Expertise
Algebraic topology, model theory, image processing
Research Interests
Algebraic topology, logic, image processing, algebraic geometry
Homotopical algebra, combinatorial structures over finite fields, mathematical morphology, categorical logic, computational topology
Education
- Ph D: Mathematics, (1998), MIT - Cambridge, MA
Dissertation/Thesis Title: Homotopy Theory and Topoi - BA: Mathematics, (1993), Princeton University - New Jersey
Selected Awards and Honors
- Fulbright Scholar (2013)
- Faculty Teaching Award (2012), Teaching - University of Massachusetts Lowell
- Faculty Teaching Award (2007), Teaching - University of Massachusetts Lowell
- Rackham Faculty Fellowship (2002) - University of Michigan
- Rackham Faculty Fellowship (2001) - University of Michigan
Selected Publications
- Beke, T. (2019). Morphisms of context-free grammars.
- Beke, T. (2017). The Grothendieck ring of varieties and of the theory of algebraically closed fields. Journal of Pure and Applied Algebra, 221(2) 393–400.
- Beke, T., Rosicky, J. (2016). Cellular objects and Shelah’s singular compactness theorem. Journal of Pure and Applied Algebra, 220(5) 1813–1836.
- Beke, T., Rosicky, J. (2016). Elementary equivalences and accessible functors. arXiv preprint arXiv:1603.02500.
- Beke, T., Rosicky, J. (2012). Abstract elementary classes and accessible categories. Annals of Pure and Applied Logic, 163 2008-2017.
- Beke, T. (2011). Categorification, term rewriting and the Knuth-Bendix procedure. Journal of Pure and Applied Algebra, 215(5) 728-740.
- Beke, T., others, . (2011). Topological invariance of the combinatorial euler characteristic of tame spaces. Homology, Homotopy and Applications, 13(2) 165–174.
- Beke, T. (2011). Zeta functions of equivalence relations over finite fields. Finite Fields and their Applications, 17(1) 68-80.
- Beke, T. (2010). Fibrations of simplicial sets. Applied Categorical Structures, 18(5) 505-516.
- Beke, T. (2010). Topological invariance of the combinatorial Euler characteristic of o-minimal sets. Homology, Homotopy and Applications, 12 1-9.
- Beke, T. (2005). Isoperimetric inequalities and the Friedlander-Milnor conjecture. Journal fur die Reine und Angewandte Mathematik, (587) 27-47.
- Beke, T., Karazeris, P., Rosicky, J. (2005). When is flatness coherent? Communications in Algebra, 33(6) 1903-1912.
- Beke, T. (2004). Higher Cech theory. K-Theory, 32(4) 293-322.
- Beke, T. (2004). Theories of presheaf type. Journal of Symbolic Logic, 69(3) 923-934.
- Beke, T. (2001). Sheafifiable homotopy model categories, Part II. Journal of Pure and Applied Algebra, 164(3) 307-324.
- Beke, T. (2001). Simplicial torsors. Theory and Applications of Categories, 9 43-60.
- Beke, T. (2000). Sheafifiable homotopy model categories. Mathematical Proceedings of the Cambridge Philosophical Society, 129(3) 447-475.
- Beke, T. (1999). Operads from the viewpoint of categorical algebra. Contemp. Math., 227 29-47.
Selected Presentations
- - 16th International Congress of Logic, Prague, Czech Republic, 2019
- - Category Theory Seminar, CUNY, 2019
- - Accessible categories and their connections, University of Leeds, 2018
- - Logic Seminar, Harvard University, 2018
- - Toposes in Como, Universita degli Studi dell'Insubria, 2018
- - Algebra Seminar, University of Washington, Seattle, 2015
- - Logic Colloquium, Helsinki, 2015
- - Algebraic Stacks: Progress and Prospects, 2012 - Banff, Canada
- - Instituto Superior Tecnico, 2012 - Lisbon
- - New Developments in the Model Theory of Fields, 2009 - Durham, NH
- - DARPA IPTO Workshop, 2008 - Arlington, MA
- - Homotopy and Category Theory Conference, 2008 - Barcelona, Spain
- - Methods in Scientific Computing Seminar, 2008 - Stanford, CA
- - Topology Seminar, 2008 - Stanford, CA
- - Gerbes, Groupoids, and Quantum Field Theory, 2006 - Vienna, Austria
- - First Czech-Catalan Conference in Mathematics, 2005 - Prague, Czech Republic
- - AMS Special Session on Group Cohomology, 2003 - North Carolina
- - AMS Special Session on Algebraic Topology, 2002 - Ann Arbor, MI
- - EuroPhD Topology Conference, 2001 - Barcelona, Spain
- - Homotopy Theory Conference, 1998 - Oberwolfach, Germany
Selected Contracts, Fellowships, Grants and Sponsored Research
- QRM: Microstructural quantification and virtual reconstruction of polymer matrix composites within the Integrated Computational Materials Engineering (ICME) approach (2018), Grant - NSF
Maiaru, M., Stapleton, S., Liu, F., Beke, T. - Geometric proof and discovery: human and artificial intelligence (2016), Grant - John Templeton Foundation
Beke, T. - Probability Quantifiers over Finite Fields (2010), Grant - NSA-AMS
Beke, T. (Principal) - Enhanced Learning and Advice through Online Assignments (2008), Grant -
Levasseur, K. (Co-Principal) - Singularity detection, nonlinear filters, and OCR (2006), Grant -
Beke, T. - Faculty-Student Collaborative Research Grant (2005), Grant -
Intoccia, B. (Supporting), Percival, J. (Supporting) - Computational and Algorithmic Representation of Geometric Objects (2003), Grant - NSF-DARPA
Kormai, A. (Other)