Serban Raianu

Professional experience: Professor, Department Chair (2006-2008), California State University Dominguez Hills, 2004-present, Associate Professor, California State University Dominguez Hills, 2002-2004, Visiting Associate Professor, Syracuse University, 2000-2002, Associate Professor, University of Bucharest, 1996-2000, Assistant Professor, University of Bucharest, 1992-1995, Instructor, University of Bucharest 1988-1992.

Ph.D. thesis: "New contributions to the structure of graded rings and modules", 1991, University of Bucharest, supervisor Constantin Năstăsescu.

Current scientific interests: Hopf algebras acting on algebras and coalgebras, Quantum Groups.

International Conferences: Bressanone, Italy (1990), Ramat Gan, Israel (1991), Chicago (1992), Antwerp, Belgium (1996), Saint John's, Canada (1997), Brussels, Belgium (1998), Berkeley (1999) (a video of the lecture is available at http://www.msri.org/publications/ln/msri/1999/hopfalg/raianu/1/), Chicago (2002), New York (2003), Haifa (2004), Santa Barbara (2005), Saint John's, Canada (2009), Sde Boker, Israel (2010), Bucharest, Romania (2013), Halifax, Canada (2014), Iasi, Romania (2015).

Invited Lectures:

Brussels, Belgium (1990, 1991, 1992, 1993, 1994, 1995, 1996, 1998), Antwerp, Belgium (1990, 1991, 1992, 1993, 1994, 1995, 1996, 1998), Hasselt, Belgium (1994, 1996, 1998), Beer Sheva, Israel (1992), Ferrara, Italy (1997), Padova, Italy (1997), Murcia, Spain (1998), University of Southern California (2001), University of Illinois at Chicago (2001), University of New Mexico, Albuquerque (2003), El Camino College, Torrance (2004), Cal Poly Pomona (2004), Cal State San Bernardino (2006), Cal State Channel Islands (2007), DePaul University (2011), Cal State Channel Islands (2013) ), Bucharest (2014).

Courses taught:

Beginning Algebra, Intermediate Algebra, Mathematics for Elementary School Teachers: Real Numbers, , Mathematics for Elementary School Teachers: Geometry and Probability, CSET I and II Content Course, Precalculus, Calculus I, II, III, Linear Algebra, Abstract Algebra, Number Theory, Complex Analysis, Probability and Statistics, General Algebra, Algebra and Arithmetic, Modern techniques in elementary mathematics, Algebra and Analytic Geometry, Geometry, Lie algebras, Algebras and coalgebras, Representation theory of finite dimensional algebras, Graded rings and modules, Applications of group theory. Systematically involved in teacher preparation.

Grants, Prizes, and Other Activities:

- First prize in the 1981 annual scientific contest for students at the University of Bucharest. Title of paper: "The Cousin complex".

- Gheorghe Titeica prize of the Romanian Academy, 2001.

- Guest researcher University of Antwerp 1995-1996.

- Visiting professor Ferrara (February 1997).

- Two grants from the Romanian Academy of Science (coordinator) 1994, 1995.

- Research project joint with the Universities of Antwerp, Brussels, Hasselt, all Belgium, (participant) 1996-1999.

- Campus coordinator for the Louis Stokes Alliance for Minority Participation, NSF-Cal State grant, 2003-2006.

- PUMP Undergraduate Research Grant 2016-2017 (with Natalia da Silva and Hector Salgado).

- Math Alliance Mentor.

- California Math Alliance Mentor.

- Reviewer for Zentralblatt für Mathematik and Mathematical Reviews.

- Member of the AMS.

- Member of the AWM.

- Member of the NAM.

- Co-organizer (with Gizem Karaali and Susan Montgomery) of AMS special section Hopf Algebras and Quantum Groups, Claremont McKenna, 2008.

- Co-organizer (with Davida Fischman) of MAA Invited Paper Session Topics in Hopf Algebras, Joint Meetings, New Orleans, 2011.

- Editorial Board ISRN Algebra, 2011-present, journal website: http://www.isrn.com/journals/algebra/

- Editorial Board Algebra Letters, 2012-present, journal website: http://scik.org/index.php/abl/

- Managing Editor PUMP Journal of Undergraduate Research, 2017-present, journal website: https://math.csudh.edu/pumpjournal

List of publications:

Books:

1. Structuri algebrice, Tipografia Univ. Buc., 1981 (with I. D. Ion and C. Manoil).

2. Lecţii de Algebră Comutativă, Tipografia Univ. Buc., 1984 (with T. Albu).

3. Algebre Hopf,Tipografia Univ. Buc. 1999 (with S. Dăscălescu and C. Năstăsescu).

4. Hopf Algebras: an Introduction, Marcel Dekker Monographs and Textbooks, vol. 235, 2001 (with S. Dăscălescu and C. Năstăsescu).

