Today : Sun, Feb 15, 2026

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Meetings  

Click on the theme item for the meeting plan for that theme.
Click on the meeting item for references, exercises, and additional reading related to it.
  • Theme 1 : Why this course? - 1 meetings
  • Theme 2 : Gröbner bases - 17 meetings

    • Meeting 02 : Wed, Jan 21, 10:00 am-10:50 am - Jayalal Sarma M N
      • Motivation for checking consistency of system of Polynomial equations: 3-coloring problem

    • Meeting 03 : Thu, Jan 22, 08:00 am-08:50 am - Harshil M.
      • Fields, rings, polynomial rings, ideals

    • Meeting 04 : Fri, Jan 23, 02:00 pm-02:50 pm - Harshil M.
      • Basis/Generating set of ideals, variety, Ideal membership problem and its relation with checking consistency of system of polynomial equations

    • Meeting 05 : Tue, Jan 27, 11:00 am-11:50 am - Harshil M.
      • Gaussian elimination and Euclidean division algorithm for special cases of linear and univariate polynomials, and viewing them as producing a new basis, identifying common features like ordering on monomials and use of leading terms

    • Meeting 06 : Wed, Jan 28, 10:00 am-10:50 am - Harshil M.
      • Ideal membership problem for univariate polynomials, and an initial understanding of `nice' basis as a basis such that checking remainder upon division by its polynomials is enough to solve ideal membership problem

    • Meeting 07 : Thu, Jan 29, 08:00 am-08:50 am - Harshil M.
      • Understanding what form of expression should a multivariate multidivisor algorithm be expected to output, and accordingly understanding `nice' basis as one with unique r property (i.e., w.r.t. which, all such expressions of a polynomial share a certain common part)

    • Meeting 08 : Fri, Jan 30, 02:00 pm-02:50 pm - Harshil M.
      • Monomial ordering and examples, leading terms, multidegree and its behaviour w.r.t. addition and multiplication of polynomials

    • Meeting 09 : Tue, Feb 03, 11:00 am-11:50 am - Harshil M.
      • Understanding general form of single divisor univariate division, adapt it to work for multi-divisor multivariate setting, and showing that the algorithm terminates and returns correct output

    • Meeting 10 : Wed, Feb 04, 10:00 am-10:50 am - Harshil M.
      • Arbitrariness in choice of reducing divisor in division algorithm, its effect on remainder, uniqueness of remainder for nice basis. Setting up the plan: showing that monomial ideals are finitely generated, how it can be used to find a finite basis whose leading terms generate the same ideal that leading terms of polynomials from original ideal generate, showing that this basis has the desired unique-r property. Monomial ideals and its properties

    • Meeting 11 : Thu, Feb 05, 08:00 am-08:50 am -
      • To Be Announced

    • Meeting 12 : Fri, Feb 06, 02:00 pm-02:50 pm -
      • To Be Announced

    • Meeting 13 : Tue, Feb 10, 11:00 am-11:50 am -
      • To Be Announced

    • Meeting 14 : Wed, Feb 11, 10:00 am-10:50 am -
      • To Be Announced

    • Meeting 15 : Thu, Feb 12, 08:00 am-08:50 am -
      • To Be Announced

    • Meeting 16 : Fri, Feb 13, 02:00 pm-02:50 pm -
      • To Be Announced

    • (Upcoming) Meeting 17 : Tue, Feb 17, 11:00 am-11:50 am -
      • To Be Announced

    • (Upcoming) Meeting 18 : Wed, Feb 18, 10:00 am-10:50 am -
      • To Be Announced

  • Theme 3 : Factorization - 18 meetings
  • Theme 4 : PIT and Algebraic complexity theory - 19 meetings