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. (with Adinayev, Arthur) Diamond Subgraphs in the Reduction Graph of a One-Rule String Rewriting System. Fundamenta Informaticae 178.3 (2021): 173-185
2. Representation theory of order-related monoids of partial functions as locally trivial category algebras. Algebr. Represent. Theory 23 (2020), no. 4, 1543--1567.
3. 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. J. Pure Appl. Algebra 223 (2019), no. 8, 3515-3536.
4. Algebras of Ehresmann semigroups and categories. Semigroup Forum 95 (2017), no. 3, 509-526.
5. 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.
6. 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.
7. Reducing the gradedness problem of string rewriting systems to a termination problem. RAIRO-Theoretical Informatics and Applications 49.3 (2015): 233-254.