(link to www.amazon.com)

Papers (published or accepted):

1. Cousin complex, local cohomology and torsion theory, Communications in Algebra, 9(16) 1982, 691-1720 (with T. Albu).

2. Gabriel dimension of graded rings, Rend. Sem. Mat. Univ. Padova, 71 (1984), 195-208 (with C. Năstăsescu).

3. Stability conditions for commutative rings with Krull dimension, Methods in Ring Theory, Reidel 1984, 391-402 (with C. Năstăsescu).

4. Finiteness conditions for graded modules (gr-∑(∆)-injective modules), Journal of Algebra, 100 (1) 1986, 179-190 (with C. Năstăsescu).

5. A remark on strongly graded rings with finiteness conditions, Bull. Math. Soc. Math. Roumanie, 30 (78) 1986, 265-269.

6. External homogeneization for finitely generated abelian groups, Ann. Univ. Ia\c{s}i, XXX, 1985, 58-60 (with C. Năstăsescu).

7. Gabriel dimension of graded rings II, Journal of Pure and Applied Algebra, 50 (1988), 73-79 (with C. Năstăsescu).

8. Cousin complex characterization of non-noetherian n-Gorenstein rings, Communications in Algebra, 15 (7), 1987, 1533-1541.

9. Modules graded by G-sets, Mathematische Zeitschrift, 203 (1990), 605-627 (with C. Năstăsescu and F. Van Oystaeyen).

10. Induction and coinduction for Hopf algebras, Journal of Algebra, 165, 1994, 204-222, (with S. Caenepeel and F. Van Oystaeyen). pdf

11. Semiinvariants for Hopf algebra actions, Israel Journal of Mathematics, 88, 1994, 279-306 (with M. Cohen and S. Westreich).

12. Graded Coalgebras and Morita-Takeuchi Contexts, Tsukuba Journal of Mathematics, 19 (1995) 395-407 (with S. Dăscălescu, C. Năstăsescu and F. Van Oystaeyen).

13. Finite Hopf-Galois Coextensions, Crossed Coproducts and Duality, Journal of Algebra, 178 (1995) 400-413 (with S. Dăscălescu and Y. Zhang).

14. Coinduction for infinite dimensional Hopf algebras, Journal of Pure and Applied Algebra, 107 (1996) 141-151 (with S. Caenepeel and B. Zhou).

15. A Maschke-type theorem for crossed coproducts, Analele Univ. Constanţa, 2 (1994), 44-51 (with S. Caenepeel and S. Dăscălescu).

16. Cosemisimple Hopf algebras coacting on coalgebras, Communications in Algebra, 24 (1996), 1649-1677 (with S. Caenepeel and S. Dăscălescu).

17. Induction functors for the Doi-Koppinen unified Hopf modules, in Abelian groups and modules, Proceedings of the Padova Conference, Padova, Italy, June 23-July 1, 1994, Kluwer, 1995, eds. A. Facchini and C. Menini, p. 73-94., (with S. Caenepeel) pdf

18. Cleft coextensions and crossed coproducts, Communications in Algebra, 24 (1996), 1229-1243 (with S. Dăscălescu and G. Militaru).

19. Strongly graded coalgebras and crossed coproducts (with S. Dăscălescu and C. Năstăsescu), in Abelian Groups, Module Theory and Topology, Proceedings of the fourth week on algebra and algebraic geometry, eds. S. Caenepeel, A. Verschoren, Marcel Dekker Lecture Notes in Pure and Appl. Math., vol. 197, 1998, 103-110.

20. Smash (Co)products from Adjunctions, (with S. Dăscălescu and F. Van Oystaeyen), Hopf Algebras, and Brauer Groups, Proceedings in honour of Adalberto Orsatti's 60th birthday, eds. D. Dikranjan, L. Salce, Marcel Dekker Lecture Notes in Pure and Appl. Math., vol. 201, 1998, 131-142.

21. Some remarks on a theorem of H.-J. Schneider, Communications in Algebra, 24 (1996), 4477-4493 (with S. Dăscălescu and F. Van Oystaeyen).

22. Galois extensions for co-Frobenius Hopf algebras (with M. Beattie and S. Dăscălescu), J. Algebra, 198 (1997), 164-183.

23. The Categories of Yetter-Drinfel'd Modules, Doi-Hopf Modules and Two-sided Two-cosided Hopf Modules,(with M. Beattie, S. Dăscălescu and F. Van Oystaeyen), Applied Categorical Structures, 6 (1998), 223-237.

