Associate Professor of Mathematics

Institute for Advanced
Studies in Basic Sciences, Zanjan

Family: Parvaneh (spouse), Kourosh and Arash (sons)

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 by 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

Associate Professor, IASBS, 2011-present.

Assistant Professor, IASBS, 1999-2011.

Vice President on Administration, Finance, Education and Research, IASBS, 2018-present.

Director of International Relations, IASBS, 2016-2018.

Vice President on Administration and Finance, IASBS, 2013.

Director of Research Affairs, IASBS, 2010-2012.

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

Member of Executive Committee of the Iranian Mathematical Society, 2021-2024.

Member of editorial board, Bulletin of the Iranian Mathematical Society, 2019-present.

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

Member of editorial board of Farhang va Andishe Riazi, 2010-2016.

Chairman of Scientific Committee of the Iranian Mathematics Competitions for University Students, 2003-2006.

Inspector of the Iranian Mathematical Society, 2012-2014.

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

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

Chair of Scientific Committee of the Mathematics House of Zanjan, 2002-2017.

Head of Secretariat, Iranian Mathematical Society, 1987-1999.

Chairman of the Board of Trustee, Sobouti-Khajehpour Prize, 2012-2017.

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).

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.

Organizer of Mathematical Summer Schools for Undergraduate University Students (two weeks each), IASBS, 2016, 2017, 2018, 2019.

Organizer of CIMPA-WAMS Summer Research School on Topics in Analytic and Transcendental Number Theory, IASBS, 2017.

Organizer of CIMPA-WAMS Summer Research Schools on Algebraic Geometry and Commutative Algebra (two weeks each), IASBS, 2017, 2018, 2019, (joint with Abbas Nasrollah Nejad and Ali Akbar Yazdan Pour).

·
(with Reza Abdolmaleki, Jurgen Herzog), On the initial behavior of the number of generators of
powers of monomial ideals,
to appear in Bulletin Mathematique.

·
(with Reza Jafarpour-Golzari), Unmixed d-uniform r-partite hypergraphs, to appear in Ars Combinatoria.

· (with Mina Bigdeli, Ali Akbar
Yazdan Pour), Decomposable clutters and a
generalization of Simon's conjecture, Journal of Algebra 531, (2019) 102-124.

·
(with Abbas Nasrollah Nejad, Ashkan Nikseresht, Ali
Akbar Yazdan Pour), On the blowup of affine
spaces along monomial ideals: Tameness, Journal of Symbolic Computation 93, (2019) 85-99.

·
(with Mina Bigdeli, Jurgen Herzog), On the index of powers of edge ideals, Communications
in Algebra 46 (3), (2018) 1080-1095.

·
(with Abbas Nasrollah Nejad, Zahra Shahidi), Torsion-free Aluffi algebras, Journal of Algebra 513, (2018) 190-207.

·
(with Ashkan Nikseresht), On generalization of cycles and chordality to clutters from
an algebraic viewpoint, Algebra colloquium 24 (04), (2017)
611-624.

·
(with Mina Bigdeli, Ali Akbar Yazdan Pour), Stability of Betti numbers under reduction processes:
Towards chordality of clutters,
Journal of Combinatorial Theory, Series A 145, (2017) 129-149.

·
(with
Mina Bigdeli, Jurgen Herzog, Ali Akbar Yazdan Pour), Simplicial orders and chordality, Journal of Algebraic Combinatorics 45 (4), (2017) 1021-1039.

·
(with Reza Jafarpour-Golzari)
Unmixed r-partite graphs, Bulletin of the Iranian Mathematical Society 43 (3),
(2017) 781-787.

·
(with Abbas Nasrollah Nejad,
Aron Simis) The Aluffi algebra of the Jacobian of points in projective space:
torsion-freeness, Journal of Algebra 467, (2016)
268-283.

·
(with Marcel Morales, Ali Akbar Yazdan Pour),
Regularity and free resolution of ideals which are minimal to $d$-linearity,
Mathematica Scandinavica 118 (2), (2016) 161-182.

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

· Cohen-Macaulayness of
bipartite graphs, revisited, Bulletin of the Malaysian Mathematical Sciences
Society 38 (4), (2015) 1601-1607.

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

·
(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.

·
(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.

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

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

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

·
(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.

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

·
(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) 360-369.

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

·
Some infinite classes of
Fullerene graphs, International Mathematical Forum 1 (40) (2006)
1997-2002.

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

·
(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.

