Associate Professor of Mathematics

Family: Parvaneh (wife), Kourosh and Arash

Ph.D.: University of Tehran (Tehran, Iran), 1999.

M. Sc.: University of Teacher Education (Tehran, Iran), 1993.

Bachelor: Sharif University of Technology (Tehran, Iran) , 1990.

Professor Rahim Zaare-Nahandi.

Grobner basis and free resolution of the ideal of 2-minors of a (2 x n) matrix of linear forms.

Algebraic Geometry, Commutative Algebra, Algebraic Combinatorics.

Computational methods in Algebraic Geometry and Commutative Algebra, Free resolution of ideals of polynomial rings, Grobner basis.

Chairman, Research Center for
Basic Sciences and Contemporary Technologies (IASBS) (2014-).

Deputy Chancellor on Administration and Finance, IASBS (2013).

Associate Professor, Institute for Advanced Studies in Basic Sciences (IASBS), (2011-present).

Assistant Professor, Institute for Advanced Studies in Basic Sciences (IASBS), (1999-2011).

Manager of
Research Affairs, IASBS (2012).

Head of the Evaluation Office, IASBS (2011-2012).

Inspector of the Iranian
Mathematical Society (2012-2014).

Chairman, Department of Mathematics, IASBS (2002-2004 and 2006-2009).

Member of Executive Committee of the Iranian Mathematical Society (1998-2000, 2003-2006, 2006-2009).

Editor-in-chief, Newsletter of the Iranian Mathematical Society (1998-2000 and 2004-2006).

Member of editorial board of Farhang va Andishe Riazi (2010-present).

Member of the National and State Councils of World Mathematical Year 2000.

Head, Scientific Committee of the Iranian Mathematics Competitions for University Students (2003-2006).

Organizer of CIMPA-UNESCO-IRAN School on Groebner Bases and Applications, 19-30 July 2005, IASBS, Iran.

Organizer of Workshop on Computational Commutative Algebra, 2-7 July 2011, IPM, Iran (joint with Hossein Sabzrou).

Member
of the National and State Councils of World Mathematical Year 2000.

Organizer of Workshop on Mathematical Writing, 3-5
November 2003, IASBS.

Organizer of Workshop on Computational Differential
Algebras, 21-25 June 2014, IPM, (joint with Amir Hashemi).

Organizer of First Festival on Mind Toys, 27-30 June
2011, Mathematics House of Zanjan.

Organizer of
Second Festival on Mind Toys, 1-4 September 2015, Mathematics House of Zanjan.

Chair of Scientific Committee of the Mathematics House of Zanjan (2002-present).

1.
(with Abbas Nasrollah Nejad,
Aron Simis) The Aluffi algebra
of the Jacobian of points in projective space: torsion-freeness, submitted.

2.
(with Reza Jafarpour-Golzari) Unmixed
r-partite graphs, to appear in Bulletin of the Iranian Math. Soc.

3.
(with Marcel Morales, Ali Akbar Yazdan Pour), Regularity and free resolution of ideals
which are minimal to $d$-linearity, to appear in Math. Scand.

4.
Pure simplicial complexes and well-covered graphs, to appear in Rocky
Mountain Journal of Mathematics 45 (2), (2015) 695-702.

5.
(with Asghar Madadi)
Perfect Matching of 3-uniform Hypergraphs, Electronic Notes in Discrete
Mathematics 45 (2014) 63-66.

6.
(with Marcel Morales, Ali Akbar Yazdan Pour) Castelnuovo-Mumford regularity under reduction processes on
Graphs and Hypergraphs, Electronic Notes in Discrete Mathematics 45 (2014)
57-62.

7.
(with Marcel Morales, Abbas Nasrollah Nejad, Ali Akbar Yazdan Pour), Monomial ideals with 3-linear resolution,
Annals de Mathematiques de Tolouse,
Series 6, 23 (4), (2014) 877-891.

8.
Cohen-Macaulayness
of bipartite graphs, revisited, Bulletin of the Malaysian Mathematical Sciences
Society (2014) 1-7.

9.
(with Asghar Madadi)
Cohen-Macaulay $r$-partite graphs with minimal clique cover, Bulletin of the
Iranian Mathematical Society 40 (3) (2014) 609-617.

10. Universally Koszul algebras defined by graphs, Journal of Discrete Mathematical Sciences and Cryptography 15 (6) (2012) 349-352.

11. Invariance of the barycentric subdivision of a simplicial complex, Bull. Iranian Math. Soc. 38 (2) (2012) 423-432.

12. (with Marcel Morales and Ali Akbar Yazdan Pour) The regularity of edge ideals of graphs, Journal of Pure and Applied Algebra 216 (2012) 2714-2719.

13. (with Abbas Nasrollah Nejad) Aluffi torsion-free ideals, Journal of Algebra 346 (2011) 284-298.

