# A direct proof of Mulmuley's weak #P versus NC result

## by Boris Alexeev and Jacob Tsimerman

### Abstract

We present a direct proof of a result Ketan Mulmuley presented at the Institute for Advanced Study during his lecture series "On $$\mathcal P$$ vs $$\mathcal{NP}$$, Geometric Complexity Theory, and the Riemann Hypothesis" on February 9–11, 2009. The result is intended as a "weak form" of $$\mathcal{\#P}$$ versus $$\mathcal{NC}$$ in characteristic zero.

### Approximate citation

Boris Alexeev and Jacob Tsimerman
A direct proof of Mulmuley's weak #P versus NC result
Note, February 2009.