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Electronic Colloquium on Computational Complexity

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REPORTS > KEYWORD > INVARIANT THEORY:
Reports tagged with Invariant theory:
TR18-151 | 29th August 2018
Ankit Garg, Rafael Oliveira

Recent progress on scaling algorithms and applications

Scaling problems have a rich and diverse history, and thereby have found numerous
applications in several fields of science and engineering. For instance, the matrix scaling problem
has had applications ranging from theoretical computer science to telephone forecasting,
economics, statistics, optimization, among many other fields. Recently, a generalization of matrix
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TR19-114 | 2nd September 2019
Visu Makam, Avi Wigderson

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

The following multi-determinantal algebraic variety plays a central role in algebra, algebraic geometry and computational complexity theory: ${\rm SING}_{n,m}$, consisting of all $m$-tuples of $n\times n$ complex matrices which span only singular matrices. In particular, an efficient deterministic algorithm testing membership in ${\rm SING}_{n,m}$ will imply super-polynomial circuit lower bounds, ... more >>>




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