Dr. Itamar Stein
I am a lecturer at the mathematics unit of SCE
My main research interest is the representation theory of semigroups and categories
I try to find a combinatorial description of fundamental invariants of category algebras - mainly homological invariants
Another research interest is ordinary group representation theory. I am interested in combinatorial interpretation of branching rules for finite groups
I have also studied string rewriting systems, a topic in theoretical computer science
I have earned my Ph.D. in mathematics at Bar-Ilan university. My advisor was Prof. Stuart Margolis
2013-2017 Ph.D. in Mathematics. Bar-Ilan University, Israel. Dissertation title: Quivers and global dimension of monoid algebras. Adviser: Prof. Margolis, S.
2009-2012 M.Sc. (Summa cum Laude) in Mathematics. Bar-Ilan University, Israel. Dissertation title: Graded monoids and graded monoid presentations. Adviser: Prof. Margolis S.
2004-2007 B.Sc. (Summa cum Laude) in Mathematics. Bar-Ilan University, Israel.
Representation theory: Algebras of groups, semigroups and categories. Combinatorial and homological properties.
Semigroup theory: Ehresmann semigroups and their corresponding categories.
Algebraic combinatorics: Representation theory of finite groups. Branching rules.
Theoretical computer science: String rewriting systems. Decision problems and algorithms
1. Representation theory of order-related monoids of partial functions as locally trivial category algebras. To appear in Algebras and Representation Theory.
2. The global dimension of the algebra of the monoid of all partial functions on an n-set as the algebra of the EI-category of epimorphisms between subsets. Journal of Pure and Applied Algebra 223.8 (2019): 3515-3536.
3. Algebras of Ehresmann semigroups and categories. Semigroup Forum. Springer US, 2017. p. 509-526.
4. The Littlewood-Richardson rule for wreath products with symmetric groups and the quiver of the category F≀FIn. Communications in Algebra 45.5 (2017): 2105-2126.
5. The representation theory of the monoid of all partial functions on a set and related monoids as EI-category algebras. Journal of Algebra 450 (2016): 549-569.
6. Reducing the gradedness problem of string rewriting systems to a termination problem. RAIRO-Theoretical Informatics and Applications 49.3 (2015): 233-254.