Monomial Ideals with Linear Resolutions
1. Clutters and their circuit ideals
2. Linear resolution of monomial ideals
3. Chordallity of clutters
4. Simplicial orders
5. Ideals with linear quotients and extendably shellable complexes.
Homology of Monomial Ideals and Algebras
1. Simplicial homology, Koszul complexes and free resolutions
2. Alexander duality and applications
3. The Eagon-Northcott complex and generalizations
4. Algebraic shifting theory I
5. Algebraic shifting theory II
Geometry and Algebra of Subdivisions
1. Subdivision of simplicial complexes
2. Subdivision and f- h-vectors
3. Subdivision and free resolutions
4. Limit behavior under iterated subdivisions.
Eric Babson (University of California at Davis, USA)
Random Simplicial Complexes
1. Random graphs
2. Isoperimetric inequalities
4. Thresholds for first homology and homotopy groups
& Rashid Zaare-Nahandi (IASBS, Zanjan, Iran)
Sara Faridi (Dalhousie University, Halifax, Canada)
Topological structures related to monomial ideals with linear resolution
1. Minimal free resolutions via simplicial complexes
2. Review of topological methods used for calculating resolutions
3. Ideals with linear resolution: from graphs to higher dimensions
4. Chordal complexes, chordal hypergraphs, chordal clutters, and open
Suggested resources for required backgraound:
Herzog, J. and Hibi, T., Monomial Ideals, in GTM 260. Springer, London, 2010.
Peeva, I., Graded Syzygies, Algebra and Applications 14, Springer, London, 2011.
Institute for Advanced Studies in Basic Sciences (IASBS), Prof. Yousef Sobouti Blvd., P. O. Box 45195-1159 Zanjan 45137-66731 Iran.
Fax: (+98) 24 3315 5142. Tel: (+98) 24 3315 5047.
May 31, 2017 Registration deadline June 30, 2017
Late registration for International applicants
July 5, 2017 Decision on acceptance
July 15, 2017
Late registration for Iranian applicants
July 20, 2017 Decision on acceptance
August 5-17, 2017
The school program
First Research School on Commutative Algebra and Algebraic Geometry
Algebra, Combinatorics and Geometry of Monomials
August 5-17, 2017