Abstract:
Although scientific computing is generally viewed as the province of differential equations and numerical analysis, combinatorial techniques have long played a crucial role. For instance, graph theory is essential to the study of molecular structures and material science, many problems in linear algebra involve discrete algorithms, and the parallelization of scientific computations leads to numerous combinatorial problems. I will review some of these many successes, and offer suggestions for new areas in which work is needed at this exciting intersection of disciplines.