Dr. Allen Herman

Professor,
Department of Mathematics and Statistics,
University of Regina
Regina, Canada S4S 0A2

Curriculum Vitae

Positions held:
Professor of Mathematics, University of Regina, 2009-present.
Associate Professor of Mathematics, University of Regina, 2002 - 2009.
Assistant Professor of Mathematics, University of Regina, 1997 - 2002.
Lecturer in Mathematics, University of Regina, 1995 - 1997.

Visiting Researcher, University of St. Andrews, Fall/Winter 2014/15.
Visiting Researcher, University of Murcia, Spring 2007.
Visiting Researcher, University of Florida, Spring 2003.

Education:
Ph.D. in Mathematical Sciences, 1995 (Alberta), M.Sc. in Mathematics, 1992 (Alberta), B.Ed. 1988 (Lethbridge).

Research Interests: Representation Theory, Algebraic Combinatorics, and Computational Algebra.

Publications:

• 41. Alyeah Alsairafi and Allen Herman, Symmetric association schemes arising from abstract regular polytopes, Contributions to Discrete Mathematics, 16 (1), (2021), 98-115. (Open access)
• 40. Allen Herman, Schur indices for noncommutative reality-based algebras with two nonreal elements, Journal of Algebra and its Applications, 20 (10), (2021), 2150177. (arXiv:1905.00445v3 [math.RA])
• 39. Allen Herman, A survey of semisimple Q-algebras in algebraic combinatorics, Indian Journal of Pure and Applied Mathematics, doi.org/10.1007/s13226-021-00181-x (Open access) -accepted April 2020.
• 38. Allen Herman and Gurmail Singh, Extending table algebras to Hopf algebras, International Electronic Journal of Algebra, 26 (2019), 13-28. (Open access)
• 37. Fernando Szechtman, Momita Shau, and Allen Herman, Weil representations of unitary groups over ramified extensions of finite local rings of odd nilpotency length, Communications in Algebra, 47 (8), (2019), 3007-3024. (arXiv:1801.10268 [math.RT])
• 36. Thomas Guedenon and Allen Herman, A Brauer-Clifford-Long group for the category of dyslectic Hopf Yetter-Drinfel'd (S,H)-module algebras, Theory and Applications of Categories, 33 (9), (2018), 216-252. (Open access)
• 35. Allen Herman and Gurmail Singh, Orders of torsion units of integral reality-based algebras with rational multiplicities, Journal of Algebra and its Applications, 17 (1), (2018), 1850015 (12 pgs).
• 34. Andreas Bachle, Allen Herman, Alexander Konovalov, Leo Margolis, and Gurmail Singh, The status of the Zassenhaus conjecture for small groups, Experimental Mathematics, 27 (4), (2018), 431-436. (arXiv:1609.00042 [math.RA])
• 33. Allen Herman, Mikhail Muzychuk, and Bangteng Xu, Non-commutative reality-based algebras of rank 6, Communications in Algebra, 46 (1), (2017), 90-113. (arXiv:1608.08463 [math.RA])
• 32. Allen Herman, Mitsugu Hirasaka, and Semin Oh, Zeta fuctions for tensor products of coprime integral adjacency algebras of association schemes, Communications in Algebra, 45 (11), (2017), 4896-4905. (arXiv:1508.07287v2 [math:RA])
• 31. Allen Herman, Mikhail Muzychuk, and Bangteng Xu, The recognition problem for table algebras and reality-based algebras, Journal of Algebra, 479, (2017), 173-191. (arXiv:1506.05476v2 [math.RA]) 31a. Corrigendum, Journal of Algebra 525 (2019), 589-590.
• 30. Fernando Szechtman, Allen Herman and Mohammad A. Izadi, Representations of McLain Groups, Journal of Algebra, 474 (2017), 288-328. (arXiv:1506.06184v12 [math.RT])
• 29. Allen Herman and Gurmail Singh, Central torsion units of integral reality-based algebras with a positive degree map, International Electronic Journal of Algebra, 21 (2017), 121-126. (Open access)
• 28. Allen Herman and Gurmail Singh, Revisiting the Zassenhaus Conjecture on torsion units for the integral group rings of small groups, Proceedings. Mathematical Sciences. Indian Academy of Sciences, 125 (2), (2015), 167-172.
• 27. Allen Herman and Gurmail Singh, Torsion units of integral C-algebras, JP Journal of Algebra, Number Theory, and Applications, 36 (2), (2015), 141-155.
• 26. Allen Herman and Gurmail Singh, On the Torsion Units of Integral Adjacency Algebras of Finite Association Schemes, Algebra, Vol. 2014, 2014, Article ID 842378, 5 pages. (Open Access)
• 25. James Cruikshank, Allen Herman, Rachael Quinlan, and Fernando Szechtman, Unitary groups over local rings, Journal of Algebra and its Applications, 13 (2), (2014), 1350093.
• 24. Allen Herman and Fernando Szechtman, The Weil representation of a unitary group associated to a ramified quadratic extension of a finite local ring, Journal of Algebra, 392 (2013), 158-184.
