## 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.

### Papers and Preprints

- Generalized Cayley's Omega process in invariant theory

Ankit Garg, Visu Makam, Rafael Oliveira and Avi Wigderson (in preparation).

- Search problems in algebraic complexity, GCT, and hardness of generators for invariant rings

Ankit Garg, Visu Makam, Rafael Oliveira and Avi Wigderson (arXiv preprint).

- Singular tuples of matrices is not a null cone (and, symmetries of algebraic varieties)

Visu Makam and Avi Wigderson (arXiv preprint).

- Invariant theory and Wheeled PROPs

Harm Derksen and Visu Makam (arXiv preprint).

- 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

- 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.

- The regularity lemma is false over small fields

Harm Derksen and Visu Makam

Communications in Algebra**48**(2020), no. 3: 1333-1339.

- Highly entangled tensors

Harm Derksen and Visu Makam

Linear and Multilinear Algebra, published online.

- Weyl's polarization theorem in positive
charateristic

Harm Derksen and Visu Makam

accepted to Transformation groups.

- Algorithms for orbit closure separation for
invariants and semi-invariants of matrices

Harm Derksen and Visu Makam (arXiv preprint).

- On the tensor rank of \(3 \times 3 \) permanent and
determinant

Siddharth Krishna and Visu Makam (arXiv preprint).

- Extensions between Verma modules for dihedral
groups

Gurbir Dhillon and Visu Makam (arXiv preprint).

- 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.

- Degree bounds for semi-invariant rings of
quivers

Harm Derksen and Visu Makam

J. Pure and Applied Algebra**222**(2018), no.10 : 3282-3292.

- Generating invariant rings of quivers in arbitrary
characteristic

Harm Derksen and Visu Makam

J. Algebra**489**(2017): 435-445.

- On non-commutative rank and tensor rank

Harm Derksen and Visu Makam

Linear and Multilinear Algebra**66**(2018), no.6: 1069-1084.

- Polynomial degree bounds for matrix
semi-invariants

Harm Derksen and Visu Makam

Advances in Mathematics**310**(2017): 44-63.

- Hilbert series and degree bounds for matrix
(semi)-invariants

Visu Makam

J. Algebra**454**(2016): 14-28.

### Talks

*Is the variety of singular tuples of matrices a null cone?*CSDM Seminar, Institute for Advanced Study.*An invitation to invariant theory*CSDM Seminar, Institute for Advanced Study.*Invariant theory meets P vs NP,*Special Colloquium, UC Irvine.*Hardness of generators for invariant rings,*Rutgers/DIMACS Theory seminar.*Adventures in 21st century invariant theory,*Auburn university.*A complexity--theoretic view of invariant theory,*ETH--ITS, Zurich.*Weyl's polarization theorem in positive characteristic,*Combinatorics seminar, LaCIM, Montreal.*Barriers to lifting techniques for tensor rank lower bounds,*CS theory seminar, Purdue University.*Singular tuples of matrices is not a null cone,*Algebraic Geometry seminar, Purdue University.*More barriers for rank methods, via a "numeric to symbolic" transfer,*FOCS 2019.*Singular tuples of matrices is not a null cone,*CAGE Seminar, University of Pennsylvania.*Singular tuples of matrices is not a null cone,*TU Berlin.*A recent perspective on invariant theory,*Members seminar, Institute for Advanced Study, Princeton.*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.*Exponential degree lower bounds for invariant rings,*Geometry seminar, Texas A&M university.*Why can't we prove tensor rank and Waring rank lower bounds?,*CSDM seminar, Institute for Advanced Study, Princeton.*Non-commutative rank,*CSDM seminar, Institute for Advanced Study, Princeton.*Generic vs symbolic behaviour and power series,*Algebraic methods workshop, Simons institute, Berkeley.*Weyl's polarization theorem in positive characteristic,*Sixth conference on geometric methods in representation theory, University of Iowa.*Degree lower bounds for SLn invariants,*AMS special session on commutative algebra and complexity, Ann Arbor.*Algorithms in invariant theory,*Optimization, Complexity and Invariant Theory, Institute for Advanced Study, Princeton.*Algorithms for orbit closure separation for invariants and semi-invariants of matrices,*AMS special session on algebraic geometry, representation theory, Nashville.*Degree bounds for invariant rings of quivers,*Commutative algebra and Algebraic geometry seminar, UC Berkeley.*Degree bounds for invariant rings of quivers,*Geometry seminar, UIUC.*Degree bounds for invariant rings of quivers,*Geometry seminar, Texas A&M university.*Polynomial degree bounds for matrix semi-invariants,*Graduate student combinatorics conference 2017.*Linear matrices and their applications to complexity,*Rice University CS Colloquium.*Polynomial degree bounds for matrix semi-invariants,*ICRA 2016 .*Polynomial degree bounds for matrix semi-invariants,*Fourth Conference on Geometric Methods in Representation Theory.*Linear matrices and their applications to semi-invariants of quivers,*Chennai Mathematical Institute.*Polynomial degree bounds for matrix semi-invariants,*Algebra and number theory seminar, Louisiana State University.*Rank computation of linear matrices and applications to circuit complexity,*CS Theory seminar, NYU.*Polynomial degree bounds for matrix semi-invariants,*Algebra and Representation theory seminar, Oklahoma University.