RSCCAAG-Speakers

Suggested resources for required backgrounds:

An installation of CoCoA and SINGULAR program on your personal laptop would be good for tutorial sessions of this school. Moreover, the following resources are very useful for preparing yourself for this school.

T. de Jong, G. Pfister: Local Analytic Geometry, Vieweg 2000. Also appeared in Springer Series: Advanced Lectures in Mathematics 2013, Chapter 1-5

G.-M. Greuel, G. Pfister: A Singular Introduction to Commutative Algebra, Springer 2002, second edition 2007, Chapter 3, 4

Cox, Little, O'Shea: Ideals, Varieties, and Algorithms, third edition, Springer 2007

Cox, Little, O'Shea: Using Algebraic Geometry, second edition, Springer 2005

B. Erocal, O. Motsak, F.-O. Schreyer, A. Steenpass: Refined Algorithms to Compute Syzygies. J. Symb. Comput. 74 (2016), 308-327.

A. Chiodo, D. Eisenbud, G. Farkas, F.-O. Schreyer: Syzygies of torsion bundles and the geometry of the level l modular variety over M_g. Inventiones Math 194 (2013), 73-118.

J. L. Massey: Shift-register synthesis and BCH decoding. IEEE Trans. Information Theory, IT-15(1) (2016): 122-127.

Christian Eder: Gröbner basis theory

1. Introduction to signature-based Gröbner basis algorithms
2. Faugère's algorithms F4 and F5
3. Specialized linear algebra tools
4. Applications in cryptography
5. Applications in coding theory

Gerhard Pfister: Singularity theory

1. Weierstrass division theorem and applications
2. Resolution of plane curve singularities
3. Finite determinancy of hypersurface singularities
4. Normalization
5. Primary decomposition

Andreas Steenpass: A computational approach to the Prym-Green conjecture

1. Introduction: Free resolutions and the Prym-Green conjecture
2. Improved algorithms to compute syzygies
3. The structure of Prym-Green matrices
4. The Berlekamp-Massey algorithm
5. Computational results regarding the Prym-Green conjecture

John Abbott: Modular methods

1. Introduction: Chinese Remainder Theorem (CRT), Hensel lifting
2. Reconstruction methods (incl. LLL-based), guaranteed and heuristic
3. Determinant of matrix over ZZ
4. Modular version of Buchberger-Moeller algorithm
5. Ideals modulo p

For the topics presented by the second and last lecturers, it would be good to have an installation of Singular.jl.
Singular.jl is a package to make the computational functionality of Singular available from within the julia programming language. It is still relatively new.

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.

Important dates

July 15, 2018
Registration deadline
(International applicants)

August 3, 2018
Registration deadline
(Iranian applicants)

July 25, 2018
Decision on acceptance
(International applicants)

August 12, 2018
Decision on acceptance
(Iranian applicants)

September 1-12, 2018
The school program