Dr Moty Katzman
Director of Computing
Been there, done that.
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
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