·
(with Hamid Usefi) A note on
minors of a generalized Hankel matrix, International Mathematical Journal, 3
(11) (2003) 1197-1201.

·
(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.

· Grobner bases of determinantal ideals, To
appear in Journal of Mathematical Researches (Kharazmi).

· 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).

· 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**

· 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., Isfahan,
Iran, 27-29 October 1999.

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

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

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

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

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

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

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

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

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

· Minimal
free resolution of associated graded rings, 40^{th} Annual Iranian
Mathematics Conference, Sharif University of Technology, Tehran, Iran, 16-19
August 2009. (Invited Speaker)

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

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

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

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

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

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

·
(with L. Sharifan) A class of
monomial curves of homogeneous type, 22^{nd} Iranian Algebra Seminar,
Hakim Sabzevari University, Sabzevar, Iran, 31 Jan - 2 Feb 2012.

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

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

· (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, Tabriz, Iran, 27-30 August 2012.

· (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, Kashan,
Iran, July 2012.

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

· Constructive algebra: a method for teaching higher algebra, Challenges of Mathematical Education, University of California, Irvine, USA, 27-29 January 2014. (Invited Speaker)

· Steps on classification of monomial ideals with linear resolution, Workshop on Computational Differential Algebra, IPM, Tehran, Iran, 21-25 June 2014. (Invited Lecturer)

· (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, Indonesia, August 18-21, 2015.

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

· Linearity of resolution of monomial ideals and the role of
characteristic of the base field, Frontiers in Mathematics, IPM, Tehran,
Iran, February 2016 (Invited Speaker).

· Linearity of resolution of monomials and the role of characteristic of the base field, Conference on Combinatirial Structures in Geometry, Osnabrueck University, Osnabrueck, Germany, 8-12 August 2016.

· Computing in Algebraic Geometry, International Workshop on Mathematics and Physics, Salahaddin University, Erbil, Iraq, 25- 26 April 2017. (Invited Speaker)

· Extendable shellability and Simon's conjecture, CIMPA School on Combinatorial Commutative Algebra, COMSETS, Lahore, Pakistan, 5 -14 March 2018. (Invited Lecturer)

·
Shellable Simplicial
Complexes, Second International Conference of Mathematics, Salahaddin
University, Erbil, Iraq, 3-5 February 2019. (Main Speaker)

**Scientific
Fellowships**

Research fellowship of ICTP, Abdus-salam ICTP, Trieste, Italy, 2000-2006.

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

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

Mathematics Education Program, World Learning & USA Academy of Sciences, 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).

**Evaluation of teaching by students: 19.70
(out of 20)**

Leila Sharifan (Joint with F. Rahmati) 2009, Ali Akbar Yazdan Pour (Joint with M. Morales) 2012, Abolfazl Tarizadeh 2013, Asghar Madadi (Joint with M. Ariannejad) 2014, Mina Bigdeli (Joint with Jurgen Herzog) 2015, Reza Jafarpour Golzari 2018, Zahra Shahidi (Joint with Abbas Nasrollah Nejad) 2019, Somayeh Vosoughian (Joint with R. Naghipour), 2021, Amirbehzad Farrahi (Joit with Abbas Nasrollah Nejad), 2020, Reza Abdolmaleki (Joint with Jurgen Herzog), 2020.

**Current Ph. D. Students**

Shekoufeh Gherekhlou (Joint with Aliakbar Yazdanpour, Volkmar Welker), Roghieh Ghorbani (Joint with Sara Faridi), Belal Sefatpanah (Joint with Giorgio Ottaviani).

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), Marjan Amirian (2014), Narges Akbarisafa (jont with Ali Akbar Yazdan
Pour) (2014), Sepehr Jafari (2015), Maryam Zamani (2015), Fatemeh Yarmohammadi
(2015), Mahmoud Ejazi (2017), Yousef Ashegh Bonabi (2017), Alireza Shamsian
(jont with Ali Akbar Yazdan Pour) (2018), Maryam Moumivand (jont with Abbas
Nasrollah Nejad) (2018), Roghieh Dameshghi (2019), Jafar
Madadi (2021), Mina Hashemi (2021), Nasrin Sadeghi (2022).

**Current M. Sc. Students**

Azerbaijan,
Armenia, Turkey, Russia, Belorussia, Georgia, Iraq, United Arab Emirates,
Pakistan, India, Morocco, Italy, Germany, Austria, France, Greece, United
States of America.

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: January 2022**