A (2+1)-dimensional Gaussian field as fluctuations of quantum random walks on quantum groups

This paper introduces a (2+1)-dimensional Gaussian field which has the Gaussian free field on the upper half-plane with zero boundary conditions as certain two-dimensional sections. Along these sections, called space-like paths, it matches the Gaussian field from eigenvalues of random matrices and from a growing random surface. However, along time-like paths the behavior is different. The Gaussian field arises as the asymptotic fluctuations in quantum random walks on quantum groups U_q(gl_n). This quantum random walk is a q-deformation of previously considered quantum random walks. The construction is accomplished utilizing Etingof-Kirillov difference operators in place of differential operators on GL(n). When restricted to the space-like paths, the moments of the quantum random walk match the moments of the growing random surface

Progress, challenges, and responsibilities in retrovirology

In this editorial, Retrovirology's choice for best basic science "retrovirus paper of the year" and a perspective on challenges and responsibilities facing HIV-1 and HTLV-I research are presented

Hybrid Bounds on Twisted L-Functions Associated to Modular Forms

For $f$ a primitive holomorphic cusp form of even weight $k \geq 4$, level $N$, and $\chi$ a Dirichlet character mod $Q$ with $(Q,N)=1$, we establish a new hybrid subconvexity bound for $L(1/2 + it, f_\chi)$, which improves upon all known hybrid bounds. This is done via amplification and taking advantage of a shifted convolution sum of two variables defined and analyzed in a recent paper of Hoffstein and Hulse.Comment: Updated version removes the restriction of level being square-fre