Professor Roozbeh Hazrat

Professor Roozbeh Hazrat

Professor,
Mathematics

Biography

Roozbeh Hazrat obtained his PhD in Pure Mathematics from the University of Bielefeld, Germany in 2002. He did research at the Australian National University, Max Planck Institute in Bonn and the City University of New York. He was a Reader (Associate Professor) in Pure Mathematics at Queen's University Belfast, United Kingdom where he worked for 8 years, before moving to University of Western Sydney in December 2011. In 2015 he was awarded a one year Fellowship for Experienced Researchers by Germany's Alexander von Humboldt Foundation.

This information has been contributed by Professor Hazrat.

Qualifications

  • PhD Bielefeld University

Interests

  • Algebraic K-theory and Noncommutative algebras

Organisational Unit (School / Division)

  • Mathematics

Contact

Email: R.Hazrat@westernsydney.edu.au
Phone: (02) 9685 9054
Mobile:
Location: EN.1.41
Parramatta
Website:

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Teaching

Current Teaching Areas

  • 301031 Computer Algebra

Publications

Books

  • Hazrat, R. (2016), 'Graded Rings and Graded Grothendieck Groups', : Cambridge University Press 9781316619582.
  • Hazrat, R. (2015), 'Mathematica?: A Problem-centered Approach', : Springer 9783319275840.
  • Hazrat, R. (2010), 'Mathematica: A Problem-Centered Approach', : Springer-Verlag 978-1-84996-250-6.

