**Tibor Beke**Associate Professor

**College**College of Sciences**Department**Mathematical Science**Phone**(978) 934-2445**Email**Tibor_Beke@uml.edu

## 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

## Awards and Honors

- Rackham Faculty Fellowship
*- University of Michigan* - 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*

## Publications

**Beke, T.**(2017) "The Grothendieck ring of varieties and of the theory of algebraically closed fields,"*Journal of Pure and Applied Algebra*221:2 pp. 393–400**Beke, T.**, Rosicky, J. (2016) "Cellular objects and Shelah’s singular compactness theorem,"*Journal of Pure and Applied Algebra*220:5 pp. 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: pp. 2008-2017**Beke, T.**(2011) "Categorification, term rewriting and the Knuth-Bendix procedure,"*Journal of Pure and Applied Algebra*215:5 pp. 728-740**Beke, T.**, others, . (2011) "Topological invariance of the combinatorial euler characteristic of tame spaces,"*Homology, Homotopy and Applications*13:2 pp. 165–174**Beke, T.**(2011) "Zeta functions of equivalence relations over finite fields,"*Finite Fields and their Applications*17:1 pp. 68-80**Beke, T.**(2010) "Fibrations of simplicial sets,"*Applied Categorical Structures*18:5 pp. 505-516**Beke, T.**(2010) "Topological invariance of the combinatorial Euler characteristic of o-minimal sets,"*Homology, Homotopy and Applications*12: pp. 1-9**Beke, T.**(2005) "Isoperimetric inequalities and the Friedlander-Milnor conjecture,"*Journal fur die Reine und Angewandte Mathematik*587 pp. 27-47**Beke, T.**, Karazeris, P., Rosicky, J. (2005) "When is flatness coherent?,"*Communications in Algebra*33:6 pp. 1903-1912**Beke, T.**(2004) "Higher Cech theory,"*K-Theory*32:4 pp. 293-322**Beke, T.**(2004) "Theories of presheaf type,"*Journal of Symbolic Logic*69:3 pp. 923-934**Beke, T.**(2001) "Sheafifiable homotopy model categories, Part II,"*Journal of Pure and Applied Algebra*164:3 pp. 307-324**Beke, T.**(2001) "Simplicial torsors,"*Theory and Applications of Categories*9: pp. 43-60**Beke, T.**(2000) "Sheafifiable homotopy model categories,"*Mathematical Proceedings of the Cambridge Philosophical Society*129:3 pp. 447-475**Beke, T.**(1999) "Operads from the viewpoint of categorical algebra,"*Contemp. Math.*227: pp. 29-47

## Presentations

*- 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

## Contracts, Fellowships, Grants and Sponsored Research

- 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)