# Dr Moty Katzman

## Research:

 Interests: Commutative algebra Research group: Algebra Publications: Preprint page, ArXiv, MathSciNet

### Grants

 Current grants, as Coinvestigator Tailorable Adaptive Connected Digital Additive Manufacturing (TACDAM) INO 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

## Roles:

Director of Computing

## Biography:

Been there, done that.

## 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 $x\mapsto x^p$. 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.