New cases of zeta functions of Shimura varieties
Pol van Hoften
Hasse–Weil zeta functions are generalizations of the famous Riemann zeta function, and play a central role in modern algebraic number theory. Mathematician Pol van Hoftens proposal suggests new strategies to compute the Hasse–Weil zeta functions of Shimura varieties. These are products of local zeta functions, one for each prime number. Local zeta functions of Shimura varieties are well understood at all but finitely many primes, and this proposal concerns the computation of the local zeta functions at the remaining primes (the so-called “very bad” primes).
Graphs and Hypergraphs: from Combinatorics to Network Science and back
Raffaella Mulas
Graphs and hypergraphs have been challenging combinatorialists since 1736 and 1931, respectively. Moreover, in the past two decades, scientists have been rapidly finding applications of graphs which has led to the emergence of network science as its own discipline, where hypergraphs are gaining increasing attention. Nevertheless, combinatorialists and network scientists often use distinct languages and methodologies. Mathematician Raffaella Mulas' goal is to exploit her interdisciplinary profile to work on a braid where combinatorics, spectral theory and applications (to areas such as network science and machine learning) will inspire each other and will advance together in a unified manner rather than independently.