This is an exposition of the contributions of L\'aszl\'o Lov\'asz to mathematics and computer science written on the occasion of the bestowal of the Abel Prize~2021 to him. Our survey, of course, cannot be exhaustive. We sketch remarkable results that solved well-known open and important problems and that -- in addition -- had lasting impact on the development of subsequent research and even started whole new theories. Although discrete mathematics is what one can call the Lov\'asz home turf, his interests were, from the beginning of his academic career, much broader. He employed algebra, geometry, topology, analysis, stochastics, statistical physics, optimization, and complexity theory, to name a few, to contribute significantly to the explosive growth of combinatorics; but he also exported combinatorial techniques to many other fields, and thus built enduring bridges between several branches of mathematics and computer science. Topics such as computational convexity or topological combinatorics, for example, would not exist without his fundamental results. We also briefly mention his substantial influence on various developments in applied mathematics such as the optimization of real-world applications and cryptography.
翻译:本文是对拉斯洛·洛瓦兹(László Lovász)在数学与计算机科学领域贡献的评述,撰写于其荣获2021年阿贝尔奖之际。尽管我们的综述难以穷尽所有成果,但我们将勾勒出那些解决著名开放重要问题、对后续研究发展产生持久影响、甚至开创全新理论体系的卓越工作。虽然离散数学堪称洛瓦兹的"主场领域",但其学术兴趣自职业生涯初期便远更为广泛。他运用代数、几何、拓扑、分析、随机过程、统计物理、优化及复杂性理论等工具,不仅为组合数学的爆炸性发展做出重大贡献,更将组合技术输出至众多其他领域,在数学与计算机科学的多个分支间架设起持久桥梁。例如计算凸性与拓扑组合学等学科,若缺乏他的基础性成果便不会存在。我们还将简要提及他对应用数学各类发展的深远影响,包括现实世界问题的优化与密码学等。