Dr Moty Katzman

School of Mathematical and Physical Sciences

Reader in Pure Mathematics

m.katzman@sheffield.ac.uk
J16, Hicks Building

Full contact details

Dr Moty Katzman
School of Mathematical and Physical Sciences
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 chomology 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

  • Katzman M & Sharp RY (2022) . Transactions of the American Mathematical Society, 375, 6621-6651.
  • 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 (2016) . 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 (2022) . Transactions of the American Mathematical Society, 375, 6621-6651.
  • Mycroft W, Katzman M, Tammas-Williams S, Hernandez-Nava E, Panoutsos G, Todd I & Kadirkamanathan V (2020) . Journal of Intelligent Manufacturing, 31(7), 1769-1781.
  • Boix A, Hernandez D, Kadyrsizova Z, Katzman M, Malec S, Robinson M, Schwede K, Smolkin D, Teixeira P & Witt E (2019) . Journal of Software for Algebra and Geometry, 9(2), 89-110.
  • Katzman M & Zhang W (2019) . Communications in Algebra, 47(6), 2450-2456.
  • Katzman M & Miranda-Neto CB (2019) . Journal of Algebra, 525, 19-41.
  • Alhazmy K & Katzman M (2019) . Journal of Algebra and its Applications, 18(11).
  • 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 (2016) . 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 & Schwede K (2012) . Journal of Symbolic Computation, 47(8), 996-1008.
  • Katzman M, Lyubeznik G & Zhang W (2012) . Bulletin of the London Mathematical Society, 44(6), 1116-1122.
  • Katzman M, Lyubeznik G & Zhang W (2011) . Proceedings of the American Mathematical Society, 139(12), 4193-4197.
  • Katzman M (2010) Some properties and applications of $F$-finite $F$-modules.
  • Katzman M (2010) . J LOND MATH SOC, 81, 589-607.
  • Katzman M (2010) A NON-FINITELY GENERATED ALGEBRA OF FROBENIUS MAPS. P AM MATH SOC, 138(7), 2381-2383.
  • 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) . COMMUN ALGEBRA, 33(4), 1141-1146.
  • Katzman M (2005) . J ALGEBR COMB, 22(3), 331-341.
  • 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.
  • Katzman M (2002) Bipartite graphs whose edge algebras are complete intersections. Journal of Algebra, 220 (1999) pp. 519-530.
  • Katzman M (2002) Finiteness of $bold{bigcup_e Ass F^e(M)}$ and its connections to tight closure. Illinois Journal of Mathematics 40 (1996) pp. 330-337.
  • 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).

Conference proceedings

  • 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) , arXiv.
  • Katzman M & Miranda-Neto CB (2018) , arXiv.
  • Alhazmy K & Katzman M (2017) , arXiv.
  • Katzman M, Murru S, Velez JD & Zhang W (2016) , arXiv.
  • Katzman M, Lyubeznik G & Zhang W (2014) , arXiv.
  • Boix AF & Katzman M (2013) , arXiv.
  • Katzman M, Schwede K, Singh AK & Zhang W (2013) , arXiv.
  • Katzman M & Schwede K (2011) , arXiv.
  • Katzman M, Lyubeznik G & Zhang W (2010) , arXiv.
  • Katzman M, Lyubeznik G & Zhang W (2010) , arXiv.
Research group

Pure Mathematics cluster

Grants

Past grants, as Principal Investigator

 
EPSRC
EPSRC
EPSRC

Past grants, as Coinvestigator

 
TailorableAdaptive Connected Digital Additive Manufacturing (TACDAM)
Teaching activities
MAS346Groups and Symmetry
MAS348Game Theory

Links