Dr Moty Katzman

School of Mathematics and Statistics

Reader

Director of Computing

M.Katzman@shef.ac.uk
+44 114 222 3710

Full contact details

Dr Moty Katzman
School of Mathematics and Statistics
J16
Hicks Building
Hounsfield Road
Sheffield
S3 7RH
Research interests

Dr Katzman's research is in the area of commutative algebra. Specifically, he is interested in the following.
 

Characteristic p methods

Certain theorems in algebra can be proved by showing that they hold in positive characteristic, and in characteristic p one has extra structure given by the Frobenius map x↦xp. There are several tools, notably tight closure, which exploit this extra structure to prove some remarkable theorems.
 

Local cohomology modules

This modules derive their importance partly from the fact that they detect interesting properties of modules over commutative rings (e.g., depth.) Unfortunately, these objects tend to be very big are rather mysterious. It is very difficult to describe them in any detail even in seemingly easy cases. Dr. Katzman has recently been producing both examples showing that these objects are more complicated than previously conjectured but also instances where they can be understood fairly well.
 

Combinatorial aspects

One of the simplest family of modules imaginable are monomial ideals in polynomial rings and, perhaps surprisingly, these objects have a very rich structure, in some sense richer than the structure of graphs. Dr Katzman has recently been studying certain monomial ideals associated with graphs a discovering some surprising connections between the algebraic and combinatorial properties of these objects.

Publications

Show: Featured publications All publications

Journal articles

All publications

Journal articles

Conference proceedings papers

  • Katzman M (2006) The support of top graded local cohomology modules. Commutative Algebra: Geometric, Homological, Combinatorial and Computational Aspects, Vol. 244 (pp 165-174) RIS download Bibtex download
Research group

Algebra and Algebraic Geometry

Grants

Past grants, as Principal Investigator

Common threads in the theories of Local Cohomology, D-modules and Tight Closure and their interactions EPSRC
Prime characteristic methods in commutative algebra EPSRC
Graded components of local cohomology modules EPSRC

Past grants, as Coinvestigator

Tailorable Adaptive Connected Digital Additive Manufacturing (TACDAM)
Teaching activities
MAS346 Groups and Symmetry
MAS348 Game Theory