Journal Articles

  • Hazrat, R. and Vas, L. (2018), 'Baer and Baer *-ring characterizations of Leavitt path algebras', Journal of Pure and Applied Algebra, vol 222, no 1 , pp 39 - 60.
  • Hazrat, R., Rangaswamy, K. and Srivastava, A. (2018), 'Leavitt path algebras : graded direct-finiteness and graded S-injective simple modules', Journal of Algebra, vol 503 , pp 299 - 328.
  • Hazrat, R. and Li, H. (2018), 'Graded Steinberg algebras and partial actions', Journal of Pure and Applied Algebra, vol 222, no 12 , pp 3946 - 3967.
  • Ara, P., Hazrat, R., Li, H. and Sims, A. (2018), 'Graded Steinberg algebras and their representations', Algebra and Number Theory, vol 12, no 1 , pp 131 - 172.
  • Hazrat, R., Vavilov, N. and Zhang, Z. (2017), 'The commutators of classical groups', Journal of Mathematical Sciences, vol 222, no 4 , pp 466 - 515.
  • Hazrat, R. and Preusser, R. (2017), 'Applications of normal forms for weighted Leavitt path algebras : simple rings and domains', Algebras and Representation Theory, vol 20, no 5 , pp 1061 - 1083.
  • Hazrat, R., Vavilov, N. and Zhang, Z. (2017), 'Multiple commutator formulas for unitary groups', Israel Journal of Mathematics, vol 219, no 1 , pp 287 - 330.
  • Ara, P., Bosa, J., Hazrat, R. and Sims, A. (2017), 'Reconstruction of graded groupoids from graded Steinberg algebras', Forum Mathematicum, vol 29, no 5 , pp 1023 - 1037.
  • Hazrat, R. and Rangaswamy, K. (2016), 'On graded irreducible representations of Leavitt path algebras', Journal of Algebra, vol 450 , pp 458 - 486.
  • Hazrat, R., Vavilov, N. and Zhang, Z. (2016), 'Generation of relative commutator subgroups in Chevalley groups', Proceedings of the Edinburgh Mathematical Society, vol 59, no 2 , pp 393 - 410.
  • Hazrat, R. and Huang, J. (2016), 'Recollements, sinks elimination, and Leavitt path algebras', Archiv der Mathematik, vol 107, no 6 , pp 589 - 594.
  • Hazrat, R. (2014), 'Leavitt path algebras are graded von Neumann regular rings', Journal of Algebra, vol 401 , pp 220 - 233.
  • Hazrat, R., Mahdavi-Hezavehi, M. and Motiee, M. (2014), 'Multiplicative groups of division rings', Mathematical Proceedings of Royal Irish Academy, vol 114, no 1 , pp 37 - 114.
  • Hazrat, R., Stepanov, A., Vavilov, N. and Zhang, Z. (2014), 'The yoga of commutators : further applications', Journal of Mathematical Sciences, vol 200, no 6 , pp 742 - 768.
  • Hazrat, R. (2013), 'The graded structure of Leavitt path algebras', Israel Journal of Mathematics, vol 195, no 2 , pp 833 - 895.
  • Hazrat, R. and Zhang, Z. (2013), 'Multiple commutator formulas', Israel Journal of Mathematics, vol 195, no 1 , pp 481 - 505.
  • Hazrat, R. (2013), 'The graded Grothendieck group and the classication of Leavitt path algebras', Mathematische Annalen, vol 355, no 1 , pp 273 - 325.
  • Hazrat, R. and Hoobler, R. (2013), 'K-theory of Azumaya algebras over schemes', Communications in Algebra, vol 41, no 4 , pp 1268 - 1277.
  • Hazrat, R. (2013), 'A note on the isomorphism conjectures for Leavitt path algebras', Journal of Algebra, vol 375 , pp 33 - 40.
  • Hazrat, R., Vavilov, N. and Zhang, Z. (2013), 'Relative commutator calculus in Chevalley groups', Journal of Algebra, vol 385 , pp 262 - 293.
  • Hazrat, R., Stepanov, A., Vavilov, N. and Zhang, Z. (2013), 'Commutator width in Chevalley groups', Note di Matematica, vol 33, no 1 , pp 139 - 170.
  • Hazrat, R. (2013), 'The dynamics of Leavitt path algebras', Journal of Algebra, vol 384 , pp 242 - 266.
  • Hazrat, R. and Huttemann, T. (2013), 'On Quillen's calculation of graded K-theory', Journal of Homotopy and Related Structures, vol 8, no 2 , pp 231 - 238.
  • Hazrat, R. (2012), 'Stability of unitary SK1 of Azumaya algebras', Archiv der Mathematik, vol 98, no 1 , pp 19 - 23.
  • Hazrat, R. and Wadsworth, A. (2012), 'Homogeneous SK1 of simple graded algebras', New York Journal of Mathematics, vol 18 , pp 315 - 336.
  • Hazrat, R., Stepanov, A., Vavilov, N. and Zhang, Z. (2011), 'The yoga of commutators', Journal of Mathematical Sciences, vol 179, no 6 , pp 662 - 678.
  • Hazrat, R., Zhang, Z. and Vavilov, N. (2011), 'Relative unitary commutator calculus, and applications', Journal of Algebra, vol 343, no 1 , pp 107 - 137.
  • Hazrat, R. and Wadsworth, A. (2011), 'Unitary and graded SK1 of division algebras', London Mathematical Society. Proceedings, vol 103, no 3 , pp 508 - 534.
  • Hazrat, R. and Wadsworth, A. (2011), 'SK1 of graded division algebras', Israel Journal of Mathematics, vol 183, no 1 , pp 117 - 163.
  • Hazrat, R. and Zhang, Z. (2011), 'Generalized commutator formulas', Communications in Algebra, vol 39, no 4 , pp 1441 - 14564.
  • Hazrat, R. (2010), 'SK1 of Azumaya algebras over Hensel pairs', Mathematische Zeitschrift, vol 264, no 2 , pp 295 - 299.
  • Hazrat, R. and Millar, J. (2010), 'On graded central simple algebras', Homotopy and related structures, vol 5, no 1 , pp 113 - 124.
  • Hazrat, R., Petrov, V. and Vavilov, N. (2010), 'Relative subgroups in Cheavelly groups', Journal of K-Theory, vol 5, no 3 , pp 603 - 618.
  • Hazrat, R. and Millar, J. (2010), 'A note on K-theory of Azumaya algebras', Communications in Algebra, vol 38, no 3 , pp 919 - 926.
  • Hazrat, R. and Wadsworth, A. (2009), 'On maximal subgroups of the multiplicative group of a division algebra', Journal of Algebra, vol 322, no 7 , pp 2528 - 2543.
  • Hazrat, R. and Vavilov, N. (2009), 'Bak's work on K-theory of rings', Journal of K-Theory, vol 4, no 1 , pp 1 - 65.
  • Hazrat, R., Bak, A. and Vavilov, N. (2009), 'Localization-completion strikes again : relative K1 is nilpotent by abelian', Journal of Pure and Applied Algebra, vol 213, no 6 , pp 1075 - 1085.
  • Hazrat, R. (2008), 'On the first Galois cohomology group of the algebraic group SL1(D)', Communications in Algebra, vol 36, no 2 , pp 381 - 387.
  • Hazrat, R. and Wadsworth, A. (2007), 'Nontriviality of certain quotients of K1 groups of division algebras', Journal of Algebra, vol 312, no 1 , pp 354 - 361.
  • Hazrat, R. (2006), 'Reduced K-theory for Azumaya algebras', Journal of Algebra, vol 305, no 2 , pp 687 - 703.
  • Hazrat, R. and Wilson, R. (2006), 'A decomposition theorem for CK1 of central simple algebras', Communications in Algebra, vol 34, no 12 , pp 4573 - 4578.
  • Hazrat, R. and Vishne, U. (2005), 'Triviality of the functor Coker(K1(F) ! K1(D)) for division algebras', Communications in Algebra, vol 33, no 5 , pp 1427 - 1435.
  • Hazrat, R. and Vavilov, N. (2003), 'K1 of Chevalley groups are nilpotent', Journal of Pure and Appl. Algebra, vol 179, no 1-2 , pp 99 - 116.
  • Hazrat, R. (2002), 'On central series of the multiplicative group of division rings', Algebra Colloquium, vol 9, no 1 , pp 99 - 106.
  • Hazrat, R. (2002), 'Wedderburn's factorization theorem, Application to reduced K-theory', Proceedings of the American Mathematical Society, vol 130, no 2 , pp 311 - 314.
  • Hazrat, R. (2002), 'Dimension theory and nonstable K1 of quadratic modules', K-Theory, vol 27, no 4 , pp 293 - 328.
  • Hazrat, R. (2001), 'SK1-like functors for division algebras', Journal of Algebra, vol 239, no 2 , pp 573 - 588.

Current Projects

Title: Graded K-theory as invariants for path algebras
Funder:
  • Australian Research Council (ACRG)
Western Researchers: Roozbeh Hazrat
Years: 2016-06-30 - 2019-07-31
ID: P00022561

Previous Projects

Title: RBA Mathematica Training - Stage 2- Software Coding, Implementation & Training + 2017 Mathematic Training Courses
Funder:
  • Reserve Bank of Australia
Western Researchers:
Years: 2014-03-10 - 2015-01-13
ID: P00024306
Title: Groupoids as bridges between algebra and analysis [via UoW]
Funder:
  • Australian Research Council (ACRG)
Western Researchers: Roozbeh Hazrat
Years: 2015-02-18 - 2017-12-31
ID: P00022485

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