Visu Makam

I am a member with the School of Mathematics at the Institute for Advanced Study. I will be a Wurru Wurru Research fellow in the School of Mathematics and Statistics at the University of Melbourne starting July 2020.

I got my Ph.D from the Department of Mathematics at the University of Michigan in April 2018. My advisor was Prof. Harm Derksen. Prior to joining grad school, I spent my undergraduate years at Chennai Mathematical Institute, where I obtained B.Sc with Honors in Mathematics and Computer Science.

My research interests are in
  • Representation theory
  • Invariant theory
  • Tensors
  • Algebraic complexity
  • Papers and Preprints

    1. Generalized Cayley's Omega process in invariant theory
      Ankit Garg, Visu Makam, Rafael Oliveira and Avi Wigderson (in preparation).

    2. Search problems in algebraic complexity, GCT, and hardness of generators for invariant rings
      Ankit Garg, Visu Makam, Rafael Oliveira and Avi Wigderson (arXiv preprint).

    3. Singular tuples of matrices is not a null cone (and, symmetries of algebraic varieties)
      Visu Makam and Avi Wigderson (arXiv preprint).

    4. Invariant theory and Wheeled PROPs
      Harm Derksen and Visu Makam (arXiv preprint).

    5. More barriers for rank methods, via a "numeric to symbolic" transfer
      Ankit Garg, Visu Makam, Rafael Oliveira and Avi Wigderson
      Proceedings of Foundations of Computer Science (FOCS) 2019: 824-844

    6. An exponential lower bound for the degrees of invariants of cubic forms and tensor actions
      Harm Derksen and Visu Makam
      accepted to Advances in Mathematics.

    7. The regularity lemma is false over small fields
      Harm Derksen and Visu Makam
      Communications in Algebra 48 (2020), no. 3: 1333-1339.

    8. Highly entangled tensors
      Harm Derksen and Visu Makam
      Linear and Multilinear Algebra, published online.

    9. Weyl's polarization theorem in positive charateristic
      Harm Derksen and Visu Makam
      accepted to Transformation groups.

    10. Algorithms for orbit closure separation for invariants and semi-invariants of matrices
      Harm Derksen and Visu Makam (arXiv preprint).

    11. On the tensor rank of \(3 \times 3 \) permanent and determinant
      Siddharth Krishna and Visu Makam (arXiv preprint).

    12. Extensions between Verma modules for dihedral groups
      Gurbir Dhillon and Visu Makam (arXiv preprint).

    13. Explicit tensors of border rank \(2d-2\) in \(K^d \otimes K^d \otimes K^d\) in arbitrary characteristic
      Harm Derksen and Visu Makam
      Linear and Multilinear Algebra 67 (2019), no. 10: 2104-2116.

    14. Degree bounds for semi-invariant rings of quivers
      Harm Derksen and Visu Makam
      J. Pure and Applied Algebra 222 (2018), no.10 : 3282-3292.

    15. Generating invariant rings of quivers in arbitrary characteristic
      Harm Derksen and Visu Makam
      J. Algebra 489 (2017): 435-445.

    16. On non-commutative rank and tensor rank
      Harm Derksen and Visu Makam
      Linear and Multilinear Algebra 66 (2018), no.6: 1069-1084.

    17. Polynomial degree bounds for matrix semi-invariants
      Harm Derksen and Visu Makam
      Advances in Mathematics 310 (2017): 44-63.

    18. Hilbert series and degree bounds for matrix (semi)-invariants
      Visu Makam
      J. Algebra 454 (2016): 14-28.

    Talks