Visu Makam

activity

20152024

most citedAlgorithms for orbit closure separation for invariants and semi-invariants of matrices

15 citations · 63 across the 17 of their papers we have counts for

collaborators

29 papers

cs.CC2024★ 1 cited

Complexity of Robust Orbit Problems for Torus Actions and the abc-conjecture

Peter Bürgisser, Mahmut Levent Doğan, Visu Makam +2

When a group acts on a set, it naturally partitions it into orbits, giving rise to orbit problems. These are natural algorithmic problems, as symmetries are central in numerous que…

math.ST2023

iPCA and stability of star quivers

Cole Franks, Visu Makam

Integrated principal components analysis, or iPCA, is an unsupervised learning technique for grouped vector data recently defined by Tang and Allen. Like PCA, iPCA computes new axe…

quant-ph2022★ 14 cited

The minimal canonical form of a tensor network

Arturo Acuaviva, Visu Makam, Harold Nieuwboer +4

Tensor networks have a gauge degree of freedom on the virtual degrees of freedom that are contracted. A canonical form is a choice of fixing this degree of freedom. For matrix prod…

cs.CC2022

Subrank and Optimal Reduction of Scalar Multiplications to Generic Tensors

Harm Derksen, Visu Makam, Jeroen Zuiddam

Since the seminal works of Strassen and Valiant it has been a central theme in algebraic complexity theory to understand the relative complexity of algebraic problems, that is, to…

cs.IT2022★ 2 cited

Generic Reed-Solomon Codes Achieve List-decoding Capacity

Joshua Brakensiek, Sivakanth Gopi, Visu Makam

In a recent paper, Brakensiek, Gopi and Makam introduced higher order MDS codes as a generalization of MDS codes. An order- $ℓ$ MDS code, denoted by $MDS (ℓ)$ , h…

math.RA2021★ 5 cited

Ranks of linear matrix pencils separate simultaneous similarity orbits

Harm Derksen, Igor Klep, Visu Makam +1

This paper solves the two-sided version and provides a counterexample to the general version of the 2003 conjecture by Hadwin and Larson. Consider evaluations of linear matrix penc…

math.ST2021

Symmetries in Directed Gaussian Graphical Models

Visu Makam, Philipp Reichenbach, Anna Seigal

We define Gaussian graphical models on directed acyclic graphs with coloured vertices and edges, calling them RDAG (restricted directed acyclic graph) models. If two vertices or ed…

math.RT2021

Polystability in positive characteristic and degree lower bounds for invariant rings

Harm Derksen, Visu Makam

We develop a representation theoretic technique for detecting closed orbits that is applicable in all characteristics. Our technique is based on Kempf's theory of optimal subgroups…

cs.IT2021★ 1 cited

Lower Bounds for Maximally Recoverable Tensor Code and Higher Order MDS Codes

Joshua Brakensiek, Sivakanth Gopi, Visu Makam

An $(m, n, a, b)$ -tensor code consists of $m \times n$ matrices whose columns satisfy ` $a$ ' parity checks and rows satisfy ` $b$ ' parity checks (i.e., a tensor code is the tensor produc…

cs.DS2021★ 2 cited

Polynomial time algorithms in invariant theory for torus actions

Peter Bürgisser, M. Levent Doğan, Visu Makam +2

An action of a group on a vector space partitions the latter into a set of orbits. We consider three natural and useful algorithmic "isomorphism" or "classification" problems, name…

math.ST2020★ 11 cited

Maximum likelihood estimation for tensor normal models via castling transforms

Harm Derksen, Visu Makam, Michael Walter

In this paper, we study sample size thresholds for maximum likelihood estimation for tensor normal models. Given the model parameters and the number of samples, we determine whethe…

math.RT2020

Maximum likelihood estimation for matrix normal models via quiver representations

Harm Derksen, Visu Makam

In this paper, we study the log-likelihood function and Maximum Likelihood Estimate (MLE) for the matrix normal model for both real and complex models. We describe the exact number…

cs.CC2019★ 8 cited

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

Ankit Garg, Christian Ikenmeyer, Visu Makam +3

We consider the problem of computing succinct encodings of lists of generators for invariant rings for group actions. Mulmuley conjectured that there are always polynomial sized su…

math.RT2019★ 1 cited

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

Visu Makam, Avi Wigderson

The following multi-determinantal algebraic variety plays a central role in algebra, algebraic geometry and computational complexity theory: $SING_{n, m}$ , consisting of all $…

math.RT2019

Invariant theory and wheeled PROPs

Harm Derksen, Visu Makam

We study the category of wheeled PROPs using tools from Invariant Theory. A typical example of a wheeled PROP is the mixed tensor algebra $V = T (V) \otimes T (V^{⋆})$ , whe…

cs.CC2019

More barriers for rank methods, via a "numeric to symbolic" transfer

Ankit Garg, Visu Makam, Rafael Oliveira +1

We prove new barrier results in arithmetic complexity theory, showing severe limitations of natural lifting (aka escalation) techniques. For example, we prove that even optimal ran…

math.RT2019

An exponential lower bound for the degrees of invariants of cubic forms and tensor actions

