Walsh has previously held a Clay Research Fellowship and was a fellow of Merton College at the University of Oxford.
He obtained his undergraduate degree in 2010 from the University of Buenos Aires and his PhD, also from the same institution, in 2012.
[3][8] In June 2017 Walsh was invited to present his research at the 2018 International Congress of Mathematicians in Rio de Janeiro, Brazil.
[11] That same year, he received the UMALCA Award of the Mathematical Union of Latin America and the Caribbean.
[12] He is one of two 2024 recipients of the Salem Prize, given "for contributions to ergodic theory, analytic number theory, and the development of the polynomial method, including a convergence theorem for nonconventional ergodic averages, bounds on the local Fourier uniformity of multiplicative functions, and bounds on rational points on varieties".