【报告摘要】Integer multiplication is one of the oldest mathematical operations and still a central problem for computer arithmetic. The complexities of many other basic operations such as division, base conversion, gcds, computing e and pi, FFTs, etc. can be expressed in terms of the complexity of integer multiplication. In our talk, we will survey a new algorithm for multiplying two n-digit integers in time O(n log n).

【报告人简介】Joris van der Hoeven is a Dutch mathematician and computer scientist. He is currently a Research Director at the French National Centre for Scientific Research and also heads the Symbolic Computation team in the Department of Computer Science at École Polytechnique in Paris. His main research areas are differential algebra, asymptotic analysis and computer algebra, especially transseries (a generalization of formal power series) and their applications in the asymptotic solutions of nonlinear differential equations. In 2018, he was invited to give a 45-minute invited talk at the International Congress of Mathematicians. In 2019, he and David Harvey discovered the fastest integer multiplication algorithm, and this achievement was published in the Annals of Mathematics in 2021. He has received the Karp Award and the N.G. de Bruijn Award. In terms of software development, he is a major developer of GNU TeXmacs (a free scientific editing platform) and Mathe Magix (a free computer algebra and analysis system).