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 a faculty member of the Universal Algebra Group. Moreover, I am a principal investigator of the Synergy Grant POCOCOP (Polynomial-time 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 employed in my group: Johanna Brunar, Piotr Kawalek, Paolo Marimon, Albert Vucaj, Tomas Nagy, Jakub Rydval, Peter Holy, and Clemens Schindler (who also holds a DOC-Fellowship of the Austrian Academy of Sciences). 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. |
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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 (Polynomial-time 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
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 Torino-Udine. [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 omega-categorical 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), Thirty-Fourth 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 first-order structures, Prague Gathering of Logicians/Beauty of Logic 2018, Prague. [slides] |
2018/01 | Canonical functions and the Ramsey property, revisited, AMS-ASL 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 omega-categorical structures, Algebra seminar, TU Wien. |
2017/03 | Double shrinking Pseudo-Siggers, 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 Kn-free 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 Doc-Course, 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 omega-categorical 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 Albert-Ludwigs-Universität 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 Ramsey-property at TU Wien (pdf) |
2010/03 | Reducts of homogeneous structures with the Ramsey-property 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 model-complete 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 Humboldt-Universität 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 two-valued 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 |