Conference: ASE60: Synergistic Interactions between Theory and Computation

“理论与计算之间的协同互动”会议将于2023年7月27日至29日在马萨诸塞州剑桥市的麻省理工学院举行。这次会议将集中讨论理论和计算之间的联系，特别是关于计算的“技巧”，这些“技巧”可以带来深刻的理论见解，以及在快速、高性能的计算中使用深刻的理论结果。三个特定的兴趣领域是随机矩阵理论，数值线性代数和现代科学计算。知名专家和有前途的初级研究人员将展示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学科边界互动的机会。许多研究人员在两个或两个以上这些领域的交叉点工作，这将促进这种相互作用。除了演讲，我们还为年轻的参与者安排了一个海报会议，这样他们就可以公布他们的成果，并从观众中的专家那里得到反馈和指导。随机矩阵理论有着无数的现代应用，从随机数值线性代数到信号处理，从优化到机器学习，通过计算和数值技巧得到了贝塔集合的三对角线理论模型和通过Kolmogorov倒向方程计算极限分布的知识和深化。另一方面，在数值线性代数中使用随机化是一个快速发展的子领域，因为处理非常大的数据集的重要性，而经典的确定性算法太慢了。新方法广泛使用随机矩阵工具，而正确解决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、结构化和快速准确的近似，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被设计为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，并希望在专家和初级参与者之间开始和培养合作，这将在未来几年结出硕果。该奖项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知识价值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.