• 23. Thomas Guedenon and Allen Herman, The Brauer-Clifford group for (S,H)-Azumaya algebras over a commutative ring, Algebras and Representation Theory, 16 (1), (2013), 101-127.
• 22. Allen Herman and Dipra Mitra, Equivalence and the Brauer-Clifford group for $G$-algebras over commutative rings, Communications in Algebra, 39 (10), (2011), 3905-3915.
• 21. Allen Herman and Amir Rahnamai Barghi, Schur indices of association schemes, Journal of Pure and Applied Algebra, 215 (2011), 1015-1023.
• 20. Allen Herman, Gabriela Olteanu, and Angel del Rio, The gap between the Schur group and the subgroup generated by cyclic cyclotomic algebras, Israel Journal of Mathematics, 176 (2010), 401-417.
• 19. Allen Herman, Invariants for Equivalence of Central Simple G-algebras, Special Issue on Groups, Rings, Lie, and Hopf Algebras, Acta Applicanda Mathematicae, 108 (2009), 57-71.
• 18. Allen Herman, Gabriela Olteanu, and Angel del Rio, The Schur Group of an Abelian Number Field, Journal of Pure and Applied Algebra, 213 (2009), 22-33.
• 17. Allen Herman, Gabriela Olteanu, and Angel del Rio, Ring isomorphism of cyclic cyclotomic algebras, Algebras and Representation Theory, 12 (2009), 365-370.
• 16. Allen Herman and Amir Rahnamai Barghi, The character values of commutative quasi-thin schemes, Linear Algebra and its Applications, 429 (11-12), (2008), 2663-2669.
• 15. Saieed Akbari and Allen Herman, Commuting decompositions of complete graphs, Journal of Combinatorial Designs, 15 (2), (2007), 133-142.
• 14. Allen Herman and Yuanlin Li, Trivial torsion units in G-adapted group rings, Journal of Algebra and its Applications, 5 (6), (2006), 781-791.
• 13. Shaun M. Fallat, Michael I. Gekhtman, Allen Herman, and Charles R. Johnson,Compressions of totally positive matrices, SIAM Journal on Matrix Analysis and Applications, , 28(1), (2006), 68-80.
• 12. Allen Herman and Yuanlin Li, Class preserving automorphisms of Blackburn groups, Journal of the Australian Mathematical Society, 80(3), (2006), 631-635.
• 11. Allen Herman, Clifford classes of primitive central simple G-algebras, Journal of Algebra and its Applications, 5(2), (2006), 129-144.
• 10. Allen Herman and Yuanlin Li, Trivial units for group rings over rings of algebraic integers, Proceedings of the American Mathematical Society, 134(3),(2005),631-635.
• 9. Allen Herman, Yuanlin Li, and M.M. Parmenter, Trivial units for group rings with G-adapted coefficient rings, Canadian Mathematical Bulletin, 48 (1), (2005), 80-89.
• 8. Allen Herman and Barry Monson, On the real Schur indices associated with infinite string Coxeter groups, in Proceedings of Finite Groups 2003, Proceedings of the Gainesville Conference on Finite Groups, March 6-12, 2003, (C.Y. Ho, P. Sin, P.H. Tiep, and A. Turull, eds.), pp. 185-194, Walter de Gruyter, 2004.
• 7. Allen Herman, Clifford theory with Schur indices in projective representation theory, Communications in Algebra, 32(10), (2004), 3797-3806.
• 6. Allen Herman, Using G-algebras for Schur index computation, Journal of Algebra, 260, (2003), 463-475.
• 5. Allen Herman, Using character correspondences for Schur index computations, Journal of Algebra, 259, (2003), 353-360.
• 4. Ulrich Dempwolff, J. Chris Fisher, and Allen Herman, Semilinear transformations over finite fields are Frobenius maps, Glasgow Mathematical Journal, 42, (2000), 289-295.
• 3. Allen Herman, On the automorphism groups of rational group algebras of metacyclic groups, Communications in Algebra, 25(7), (1997), 2085-2098.
• 2. Allen Herman, A constructive Brauer-Witt theorem for certain solvable groups, Canadian Journal of Mathematics, 48, (1996), 1196-1209.
• 1. Allen W. Herman, Metabelian groups and the Brauer-Witt theorem, Communications in Algebra, 23(11), (1995), 4073-4086.

Computer Programs for use in the Public Domain

• ZCTU, by A. Bachle, A. Herman, A. Konovalov, L. Margolis, and G. Singh. Supplement to GAP package HeLP which determines critical cases for the Zassenhaus conjecture among groups of order n, released August 31, 2016.
  (http://github.com/drallenherman/ZCTU-Source-Code)
  
• wedderga 4.10.1: Wedderburn decomposition of group algebras, by G. Kaur Bakshi, O. Broche Cristo, A. Herman, A. Konovalov, S. Maheshwary, G. Olteanu, A. Olivieri, A. del Rio, I. van Gelder. Included as a package of GAP 4.11.1 , released May 2020.
  (http://www.gap-system.org/Packages/wedderga.html)

Recent Conference Presentations (last 6 years):