24. Morphisms of Relative Hopf Modules, Smash Products and Duality, (with C. Menini), J. Algebra 219 (1999) 547-570.

25. Classifying pointed Hopf algebras of dimension 16, (with S. Dăscălescu and S. Caenepeel), Comm. Algebra 28 (2000), 541-568.

26. An easy proof of the uniqueness of integrals, in Hopf Algebras and Quantum Groups, Proceedings of the Brussels Conference 1998, (eds. S. Caenepeel and F. Van Oystaeyen), Marcel Dekker Lecture Notes in Pure and Appl. Math., vol 209, 2000, 237-240.

27. Co-Frobenius Hopf algebras with a separable Hopf-Galois extension are finite dimensional, (with M. Beattie and S. Dăscălescu), Proceedings of the AMS 128, nr. 11 (2000), 3201-3203.

28. Finite Hopf-Galois extension equivalent to crossed products (with M. Saorín), Comm. Algebra 29 (2001), 4871-4882.

29. Semiprime crossed products over copointed Hopf algebras, (with D. Quinn), Proceedings of the AMS 131 (2003), 29-33.

30. Lifting of Nichols algebras of type B₂ (with M. Beattie and S. Dăscălescu), with an appendix "A generalization of the q-binomial theorem", with I. Rutherford, Israel J. of Math 132 (2002), 1-28.

31. Coalgebras from formulas, in Hopf Algebras, Proceedings of the International Conference on Hopf Algebras held at DePaul University, Chicago, Illinois, edited by Jeff Bergen, Stefan Catoiu, William Chin, Lecture Notes In Pure and Applied Mathematics, Vol. 237, Marcel Dekker, 2004, 215-224. pdf

32. Does the Jordan Form of a Matrix have the Maximum Number of Zeros? (with F. Brulois and G. Jennings), Bull. Math.Soc. Sc. Math. Roumanie Tome 48(96) No. 4, 2005, 359-360. pdf

33. Duality for Finite Hopf Algebras explained by Corings, (with S. Caenepeel and D. Quinn), Applied Categorical Structures 14 (2006), no. 5-6, 531-537. pdf

34. Balanced bilinear forms for corings (with M. Beattie and D. Bulacu), "Modules and Comodules" Proceedings of a conference dedicated to Robert Wisbauer, Trends in Mathematics, 87-99, 2008, Birkhäuser, (Editors: Tomasz Breziński, José Luis Gomez Pardo, Ivan Shestakov, Patrick Smith). pdf

35. The antipode of a dual quasi-Hopf algebra with non-zero integrals is bijective (with M. Beattie and M.C. Iovanov), Algebras and Representation Theory 12 (2009), no. 2-5, 251-255. pdf

36. The bijectivity of the antipode revisited (with M.C. Iovanov), Comm. Algebra 39 (2011), no. 12, 4662–4668. pdf

37. Stable equivalences of Morita type and Frobenius extensions (with M. Beattie and S. Caenepeel), Annals of The Univ. of Bucharest (mathematical series) 2 (LX) (2011), 123-126. pdf

38. External homogenization for Hopf algebras: a coring point of view, Bull. Math. Soc. Sci. Math. Roumanie (NS) 56(104) (2013), no. 3, 369–375.

39. Arithmetic properties of 3-cycles of quadratic maps over ℚ (with Patrick Morton), J. Number Theory, 240 (2022), 685-729. (see https://arxiv.org/abs/2105.07435 )

Expository articles:

1. Module Cohen-Macaulay, in Seminar de Algebră, Univ. Iaşi, 1986.

2. Smash products and applications, Proceedings of the Algebra Conference, Braşov, 1988 (with C. Năstăsescu).

3. Crossed coproducts, Proceedings of the International Conference on Representation Theory, Constanţa, 1995.

4. The Integral of Secant and Stereographic Projections of Conic Sections (with George Jennings, David Ni, Wai Yan Pong), https://arxiv.org/abs/2204.11187

Undergraduate Student Research Projects:

1. Computing areas using Green’s Theorem and a Software Planimeter, (with Paul Davis) Teaching Mathematics Applications 2007, Volume 26, Number 2, 103-108, Oxford University Press, pdf

2. Differences of Harmonic Numbers and the abc-Conjecture, (with Natalia da Silva and Hector Salgado), PUMP J. Undergrad. Res., 1 (2018), 1-13. pdf

3. Partition Problems and a Pattern of Vertical Sums, (with Eunice Krinsky and Alexander Wittmond), PUMP J. Undergrad. Res., 1 (2018), 30-47. pdf