14. (with L. Sharifan) Minimal free resolution of associated graded ring of monomial curves of generalized arithmetic sequences, Journal of Pure and Applied Algebra 213 (2009), pp. 360-369.

15. On isomorphism of simplicial complexes and their related algebras, Bull. Iranian Math. Soc. 35 (1) (2009) 41-48.

16. Some infinite classes of Fullerene graphs, Intern. Math. Forum, Vol. 1, no. 40 (2006) 1997-2002.

17. Perfect matchings in graphs, an approach via Grobner basis, Southeast Asian Bulletin of Mathematics, Vol. 30 (2006) 341-345.

18. (with Rahim Zaare-Nahandi) The minimal free resolution of a class of square-free monomial ideals, Journal of Pure and Applied Algebra 189 (2004) 264-278.

19. (with Hamid Usefi) A note on minors of a generalized Hankel matrix, Intern. Math. J., Vol. 3, no. 11 (2003) 1197-1201.

20. (with Rahim Zaare-Nahandi) Grobner basis and free resolution of the ideal of 2-minors of a 2 x n matrix of linear forms, Communications in Algebra, 28 (9) (2000) 4433-4453.

1.
History of
Iranian mathematics competitions for university students, a chapter in the book "Iranian Mathematics Competitions for
University Students", by B. Yahaghi, Iranian
Math. Soc. and Iran University Press, Tehran, 2009. (English version is
published by Hindustan Publishing Co. 2009).

2.
Buchberger and Grobner bases (an expository and
review article on history of Grobner bases and role
of Buchberger in improving the theory), Farhang va Andishe
Riazi, 44 (2010) 55-80.

**Talks in International Conferences**

1.
Free resolution of the ideal of
2-minors of a (2* *x* n*) matrix of linear forms, 11^{th}
Seminar on Algebra, Isfahan Univ. of Tech., 27-29 October 1999.

2.
Generalized Hankel matrices and
their applications in algebraic geometry, 3^{rd} Joint Seminar on
Applied Math, Baku State University, 6-8 September 2002,

3.
(with Rahim Zaare-Nahandi)
Minimal free resolution of some monomial ideals, a survey, 15^{th}
Seminar on Algebra, Guilan University, 19-20 July
2003. (Main Invited Speaker)

4.
Domination ideal of a graph, 2^{nd}
Seminar on Commutative Algebra, IPM, 16-17 November 2005. (Invited Speaker)

5.
On isomorphism of simplicial
complexes and their related rings, 3^{rd} Seminar on Commutative
Algebra, IPM, 10-11 January 2007. (Invited Speaker)

6.
Minimal free resolution of the
associated graded ring of monomial affine curves, International Conference on
Commutative Algebra, IIT Mumbai, 8-12 January 2008. (Invited Speaker)

7.
Some infinite classes of
Fullerene graphs, The first Conference and Workshop on
Mathematical Chemistry, Tarbiat Modares
University, 29-31 January 2008.

8.
Betti numbers of the
associated graded ring of certain monomial curves, 5^{th} International
Fez Conference on Commutative Algebra and Applications, 23-28 June 2008, Fez
University. (Invited Speaker)

9.
(with Abbas Nasrollah
Nejad) Hilbert Series of monomial algebras, 39^{th}
Annual Iranian Mathematics Conference, University of Kerman, 24-27 August 2008.

10. Homomorphism
of simplicial complexes, 4^{th} Seminar on Commutative Algebra, 5^{th}
Seminar on Commutative Algebra, Isfahan University of Technology 10-11 December
2008. (Invited Speaker)

11. Minimal
free resolution of associated graded rings, 40^{th} Annual Iranian
Mathematics Conference, Sharif University of Technology, 16-19 August 2009.

12. Universally
Koszul graphs, 21th Seminar on Algebra, University of
Tabriz, 10-11 November 2010.

13. Barycentric subdivision of simplicial
complexes, 7^{th} Seminar on Commutative Algebra, IPM, 1-2 December
2010. (Main Speaker)

14. Pure
simplicial complexes and well-covered graphs, 3^{rd} Algebraic
Combinatorics Conference of Iran, University of Isfahan, 24-25 February 2011.

15. Aluffi torsion-free ideals, 42^{nd}
Annual Iranian Mathematics Conference, University of Rafsanjan,
5-8 September 2011. (Invited Speaker)

16. A
new method for checking Cohen-Macaulayness of
bipartite graphs, 8^{th} Seminar on Commutative Algebra, IPM, 30
November-1 December 2011.

17. A
classification of monomial ideals with 3-linear minimal free resolution, 22^{nd}
Iranian Algebra Seminar, Sabzevar Tarbiat
Moallem University, 31 Jan - 2 Feb 2012. (Keynote
speaker)

18. Regularity of monomial ideals generated in degree 2
and 3,
2^{nd} Seminar on Combinatorial Commutative Algebra, IPM, February
2012.