• The results of a search for small noncyclotomic association schemes, Algebraic Graph Theory Seminar, University of Waterloo, November 1, 2021. (Online)
• Semisimple Q-algebras in Algebraic Combinatorics, ICTS Thematic Program on ``Group Algbras, Representations, and Computation'', Tata Institute, Bangalore, India, October 19 to 23, 2019.
• On the Terwilliger algebras of regular tournaments, Special Session on Special Functions and Orthogonal Polynomials, AMS Central Sectional Meeting, Madison, WI, September 14-15, 2019.
• Rationality for irreducible representations of association schemes of rank 6 and 7, 9th Slovenian International Conference on Graph Theory, Bled, Slovenia, June 23 ot 29, 2019.
• From association schemes to Hopf algebras, 2018 Prairie Discrete Mathematics Workshop, University of Brandon, June 13, 2018.
• How to find Hopf algebra comultiplications on Bose-Mesner algebras of association schemes, AMS Spring Central Sectional Meeting, Ohio State University, Columbus, OH, March 17, 2018.
• The recognition problem for table algebras, AMS Fall Western Fall Sectional Meeting, University of Denver, October 8, 2016.
• Unitary groups over $p$-adic integers - the ramified case, CMS Summer Meeting, Edmonton, June 2016.
• Torsion Units of Integral Table Algebras and RBAs, in Special Session on Algebraic Methods Common to Association Schemes, Hopf Algebras, Tensor Categories, Finite Geometry, and Related Areas, AMS Central Fall Sectional Meeting, Loyola University, Chicago, IL, October 3, 2015.
• The Wedderburn decomposition of the rational adjacency algebras of association schemes, PNU Math Forum 2015, Pusan National University, Busan, Korea, July 17, 2015.
• Torsion Units of ZS, 71st KPPY Combinatorics Seminar, Yeungnam University, Daegu, Korea, July 11, 2015.
• Calculating fusions of association schemes,8th Slovenian Conference on Graph Theory in Kranjska Gora, Kranjska Gora, Slovenia, June 23, 2015.

  External Research Funding:

  • Mitacs Globalink Summer Student Fellowship, $7500, 2018.
  • NSERC Discovery Grant, $16000 per annum, 2017 - 2022.
  • NSERC Discovery Grant, $12000 per annum, 2012 - 2017.
  • Mitacs Globalink Summer Student Fellowship, $7500, 2011.
  • Visiting Research Grant, Fundacion Seneca, Region de Murcia, Spain, 10300 Euros, 2007.
  • NSERC Discovery Grant, $10000 per annum, 2007 - 2012.
  • NSERC Discovery Grant, $11000 per annum, 2002 - 2007.
  • NSERC Individual Research Grant, $9000 per annum, 1997 to 2001.

  HQP Training:

  • Neha Joshi, PhD Mathematis, University of Regina, in progress (Co-supervisor)
  • Roghayeh Maleki, PhD Mathematics, University of Regina, in progress (Supervisor)
  • Roqayia Shalabi, PhD Mathematics, University of Regina, in progress (Co-supervisor)
  • 10. Alyeah Alsairafi, PhD Mathematics, University of Regina, 2020. (Co-supervisor)
  • 9. Moumita Shau, PhD Mathematics, University of Regina, 2019. (Co-supervisor)
  • 8. Mehwish Mohammad Anwar, NSERC USRA, University of Regina, Summer 2019. (Supervisor)
  • 7. Abhay Sobhanan, MITACS Globalink Summer Student Project, 2018. (Supervisor)
  • 6. Gurmail Singh, PhD Mathematics, University of Regina, 2015. (Co-supervisor)
  • 5. Sourav Sikdar, MITACS Globalink Summer Student Project, 2011. (Supervisor)
  • 4. Thomas Guedenon, Postdoctoral Fellow, University of Regina, 2010-2011. (Supervisor)
  • 3. Dipra Mitra, PhD Mathematics, University of Regina, 2010. (Co-supervisor)
  • 2. Andrew Douglas, Postdoctoral Fellow, University of Regina, 2005. (Co-supervisor)
  • 1. Alejandra Premat, Postdoctoral Fellow, University of Regina, 2004-2005. (Co-supervisor)

  Courses taught (last six years):

  • Math 101 Finite Mathematics I (F 2015, F 2016, F 2019)
  • Math 103 Calculus for Business and Management Sciences (F 2017)
  • Math 110 Calculus I (F 2016)
  • Math 111 Calculus II (F 2018, W 2019, F 2020)
  • Math 217 Differential Equations I (F 2018)
  • Math 223 Introduction to Modern Algebra (F 2017)
  • Math 301 Introduction to Mathematical Logic (W 2020)
  • Math 308 Topics in the History of Mathematics (W 2017, W 2021)
  • Math 321 Number Theory I (W 2018)
  • Math 323 Modern Algebra I (W 2017, W 2018, W 2020, W 2021)
  • Math 423/823 Modern Algebra II (F 2015)
  • Math 424/824 Topics in Applied Algebra (W 2016, F 2019)
  • Math 438/838 Representation Theory (W 2019)