Harm Derksen, Visu Makam

Using the Grosshans Principle, we develop a method for proving lower bounds for the maximal degree of a system of generators of an invariant ring. This method also gives lower boun…

math.RA2018

The regularity lemma is false over small fields

Harm Derksen, Visu Makam

The regularity lemma is a stringent condition of the possible ranks of tensor blow-ups of linear subspaces of matrices. It was proved by Ivanyos, Qiao and Subrahmanyam when the und…

math.OC2018

Highly entangled tensors

Harm Derksen, Visu Makam

A geometric measure for the entanglement of a unit length tensor $T \in (C^{n})^{\otimes k}$ is given by $- 2 lo g_{2} ∣∣ T ∣ ∣_{σ}$ , where $∣∣.∣ ∣_{σ}$ denotes the spectral norm. A s…

math.RT2018

Weyl's polarization theorem in positive characteristic

Harm Derksen, Visu Makam

Let $V$ be an $n$ -dimensional algebraic representation over an algebraically closed field $K$ of a group $G$ . For $m > 0$ , we study the invariant rings $K [V^{m}]^{G}$ for the diagon…

math.RA2018★ 15 cited

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

Harm Derksen, Visu Makam

We consider two group actions on $m$ -tuples of $n \times n$ matrices. The first is simultaneous conjugation by $GL_{n}$ and the second is the left-right action of $\op…

math.CO2018

On the tensor rank of $3 \times 3$ permanent and determinant

Siddharth Krishna, Visu Makam

The tensor rank and border rank of the $3 \times 3$ determinant tensor is known to be $5$ if characteristic is not two. In this paper, we show that the tensor rank remains $5$ for…

math.RT2017★ 2 cited

Extensions between Verma modules for dihedral groups

Gurbir Dhillon, Visu Makam

Computing the extensions between Verma modules is in general a very difficult problem. Using Soergel bimodules, one can construct a graded version of the principal block of Categor…

math.RA2017★ 1 cited

Explicit tensors of border rank at least $2 d - 2$ in $K^{d} \otimes K^{d} \otimes K^{d}$ in arbitrary characteristic

Harm Derksen, Visu Makam

For tensors in $C^{d} \otimes C^{d} \otimes C^{d}$ , Landsberg provides non-trivial equations for tensors of border rank $2 d - 3$ for $d$ even and $2 d - 5$ for $d$ …

Complexity of Robust Orbit Problems for Torus Actions and the abc-conjecture

iPCA and stability of star quivers

The minimal canonical form of a tensor network

Subrank and Optimal Reduction of Scalar Multiplications to Generic Tensors

Generic Reed-Solomon Codes Achieve List-decoding Capacity

Ranks of linear matrix pencils separate simultaneous similarity orbits

Symmetries in Directed Gaussian Graphical Models

Polystability in positive characteristic and degree lower bounds for invariant rings

Lower Bounds for Maximally Recoverable Tensor Code and Higher Order MDS Codes

Polynomial time algorithms in invariant theory for torus actions

Maximum likelihood estimation for tensor normal models via castling transforms

Maximum likelihood estimation for matrix normal models via quiver representations

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

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

Invariant theory and wheeled PROPs

More barriers for rank methods, via a "numeric to symbolic" transfer

An exponential lower bound for the degrees of invariants of cubic forms and tensor actions

The regularity lemma is false over small fields

Highly entangled tensors

Weyl's polarization theorem in positive characteristic

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

On the tensor rank of 3×3 permanent and determinant

Extensions between Verma modules for dihedral groups

Explicit tensors of border rank at least 2d−2 in Kd⊗Kd⊗Kd in arbitrary characteristic

On the tensor rank of $3 \times 3$ permanent and determinant

Explicit tensors of border rank at least $2 d - 2$ in $K^{d} \otimes K^{d} \otimes K^{d}$ in arbitrary characteristic