19. (with M. Morales, A. Yazdan
Pour) Resolution of Ideals which are Minimal to d-linearity, The 43rd Annual
Iranian Mathematics Conference, University of Tabriz , 27-30 August 2012.

20. (with S. Faghfouri, J. Hossein Pour)
Hilbert series of zero-dimensional ideals with 2 and 3 variables, The 43rd Annual Iranian Mathematics
Conference, University of Tabriz , 27-30 August 2012.

21. (with M. Morales , A. Yazdan
Pour) Castelnuovo-Mumford regularity under reduction
processes on graphs and hypergraphs, 5th Conference on Algebraic Combinatorics
and Graph Theory , University of Kashan, Iran, July
2012.

22. (with
A. Madadi) Perfect matching of 3-uniform hypergraphs,
5th Conference on Algebraic
Combinatorics and Graph Theory , University of Kashan,
Iran, July 2012.

23. Constructive algebra: a method
for teaching higher algebra, Challenges of Mathematical Education, University
of California, Irvine, 27-29 January 2014.

24. Steps on classification of
monomial ideals with linear resolution, Workshop on Computational Differential
Algebra, IPM, 21-25 June 2014.

25.
(with A. Nikseresht) On Generalizations of
Cycles and Chordal Graphs to Clutters of Higher Dimensions, The 7-th SEAMS-UGM
2015 International Conference on Mathematics and Its Applications, August
18-21, 2015.

26. (with A. Nikseresht)
Linear resolution, chordality and ascent of clutters,
12th Seminar
on Commutative Algebra, IPM, 11-12 November 2015.

**Visiting Positions**

Research fellowship of ICTP, Abdus-salam ICTP, Trieste, Italy, June-September 2001.

Research fellowship of Austrian Academy of Science, Research Institute for Symbolic Computation, Linz, Austria, March-July 2006.

Sabbatical Leave, University of Genova, Genova, Italy, September 2009-June 2010.

Visit to University of Grenoble 1, Grenoble, France, 7 - 30 March 2012.

Mathematics Education Program, World Learning, 10 January - 2 February 2014, USA.

Calculus (undergraduate); Algebra I & II (undergraduate); Projective Geometry (undergraduate); Introduction to Algebraic Geometry (undergraduate); Complex Variables (undergraduate); Linear Algebra (undergraduate); Commutative Algebra I & II (graduate); Algebraic Geometry I & II (graduate); Computational Methods in Commutative Algebra and Algebraic Geometry I & II (graduate); Advanced Algebra I & II (graduate); Algebraic Graph Theory (graduate); Algebraic Topology (graduate); Combinatorial Commutative Algebra (graduate).

Leila Sharifan (Joint with F. Rahmati), graduated; Ali Akbar Yazdan Pour (Joint with M. Morales), graduated; Abolfazl Tarizadeh, graduated; Asghar Madadi (Joint with M. Ariannejad), graduated; Mina Bigdeli (Joint with Jurgen Herzog), graduated; Reza Jafarpour Golzari; Somayeh Vosoughian; Amirbehzad Farrahi (Joit with Abbas Nasrollah Nejad).

Ali Moharrami (2000), Rasoul Moghaddam (2002), Hamid Usefi (2002), Firouz Alipour (2002), Mojtaba Zamani (2003), Vajiheh Tarviji (2003), Seyyed Mohammad Ajdani (2004), Abbas Nasrollah Nejad (2006), Pouya Nikoo (2006), Saeed Alirezazadeh (2007), Abolghasem Dashtban (2007), Aliakbar Yazdanpour (2007), Saeed Shaabani (2007), Mohammad Pirhayati (2007), Ehsan Hesamifard (2008), Zeinab Kodaee (joint with M. Zaker) (2008), Leila Tajdoust (joint with A. Rahnama) (2008), Neda Mohammadzadeh (2009), Masoud Mohammadpour (2009), Asghar Madadi (2009), Zabihollah Fallah (2009), Farzad Elmi (joint with S. Salehi) (2010), Hossein Kheyri (2011), Zahra Shahidi (2011), Sahar Faghfori (2012), Jamal Hossein Pour (2012), Javad Tavakoli (2012) Mohammad Bagher Safari (2012), Mohsen Shekari (join with Aliakbar Yazdanpour) (2013), Masoumeh Danesfahani (2013), Kobra Khanahmadlou (Joint with Abbas BasrollahNejad) (2014), Iman Bahmani (2014), Narges Akbarisafa (2014), Sepehr Jafari (2015), Maryam Zamani (2015), Fatemeh Yarmohammadi (2015).

e-mail: rashidzn at sign iasbs dot ac dot ir

Mailing address: IASBS , P.O. Box 45195-1159, Zanjan, Iran

Tel : +(98)(241) 4155109

Fax: +(98)(241) 415142

**Last update: February 2016**