Katzman, Moty, Dr

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

Featured publications

Journal articles

Katzman M & Zhang W (2018) . International Mathematics Research Notices, 2018(23), 7137-7155.
Katzman M, Ma L, Smirnov I & Zhang W (2018) . Transactions of the American Mathematical Society, 370, 8551-8580.
Katzman M, Murru S, Velez JD & Zhang W (2017) . Journal of Algebra.
Katzman M, Lyubeznik G & Zhang W (2015) . Proceedings of the American Mathematical Society, 144(3), 955-962.
Katzman M, Schwede K, Singh AK & Zhang W (2014) . Mathematical Proceedings of the Cambridge Philosophical Society, 157(1), 151-167.

All publications

Journal articles

Katzman M & Sharp RY (2020) Lyubeznik numbers, $F$-modules and modules of generalized fractions.
Katzman M, Mycroft W, Tammas-Williams S, Hernandez-Nava E, Panoutsos G, Todd I & Kadirkamanathan V (2020) . Journal of Intelligent Manufacturing.
Boix AF, Hernandez DJ, Kadyrsizova Z, Katzman M, Malec S, Robinson M, Schwede K, Smolkin D, Teixeira P & Witt EE (2019) . Journal of Software for Algebra and Geometry, 9(2), 89-110.
Alhazmy K & Katzman M (2019) . Journal of Algebra and its Applications.
Katzman M & Miranda-Neto CB (2019) . Journal of Algebra, 525, 19-41.
Katzman M & Zhang W (2019) . Communications in Algebra, 47(6), 2450-2456.
Katzman M & Zhang W (2018) . International Mathematics Research Notices, 2018(23), 7137-7155.
Katzman M, Ma L, Smirnov I & Zhang W (2018) . Transactions of the American Mathematical Society, 370, 8551-8580.
Katzman M, Murru S, Velez JD & Zhang W (2017) . Journal of Algebra.
Katzman M, Lyubeznik G & Zhang W (2015) . Proceedings of the American Mathematical Society, 144(3), 955-962.
Boix AF & Katzman M (2014) . Archiv der Mathematik, 103(5), 421-433.
Katzman M, Schwede K, Singh AK & Zhang W (2014) . Mathematical Proceedings of the Cambridge Philosophical Society, 157(1), 151-167.
Katzman M & Zhang W (2014) . Transactions of the American Mathematical Society, 7(366), 3519-3533.
Katzman M & Zhang W (2014) . Journal of Symbolic Computation, 60, 29-46.
Katzman M, Lyubeznik G & Zhang W (2012) . Bulletin of the London Mathematical Society, 44(6), 1116-1122.
Katzman M & Schwede K (2012) . Journal of Symbolic Computation, 47(8), 996-1008.
Katzman M, Lyubeznik G & Zhang W (2011) . Proceedings of the American Mathematical Society, 139(12), 4193-4197.
Katzman M (2010) A NON-FINITELY GENERATED ALGEBRA OF FROBENIUS MAPS. P AM MATH SOC, 138(7), 2381-2383.
Katzman M (2010) . J LOND MATH SOC, 81, 589-607.
Katzman M, Lyubeznik G & Zhang WL (2009) . J ALGEBRA, 322(9), 3238-3247.
Katzman M (2008) . COMPOS MATH, 144(4), 933-948.
Katzman M (2008) . COMMUN ALGEBRA, 36(1), 104-111.
Huneke C, Katzman M, Sharp RY & Yao Y (2006) . J ALGEBRA, 305(1), 516-539.
Katzman M (2006) . J COMB THEORY A, 113(3), 435-454.
Brenner H & Katzman M (2006) On the arithmetic of tight closure. J AM MATH SOC, 19(3), 659-672.
Katzman M & Sharp RY (2006) . J ALGEBRA, 295(1), 231-246.
Katzman M (2005) . J ALGEBR COMB, 22(3), 331-341.
Katzman M (2005) . COMMUN ALGEBRA, 33(4), 1141-1146.
Katzman M & Sharp RY (2003) Some properties of top graded local cohomology modules. J ALGEBRA, 259(2), 599-612.
Katzman M (2002) An example of an infinite set of associated primes of a local cohomology module. J ALGEBRA, 252(1), 161-166.
Brodmann MP, Katzman M & Sharp RY (2002) Associated primes of graded components of local cohomology modules. T AM MATH SOC, 354(11), 4261-4283.
Aberbach I, Katzman M & MacCrimmon B (1998) . Journal of Algebra, 204(1), 281-285.
Katzman M (1998) . Journal of Algebra, 203(1), 211-225.
Katzman M (1997) . Journal of Algebra, 191(2), 510-517.
Katzman M (1996) . Illinois Journal of Mathematics, 40(3), 453-463.
Katzman M () Some properties and applications of $F$-finite $F$-modules.
Katzman M () Finiteness of $bold{bigcup_e Ass F^e(M)}$ and its connections to tight closure. Illinois Journal of Mathematics 40 (1996) pp. 330-337.
Katzman M () Bipartite graphs whose edge algebras are complete intersections. Journal of Algebra, 220 (1999) pp. 519-530.

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)

Preprints

Katzman M & Sharp RY (2020) , arXiv.
Boix AF, Hernández DJ, Kadyrsizova Z, Katzman M, Malec S, Robinson M, Schwede K, Smolkin D, Teixeira P & Witt EE (2018) The TestIdeals package for Macaulay2, arXiv.
Katzman M & Miranda-Neto CB (2018) Strong $F$-regularity and generating morphisms of local cohomology modules, arXiv.
Alhazmy K & Katzman M (2017) FFRT Properties of hypersurfaces and their F-signature, arXiv.
Katzman M, Murru S, Velez JD & Zhang W (2016) Global parameter test ideals, arXiv.
Katzman M, Lyubeznik G & Zhang W (2014) An extension of a theorem of Hartshorne, arXiv.
Boix AF & Katzman M (2013) An algorithm for producing F-pure ideals, arXiv.
Katzman M, Schwede K, Singh AK & Zhang W (2013) Rings of Frobenius operators, arXiv.
Katzman M & Schwede K (2011) An algorithm for computing compatibly Frobenius split subvarieties, arXiv.
Katzman M, Lyubeznik G & Zhang W (2010) Two interesting examples of $mathcal{D}$-modules in characteristic $p>0$, arXiv.
Katzman M, Lyubeznik G & Zhang W (2010) An upper bound on the number of F-jumping coefficients of a principal ideal, arXiv.

Research group

Algebra and Algebraic Geometry

Grants

Past grants, as Principal Investigator
	EPSRC
	EPSRC
	EPSRC
Past grants, as Coinvestigator
Tailorable	Adaptive Connected Digital Additive Manufacturing (TACDAM)

Teaching activities

MAS346	Groups and Symmetry
MAS348	Game Theory

91ֱ��

School of Mathematical and Physical Sciences

School of Mathematical and Physical Sciences

Dr Moty Katzman

Characteristic p methods

Local cohomology modules

Combinatorial aspects

Featured publications

Journal articles

All publications

Journal articles

Conference proceedings papers

Preprints

Past grants, as Principal Investigator

Past grants, as Coinvestigator

91ֱ��

School of Mathematical and Physical Sciences

School of Mathematical and Physical Sciences

Dr Moty Katzman

Characteristic p methods

Local cohomology modules

Combinatorial aspects

Featured publications

Journal articles

All publications

Journal articles

Conference proceedings papers

Preprints

Past grants, as Principal Investigator

Past grants, as Coinvestigator

Links