Conference: ASE60: Synergistic Interactions between Theory and Computation

“理论和计算之间的协同互动”会议将于2023年7月27-29日在麻省理工学院剑桥举行。这次会议将集中讨论理论和计算之间的关系，特别是导致深刻的理论洞察的计算“技巧”，以及在快速、高性能计算中使用深刻的理论结果。感兴趣的三个具体领域是随机矩阵理论、数值线性代数和现代科学计算。资深专家和有前途的初级研究人员将介绍最新的进展和最先进的技术。我们寻求富有成效的思想交流和跨越学科界限的互动机会。在这些领域的两个或多个交叉领域工作的众多研究人员的到场，将促进这种互动。除了演讲外，我们还为年轻参与者安排了一个海报会议，以便他们可以公布他们的结果，并从观众中的专家那里获得反馈和指导。随机矩阵理论具有从随机化数值线性代数到信号处理以及从优化到机器学习的无数现代应用，它被计算和数值技巧所启发和深化，这些技巧产生了贝塔系综的三对角线理论模型，并通过科尔莫戈洛夫的反向方程计算极限分布。另一方面，在数值线性代数中使用随机化是一个快速增长的子领域，这是因为处理超大数据集的重要性，而经典的确定性算法对这些数据集来说太慢了。新方法广泛使用了随机矩阵工具，而适当处理机器学习和优化应用的需要反过来又指导了随机矩阵理论的现代发展。最后，现代高性能计算需要在后端处理稀疏性、结构化以及快速和准确的近似，并且必须允许用户在前端编写读起来像数学的代码；像Julia这样的现代编程语言的设计允许使用高性能代码进行高级数学抽象。我们的目标是将上述三个社区聚集在一起，以促进跨学科研究，并希望开始和促进专家和初级参与者之间的合作，这些合作将在未来几年取得成果。会议的网站是：https://math.mit.edu/events/ase60celebration/This奖反映了美国国家科学基金会的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The conference "Synergistic Interactions Between Theory and Computation" will be held at the Massachusetts Institute of Technology, Cambridge, MA, July 27-29, 2023. This meeting will focus on the nexus between theory and computation, particularly on computational "tricks'' that lead to deep theoretical insight, and on the use of deep theoretical results in fast, high-performing computation. Three specific areas of interest are random matrix theory, numerical linear algebra, and modern scientific computing. Established experts and promising junior researchers will present the latest advances and state-of-the-art techniques. We seek a fruitful exchange of ideas and the opportunity to interact across disciplinary boundaries. This interaction will be facilitated by the presence of numerous researchers who work at the intersection of two or more of these areas. In addition to the presentations, we have scheduled a poster session for young participants so they can publicize their results and receive feedback and guidance from the experts in the audience. Random matrix theory, with its myriad modern applications from randomized numerical linear algebra to signal processing and from optimization to machine learning, is informed and deepened by computational and numerics tricks of the sort that have yielded tridiagonal theoretical models for beta-ensembles and calculating limiting distributions via Kolmogorov's backward equation. On the other hand, the use of randomization in numerical linear algebra is a fast-growing subfield, due to the importance of working with extremely large datasets for which classical, deterministic algorithms are too slow. The new methods make extensive use of random matrix tools, while the need to properly address machine learning and optimization applications has in turn guided the modern development of random matrix theory. Finally, modern high-performance computing needs to deal with sparseness, structure, and fast and accurate approximation on the back end, and must allow the users to write code that reads like mathematics on the front end; modern programming languages like Julia are designed to allow for high-level mathematical abstraction with high-performance code. We aim to bring together the three aforementioned communities in order to foster interdisciplinary research and hopefully start and nurture collaborations among both experts and junior participants that will bear fruit in the years to come. The conference website is at: https://math.mit.edu/events/ase60celebration/This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.