Ankit Garg, Rafael Oliveira

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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Visu Makam, Avi Wigderson

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 >>>

Ankit Garg, Visu Makam, Rafael Mendes de Oliveira, Avi Wigderson

We consider the problem of outputting succinct encodings of lists of generators for invariant rings. Mulmuley conjectured that there are always polynomial sized such encodings for all invariant rings. We provide simple examples that disprove this conjecture (under standard complexity assumptions).

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