The field of polynomial systems and stochastic processes is witnessing significant developments, with a focus on innovative techniques and applications. Researchers are exploring new methods for analyzing and solving polynomial systems, such as geometric approaches to program synthesis and algebraic geometry tools for designing and implementing algorithms. Furthermore, stochastic processes are being investigated in various contexts, including multiplicative rewards in Markovian models and stochastic rounding with few random bits. These advances have the potential to impact a wide range of areas, from machine learning and optimization to formal program verification. Noteworthy papers in this area include:

• Smooth Approximations of the Rounding Function, which proposes novel smooth approximations to the classical rounding function, and
• Positive Almost-Sure Termination of Polynomial Random Walks, which shows that a general class of polynomial random walks is positive almost-sure termination.