## Visu Makam

I am a member with the School of Mathematics at the Institute for Advanced Study from Sep 2018 to Aug 2020. I am on the job market in Fall 2019.

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
accepted to FOCS 2019.

6. An exponential lower bound for the degrees of invariants of cubic forms and tensor actions
Harm Derksen and Visu Makam (arXiv preprint).

7. The regularity lemma is false over small fields
Harm Derksen and Visu Makam
accepted to Communications in Algebra (pending minor revisions).

8. Highly entangled tensors
Harm Derksen and Visu Makam (arXiv preprint).

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 (published online).

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

• Nov 2019, Weyl's polarization theorem in positive characteristic, Combinatorics seminar, LaCIM, Montreal.

• Nov 2019, Barriers to lifting techniques for tensor rank lower bounds, CS theory seminar, Purdue University.

• Nov 2019, Singular tuples of matrices is not a null cone, Algebraic Geometry seminar, Purdue University.

• Nov 2019, More barriers for rank methods, via a "numeric to symbolic" transfer, FOCS 2019.

• Oct 2019, Singular tuples of matrices is not a null cone, CAGE Seminar, University of Pennsylvania.

• Sep 2019, Singular tuples of matrices is not a null cone, TU Berlin.

• Apr 2019, A recent perspective on invariant theory, Members seminar, Institute for Advanced Study, Princeton.

• Mar 2019, Invariant theory, tensors and computational complexity, Sumner Myers Colloquium (for the best thesis award in the department of mathematics, UM) University of Michigan at Ann Arbor.

• Mar 2019, Exponential degree lower bounds for invariant rings, Geometry seminar, Texas A&M university.

• Feb 2019, Why can't we prove tensor rank and Waring rank lower bounds?, CSDM seminar, Institute for Advanced Study, Princeton.

• Feb 2019, Non-commutative rank, CSDM seminar, Institute for Advanced Study, Princeton.

• Dec 2018, Generic vs symbolic behaviour and power series, Algebraic methods workshop, Simons institute, Berkeley.

• Nov 2018, Weyl's polarization theorem in positive characteristic, Sixth conference on geometric methods in representation theory, University of Iowa.

• Oct 2018, Degree lower bounds for SLn invariants, AMS special session on commutative algebra and complexity, Ann Arbor.

• Jun 2018, Algorithms in invariant theory, Optimization, Complexity and Invariant Theory, Institute for Advanced Study, Princeton.

• Apr 2018, Algorithms for orbit closure separation for invariants and semi-invariants of matrices, AMS special session on algebraic geometry, representation theory, Nashville.

• Nov 2017, Degree bounds for invariant rings of quivers, Commutative algebra and Algebraic geometry seminar, UC Berkeley.

• Oct 2017, Degree bounds for invariant rings of quivers, Geometry seminar, UIUC.

• Sep 2017, Degree bounds for invariant rings of quivers, Geometry seminar, Texas A&M university.

• Apr 2017, Polynomial degree bounds for matrix semi-invariants, Graduate student combinatorics conference 2017.

• Oct 2016, Linear matrices and their applications to complexity, Rice University CS Colloquium.

• Aug 2016, Polynomial degree bounds for matrix semi-invariants, ICRA 2016 .

• Nov 2016, Polynomial degree bounds for matrix semi-invariants, Fourth Conference on Geometric Methods in Representation Theory.

• Jun 2016, Linear matrices and their applications to semi-invariants of quivers, Chennai Mathematical Institute.

• Apr 2016, Polynomial degree bounds for matrix semi-invariants, Algebra and number theory seminar, Louisiana State University.

• Apr 2016, Rank computation of linear matrices and applications to circuit complexity, CS Theory seminar, NYU.

• Apr 2016, Polynomial degree bounds for matrix semi-invariants, Algebra and Representation theory seminar, Oklahoma University.