Seminar on Combinatorial Aspects of Commutative Algebra and Algebraic Geometry (in IITB)

  • Update from 8-th September meeting:
  • This semester (probably the next) we plan to focus on aspects of syzygies: combinatorial, algebraic, geometric. We’ll devote the first few lectures to the basics of syzygies.

    In the future, we plan to cover various aspects of the interplay between Combinatorics and Commutative Algebra-Algebraic Geometry. Some possible topics are

    i. Syzygies: connections to Combinatorics, Syzygies of curves particularly Green’s conjecture and the related conjecture for Graph Curves, Boij-Soederberg theory, Syzygies in Tropical geometry.

    ii. Vector Bundles with potential connections to Tropical Geometry.

    iii. Dessins on D’enfants:

    iv. Brill-Noether theory on Algebraic curves and Tropical curves, Combinatorial Aspects of Moduli Spaces.

    v. Non-archimedean Geometry in connection with Tropical Geometry, particular Berkovich Spaces,

    vi. Combinatorics and Hodge theory, Vector Partition Functions.

    vii. Ideals of Powers of Linear Forms.

    viii. Tutte Polynomials of Graphs, Zeta Functions associated to Graphs.

    ix. Syzygies in Real Algebraic Geometry.

    x. Tropical Geometry in Dimensions Two and Higher.

    We plan to pick a theme every semester followed by talks by local faculty and students. These talks will be introductory and will assume very little background. We will then invite speakers from outside for more specialized talks on this theme.


    Madhusudan Manjunath

    Welcome to my homepage! I am an Assistant Professor in the Department of Mathematics, IIT Bombay.

    I was visiting the IHES, October 20-December 2, 2017.
    Earlier this year I spent four months at the Erwin Schroedinger Institute for Mathematics and Physics, Vienna as a Junior Research Fellow and three months at the Mathematics Institute at Oberwolfach (MFO) as a Leibniz Fellow .
    Until recently, I have been a postdoctoral researcher at the School of Mathematical Sciences at Queen Mary University of London and a Visiting Assistant Professor at the Mathematics Department at University of California Berkeley. My position in Berkeley was partially funded by Feoder-Lynen Fellowship of the Humboldt Foundation. My mentor was Prof. Bernd Sturmfels. Previously, I was a visiting assistant professor at the School of Mathematics, Georgia Institute of Technology where my mentor was Prof. Matt Baker.


    August 4, 2017, Currently in Bangalore, will join IITB mid-August. Visiting IHES, Paris October 20-December 20, 2017.

    July 6, 2017, We are planning to a start a seminar on “Combinatorial Aspects of Algebraic Geometry and Commutative Algebra” in IIT Bombay starting August, 2017. More details will follow soon.

    May 23, 2017, I’ll be starting as an Assistant Professor in the Department of Mathematics, IIT Bombay from August 2017.

    April 1, 2017, Commutative Algebra of Generalised Frobenius Numbers is on the arxiv.

    January 8, 2017: I will spend time at MFO, Schroedinger Institute in Vienna and IHES Paris this year.

    November 4, 2016: Back to London and expect to be here till the end of December.

    October 24, 2016: Visiting Rice University, 26, 27 October and then Minneapolis for the AMS Special Session on “Chip Firing, Divisors on Graph and Simplicial Complex”, October 28-30. My talk is on Saturday, 29 October.

    October 6, 2016: We are holding a Tropical Geometry Seminar at Imperial this term. Our first meeting will be at Huxley 109, 4pm tomorrow (October 7). Please drop by or write to me if you want to know more about it.

    September 13, 2016: Back to London and expect to be in this area throughout September.

    August 1, 2016: Visiting India August 5-September 7, 2016. I will visit TIFR, Mumbai, IIT Bombay and IIT Madras.

    July 25, 2016: I am attending Latin American Algebra at Buones Aires, Argentina 26-29 July. I’ll speak at the special session on Computational Algebra and Applications of Algebra on Friday 29 July.

    July 20, 2016: I will visit MFO, Oberwolfach on a Leibniz Fellowship from January-March 2017.

    June 24, 2016: Syzygies over the Polytope Semiring is up on the arxiv.


    School of Mathematical Sciences,
    Queen Mary University of London,
    Mile End Road,
    London, E1 4NS.



    My research interests are in the combinatorial aspects of algebraic geometry and commutative algebra. Specifically,