The 19th Seminar on Commutative Algebra and Related Topics will be held on January 31-February 1, 2024.
Prior to the seminar, we will hold a CIMPA course on Algebraic and Geometric Methods in Coding Theory on January 27-30, 2024.

Seminar (January 31-February 1, 2024)

Confirmed Speakers

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Contributed Speakers

Call for Papers

Papers will be accepted for presentation at the seminar subject to approval by the organizers. Please send submissions (extended abstract or full paper) electronically (in PDF and Tex formats) to ipmcommalg@ipm.ir with the subject: "19th_commalg_abstract".
The requests for contributed talks should be sent by November 6, 2023.

Seminar Schedule (printable version)

Abstracts of the Seminar

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List of Participants

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CIMPA course (January 27-30, 2024)

Prior to the seminar, a CIMPA course on Algebraic and Geometric Methods in Coding Theory will be held on January 27-30, 2024.

The aim of this course is to introduce some new research directions in coding theory and especially its interactions with commutative algebra and algebraic geometry. The course is meant for young researchers and PhD students, and it is intended for them to be acquainted with some topics of contemporary research interest. Considering the short duration of this course, we will assume familiarity with the basics of coding theory, and also some rudimentary knowledge of commutative algebra and algebraic geometry. We will focus mainly on the following topics.

  • Toric Varieties and Toric Codes
    The main theme of this part will be the linear codes defined on zero-dimensional subvarieties of a toric variety over a finite field. We briefly discuss local structure of an abstract toric variety, namely we review basics of (normal) affine toric varieties, (saturated) affine semigroups, toric ideals and their relations to strongly convex rational polyhedral cones. We discuss certain properties of projective toric varieties and give several examples. We exhibit the precise relation between the combinatorics of a fan and the geometry of the corresponding normal toric variety. We also discuss the GIT quotient representation of a simplicial normal toric variety and introduce homogeneous coordinates as done for a projective space. These will enable us to introduce and study the main parameters of a toric code, i.e. an evaluation code defined on some subset of rational points on a normal toric variety over a finite field.


  • Linear Codes associated to higher dimensional varieties
    Geometric approach to linear codes via the language of projective systems. The following specific classes of linear codes and some of their fundamental properties including determination of basic parameters will be discussed.

    - Codes associated to Veronese varieties (Projective Reed-Muller Codes)
    - Grassmann codes
    - Schubert codes


  • Betti numbers of linear codes and matroids
    Matroids and simplicial complexes associated to linear codes. Graded minimal free resolutions and Betti numbers of Stanley-Reisner rings of these simplicial complexes. Relations with generalized Hamming weights and generalized weight enumerator polynomials of linear codes.


Lecturers

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Course Schedule (printable version)

Registration

To participate in the seminar and the minicourse, please fill out the Pre-registration form by November 6, 2023.
The organizing committee has requested financial support to cover part of the travel expenses of the participants.




Registration Form

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Organizers

  • Sara Faridi (Dalhousie University, Canada)
  • Hassan Haghighi (K. N. Toosi University of Technology, Iran)
  • Raheleh Jafari (IPM and Kharazmi University, Iran)
  • Abbas Nasrollah Nejad (IPM and Institute for Advanced Studies in Basic Sciences, Zanjan, Iran)


Sponsors

AARMS  AARMS (Atlantic Association for Research in the Mathematical Sciences)

 

Compositio Mathematica  Compositio Mathematica

 



Compositio Mathematica 

 

 

 

IPM Institute for Research in Fundamental Sciences

Niavaran

School of Mathematics,

P.O. Box 19395-5746, Tehran - Iran

  • Tel: +98 21 222 90 928, Fax: +98 21 222 90 648
  • ipmcommalg@ipm.ir
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