**Thesis Information**

**Title:** Invariant theory, tensors and computational complexity

**Adviser:** Harm Derksen

**Institution:** University of Michigan

**Graduation Date:** April 2018

**Contact Information**

Email Candidate

Candidate Website

SIGACT Membership No.: 5056964

**Candidate Bio:**

My name is Visu Makam. I am a postdoctoral researcher at the Institute for Advanced Study at Princeton, where my mentor is Avi Wigderson. I received my Ph.D. in mathematics at the University of Michigan in April 2018 under the direction of Harm Derksen.

**Research Summary:**

My research is at the interface of mathematics and theoretical computer science, broadly falling under the purview of invariant theory, representation theory, tensors and complexity. More specifically, I develop and use tools from abstract algebraic subjects to tackle problems in tensors, complexity and other areas of theoretical computer science.

**Teaching Aims:**

My overarching goal in teaching is to teach the students how to think rather than what to think.

**Paper 1:**

More barriers for rank methods, via a "numeric to symbolic" transfer, Ankit Garg, Visu Makam, Rafael Oliveira and Avi Wigderson, FOCS 2019

Link to PDF**Paper 2:**

Polynomial degree bounds for matrix semi-invariants, Harm Derksen and Visu Makam, Advances in Mathematics, 13 April 2017

Link to PDF**Paper 3:**

Singular tuples of matrices is not a null cone (and, the symmetries of algebraic varieties), Visu Makam and Avi Wigderson, arXiv preprint, 2019

Link to PDF**Keywords:** polynomial identity testing, algebraic complexity, geometric complexity theory, invariant theory, tensors