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**UNC PHYSICS AND ASTRONOMY COLLOQUIUM **

Andre LeClair, Cornell University

**“The Riemann Hypothesis for Physicists”**

I will first describe some important appearances of Riemann’s zeta function

in quantum statistical mechanics. The intimate connection of the zeros of Riemann’s zeta function with the distribution of the Prime Numbers, the Riemann Hypothesis, and how the statistics of the zeros is that of the Gaussian Unitary Ensemble in random matrix theory, will all be reviewed. Then I will turn to recent work on characterizing the zeros as solutions to novel transcendental equations, and describe how these results could perhaps be used to prove the Riemann Hypothesis.