Sage-Days Workshop on Computational Arithmetic Dynamics 2019

该奖项支持参加2019年11月17日至20日在圣刘易斯大学举行的计算算术动力学圣人日研讨会。在过去的几十年里，计算机在科学领域的应用得到了极大的扩展。随着要解决的问题的复杂性越来越高，硬件解决这些问题的能力越来越大，学生和研究人员必须拥有尖端的计算工具。该研讨会汇集了动力系统的研究人员，以进一步开发用于研究和应用的开源计算工具。算术动力学是一个相对较新的数学领域，在数论，动力系统和算术几何的交叉点。在其最基本的，它涉及的决议的方程组所产生的迭代系统。它对其他学科的价值在于具体的结构和计算工具。应用范围从天气预测到细胞建模，再到密码学。现代计算工具在这些应用中具有巨大的潜力。这些工具将在开放源码软件Sage中实施，并根据GNU公共许可证免费向公众提供。除了开发计算工具外，讲习班的另一个主要目标是培训如何使用这些计算工具。该研讨会的参与者将精通当前的工具，并能够培训同事和学生使用这些工具。最后，这些工具将用于改进动力系统的数据库。多年来，数学家们一直在编制计算密集型信息的表格，以供广泛使用。这些工具目前能够计算一组广泛的属性，将使用的研究社区在一个有组织的搜索形式。动力系统的数据库为动力系统社区提供这种服务。本次研讨会的目标是改进计算机代数系统Sage中包含的动力系统的当前计算工具集。这些工具允许人们快速有效地使用明确的例子来测试和证明新的理论，计算太复杂而无法手工计算的例子，并允许学生明确地研究结构和具体的例子。随着当前工具集的成熟，我们已经达到了可以计算动力系统的许多属性的地步。因此，建立一个数据库来组织已知的例子是可行的。一个全面、有效、可搜索的例子集将对研究界有很大的用处。动力系统数据库的现有原型将在这次讲习班上得到改进和扩大。由于这些工具是免费提供的，使用这些工具的主要障碍是培训/教育。组织者将积极招募女性和其他在数学团体中代表不足的人参加这个研讨会，重点是研究生，博士后和早期职业教师。更多信息可在研讨会网页www.example.com上获得http://mathstat.slu.edu/~hutzba/sage_days_2019.htmlThis奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

This award supports participation in the Sage-Days Workshop on Computational Arithmetic Dynamics held November 17-20, 2019 at Saint Louis University. The use of computers in the sciences over the last several decades has expanded enormously. With the increasing complexity of problems to be solved and increasing capacity of hardware to solve these problems, it is essential that students and researchers have cutting-edge computational tools available to them. This workshop brings together researchers in dynamical systems to further the development of open-source computational tools for use both in research and applications. Arithmetic dynamics is a relatively new area of mathematics at the intersection of number theory, dynamical systems, and arithmetic geometry. At its most fundamental, it concerns the resolution of systems of equations that arise from iterated systems. Its value to other disciplines lies in concrete constructions and computational tools. Applications range from weather prediction, to cellular modelling, to cryptography. Modern computational tools have great potential in these applications. These tools will be implemented in the open-source software Sage and made freely available to the public under the GNU public license. In addition to the development of computational tools, another main goal of the workshop is the training in the use of these computational tools. Participants of this workshop will become proficient in the current tools and be able to train colleagues and students in their use. Finally, these tools will be used to improve the database of dynamical systems. For ages, mathematicians have been compiling tables of computationally intensive information for widespread use. These tools are currently capable of computing an extensive set of properties that would be of use to the research community in an organized searchable form. The database of dynamical systems performs this service for the dynamical systems community.A goal of this workshop is to improve the current set of computational tools for dynamical systems included in the computer algebra system Sage. The tools allow one to quickly and efficiently work with explicit examples to test and prove new theories, to compute examples too complicated to be worked out by hand, and to allow students to explicitly investigate conjectures and specific examples. With the maturity of the current set of tools, we have reached the point where we can compute many properties of dynamical systems. Consequently, the creation of a database to organize the known examples is feasible. A comprehensive efficiently searchable collection of examples will be of considerable use to the research community. The current prototype of the database of dynamical systems will be improved and expanded at this workshop. With the tools freely available, the main barrier to their use is training/education. The organizers will actively recruit women and other under-represented in mathematics groups to this workshop, with a focus on graduate students, post-docs, and early career faculty.More information is available at the workshop web page http://mathstat.slu.edu/~hutzba/sage_days_2019.htmlThis 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.