Mathematics

The Selberg integral, originally relegated by its namesake to the pages of a regional publication targeted at secondary education students, has now found bountiful application throughout a wide swath of mathematical disciplines. Of particular interest, the Selberg integral (along with the closely related Mehta and Dixon-Anderson integrals) arise in random matrix theory as the normalization for several classes of $\beta$-ensembles, and are also use in the subsequent calculation of correlation functions for these ensembles. In this talk, we will discuss a technique for evaluating certain Selberg-type integrals using the shuffle algebra that realizes the result as a Hyperpfaffian of a particular anti-symmetric form.