudoSiggers, LIAFA, Paris 7. 
2017/02  Equations in oligomorphic algebras, 93rd Workshop on General Algebra, Bern. [slides] 
2016/10  Functions on homogeneous Ramsey structures (3 lectures), Ramsey DocCourse 2016, Charles University Prague. [poster] [Mike Pawliuk's notes] 
2016/07  The algebraic dichotomy conjecture for infinite domain constraint satisfaction problems, LICS 2016, New York City. [slides] 
2016/06  The algebraic dichotomy conjecture for infinite domain constraint satisfaction problems, Algebra Seminar, TU Wien. 
2016/05  The algebraic dichotomy conjecture for infinite domain constraint satisfaction problems, Arbeitstagung Allgemeine Algebra 92, Prague. 
2016/03  CSPs over homogeneous graphs, KAFKA seminar, Department of Algebra, Charles University Prague. 
2016/01  Projecting function clones, Czech Academy of Sciences. 
2015/12  Uniform Birkhoff, TU Dresden. 
2015/11  Conjectures for clones over finitely bounded homogenous structures at the workshop Homogeneous Structures, Banff International Research Station [pdf] 
2015/10  Uniform Birkhoff at the workshop Duality in Computer Science, Schloss Dagstuhl 
2015/10  Uniform Birkhoff in the KAFKA seminar, Department of Algebra, Charles University Prague. 
2015/09  New Topological Clones at LIAFA, Paris 7. 
2015/07  Topological Clones at the LMS Durham Research Symposium Permutation Groups and Transformation Semigroups (2 lectures) [pdf] 
2015/07  Constraint satisfaction problems on Knfree graphs at the workshop The Constraint Satisfaction Problem: Complexity and Approximability, Schloss Dagstuhl 
2015/06  Topological Clones in Constraint Satisfaction at the conference Topology, Algebra, and Categories in Logic, Ischia, Italy [poster] [SLIDES] 
2014/11  Constraint Satisfaction on infinite domains (tutorial) at Algebraic and Model Theoretical Methods in Constraint Satisfaction, Banff International Research Station. [pdf 1] [pdf 2] [pdf 3] [videos] 
2014/11  Homogeneous structures: the older, the more descendants? at the University of Calgary. 
2014/11  Algebraic and model theoretic methods in constraint satisfaction at CUNY Logic Workshop, New York. [pdf] 
2014/10  Projective clone homomorphisms at STRUCO Meeting, Prague. [poster] 
2014/10  Algebraic and model theoretic methods in constraint satisfaction at the DocCourse, Prague. [pdf 1] [pdf 2] [pdf 3] [pdf 4] [poster] 
2014/07  Clones on Ramsey structures at the Algebra and Clones Fest, Prague. [pdf] 
2014/05  Reconstructing structures from their abstract clones at the ASL North American Annual Meeting (Special Session on Universal Algebra and CSPs), Boulder, Colorado. [pdf] 
2014/04  Decomposing function clones on infinite sets in the Algebra Seminar at University of Colorado, Boulder. 
2014/04  Introduction to Constraint Satisfaction over infinite structures at the Logic Seminar of the University of Colorado, Boulder [pdf]. 
2014/02  The topology of countable algebras, or: Polish clones at AAA 87, JKU Linz. 
2014/01  Topological Birkhoff and Constraint Satisfaction at LIAFA, Automates et Applications, Paris. 
2013/12  Reconstructing omegacategorical structures from their clones at Oberseminar mathematische Logik, Bonn. 
2013/11  Topological Birkhoff and reconstructing the random graph at the Hausdorff Research Institute for Mathematics, Bonn. 
2013/10  Reconstructing the topology of clones at Workshop on Homogeneous Structures (Hausdorff Research Institute for Mathematics, Bonn) [pdf]. 
2013/08  The 42 reducts of the random ordered graph at BLAST 2013: Boolean algebras, Lattices, Algebraic Logic, Set Theory, and Topology (Chapman University, Orange, California) [pdf slides] [pdf poster] 
2013/06  The 42 reducts of the random ordered graph at the Vienna University of Technology 
2013/06  The 42 reducts of the random ordered graph at the 4th Novi Sad Algebraic Conference  NSAC 2013 [pdf slides] [jpg poster] 
2013/05  Finitary aspects of reducts of homogeneous structures at Eötvös University, Budapest 
2012/11  Topological Birkhoff at the workshop The Constraint Satisfaction Problem: Complexity and Approximability, Schloss Dagstuhl [pdf] 
2012/07  TBA (=Topological Birkhoff and Applications) at the 2nd Workshop on Homogeneous Structures, Prague [pdf] 
2012/06  Lattices of subgroups of the symmetric group at the AAA 84, Dresden [pdf] 
2012/05  Schaefer's theorem for graphs, or: why to consult the infinite at times at the Tel Aviv University [pdf] 
2012/05  Reducts of the random partial order at the Université Lyon 1 
2012/03  Reducts of the random partial order at the Serbian Academy of Sciences and Arts, Belgrade 
2012/03  Reducts of Ramsey structures: the canonical approach at the University of Novi Sad [pdf] 
2012/03  Topological Birkhoff at the Technische Universität Wien 
2012/03  Reducts of the random partial order at the Kurt Gödel Research Centre, Vienna 
2011/12  Reducts of the random partial order at Paris 7  Diderot 
2011/11  Reducts of Ramsey structures: the canonical approach at AlbertLudwigsUniversität Freiburg [pdf] 
2011/10  Cooking with model theory, universal algebra and Ramsey theory in the complexity theory kitchen at Yeshiva University, New York [pdf] 
2011/08  Making the infinite finite: Polymorphisms on Ramsey structures at Workshop on Algebra and CSPs , Fields Institute, Toronto (pdf, audio mp3, Talk at Fields website) 
2011/07  Reducts of Homogeneous Structures I: the Ramsey Property at London Mathematical Society Northern Regional Meeting and Workshop on Homogeneous Structures, University of Leeds (pdf) 
2011/06  Constraint satisfaction with homogeneous templates at MALOA  From MAthematical LOgic to Applications, University of Leeds (pdf) 
2011/06  Schaefer's theorem for graphs at STOC 2011, San Jose, California (pdf, video mp4) 
2011/04  Decidability of definability at Eötvös University, Budapest 
2011/04  Clone vs. permutation group lattices at Eötvös University, Budapest 
2011/01  Ramsey clones and Schaefer's theorem for graphs in my habilitation colloquium at TU Wien (pdf) 
2011/01  Decidability of definability at TU Wien 
2010/10  Schaefer's theorem for graphs at Laboratoire d'Informatique de l'École Polytechnique (LIX), Palaiseau, France (pdf) 
2010/07  Functions on reducts of the random graph at Logic Colloquium 2010, Paris 7 Diderot (pdf) 
2010/06  Decidability of primitive positive definability at the Workshop on Algebra, Complexity, CSP, and sunshine, Centro de Algebra de Universidade de Lisboa (abstract) 
2010/06  Clones on homogeneous structures and Schaefer's theorem for graphs at ICAL 2010 (``Jardafest''), Prague (abstract / slides) 
2010/04  Reducts of homogeneous structures with the Ramseyproperty at TU Wien (pdf) 
2010/03  Reducts of homogeneous structures with the Ramseyproperty at Paris 7 (pdf) 
2009/10  Clones on the random graph: Towards Schaefer's theorem for graphs at at the RIMS research meeting on Logic and Algebra related to Computer Science, Kyoto 
2009/08  Structure in mappings on the random graph at NSAC09, Novi Sad (pdf) 
2009/06  All reducts of the random graph are modelcomplete in the Wiener Algebra Seminar at TU Wien 
2009/05  Mappings on the random graph at Université Claude Bernard, Lyon 
2009/01  Clones on infinite sets: Interactions with Set theory and Model theory at Paris 7 (pdf) 
2008/11  Closed permutation groups and reducts of relational structures at Université de Caen 
2008/10  Unterverbände des lokalen Klonverbandes in the Wiener Algebra Seminar at TU Wien 
2008/08  Many independent equality constraints at SSAOS 2008 in Trest, Czech Republic (pdf) 
2008/07  Monoidal intervals and algebraic lattices beyond ZFC at the RIMS research meeting on Clone Theory and Discrete Mathematics in Kyoto 
2008/05  Sublattices of the lattice of local clones at ROGICS'08 in Mahdia, Tunisia (pdf) 
2008/05  Clones on infinite sets at Université de Caen 
2007/11  Applied Algebra 3: Further reducts of relational structures at TU Wien 
2007/11  Sublattices of the clone lattice at Technische Universität Graz 
2007/10  Reducts of relational structures and local clones in the Kafka seminar at Univerzita Karlova, Prague 
2007/10  Clones I have met since 2004 in the legendary Trnková seminar at Univerzita Karlova, Prague 
2007/10  Applied Algebra 2: Reducts of relational structures, CSP and local clones at TU Wien 
2007/06  The reducts of (N,=) at OAL2007 in Nashville, Tennessee (pdf) 
2007/06  Clones from ideals at the AAA 74 in Tampere (pdf) 
2007/05  Clones in universal algebra in the lecture series ``Wissenswertes aus der Mathematik'' held at TU Wien (pdf) 
2007/03  Cardinalities of intervals in the clone lattice at TU Wien 
2007/02  Local clones containing the permutations at the AAA 73 in Klagenfurt 
2007/01  The Constraint Satisfaction Problem and local clones at TU Wien 
2006/11  An introduction to clones at the HumboldtUniversität zu Berlin 
2006/06  Algebraische Verbände sind Unterverbände von Klonverbänden in the Wiener Algebra Seminar at TU Wien (pdf) 
2006/06  Algebraic lattices are complete sublattices of the clone lattice over an infinite set at the AAA 72 in Budapest (pdf) 
2006/02  Intervals of the clone lattice at the Warsaw University of Technology 
2006/02  The minimal clones above the permutations at the AAA 71 in Bedlewo, Poland (pdf) 
2005/08  Monoids above the permutations at the International Algebraic Conference in Ekaterinburg (pdf) 
2005/07  Lattices of order ideals as monoidal intervals at NSAC'05 in Novi Sad (pdf) 
2005/07  Monoids above the permutations at the conference on Universal Algebra and Lattice Theory in Szeged (pdf) 
2005/06  The clone generated by all binary twovalued operations: An application of infinite to finite clone theory at RIMS in Kyoto 
2005/06  A survey of clones on infinite sets at RIMS in Kyoto 
2005/06  The interval above the clone T2 at Meiji University Tokyo 
2005/01  The clone lattice: Introduction and partition at International Christian's University Tokyo 
Older Talks 