Mid-Atlantic Topology Symposium: New Directions

大西洋中部拓扑研讨会：新方向

• 批准号: 1619569
• 负责人: Jack Morava
• 金额: $ 1.2万
• 依托单位: Johns Hopkins University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-03-01 至 2017-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1619569&HistoricalAwards=false
• 关键词: Mid; Atlantic; Topology; Symposium; New

The Mathematics Department at Johns Hopkins University is hosting a "Mid-Atlantic Topology Symposium: New Directions" at the Homewood campus in Baltimore, Maryland, Saturday-Sunday, March 12-13 2016. This meeting is inspired by a similar conference which took place in Spring 2015 at the University of Virginia. The PIs intend to establish a tradition of such meetings. Algebraic topology, geometry, and category theory are in the midst of a generational shift of language, techniques and paradigms, rooted in new ideas about higher homotopy-theoretic structures in geometry, physics, category theory, and data analysis. These fields are in ferment, with a forefront defined by a younger generation of researchers who bring new ideas from higher algebra to classical areas of geometry, physics, and applied mathematics. This conference is intended to help clarify the shifting boundaries and intersections in these closely related fields. Recent developments in computer science, physics, and big data are changing profoundly our notions of what constitutes geometry; in response, ideas from homotopy and category theory have provided new algebraic methods for (re)organizing our understanding of these questions, and how to approach them.The conference will focus on a developing new global language for both geometry and algebra, with connections to fields such as the following:1. arithmetic geometry (new approaches to motives, for example, via motivic homotopy theory; new techniques in K-theory via Hochschild and cyclic homology; homotopy-theoretic methods in automorphic forms, with applications to classical homotopy theory)2. geometric quantum field theory, for example, through various cobordism hypotheses (via chiral homology and related not-so-commutative ring spectra)3. category theory (e.g., through Voevodsky's univalent foundations project and related work on homotopy type theory in computer science, and involving foundational work in and applications of higher category theoryDemographic and intellectual developments in these areas have brought a diverse population of new researchers into the field, and the organizers hope that the conference will foster and encourage this development. The roster of speakers emphasizes junior researchers and diversity, but makes no compromises with the strength of the work under discussion. The speakers exemplify ground-breaking work in new directions, which points the way toward a new synthesis of algebra and geometry. This conference is an opportunity to expose graduate students and new researchers to these developments, and could have significant impact on their careers.A list of speakers and other details can be found at the conference websitehttp://www.math.jhu.edu/matc/

约翰霍普金斯大学数学系将于2016年3月12日至13日在马里兰州巴尔的摩的霍姆伍德校区举办“中大西洋拓扑研讨会：新方向”。这次会议的灵感来自于2015年春季在弗吉尼亚大学举行的一次类似会议。PI打算建立这种会议的传统。 代数拓扑学、几何学和范畴论正处于语言、技术和范式的世代转变之中，这些转变植根于几何学、物理学、范畴论和数据分析中关于更高同伦理论结构的新思想。这些领域处于动荡之中，年轻一代的研究人员将新的想法从高等代数带到几何，物理和应用数学的经典领域。本次会议旨在帮助澄清这些密切相关的领域中不断变化的边界和交叉点。计算机科学、物理学和大数据的最新发展正在深刻地改变我们对几何构成的概念;作为回应，同伦和范畴论的思想为（重新）组织我们对这些问题的理解以及如何处理这些问题提供了新的代数方法。会议将重点关注开发一种新的几何和代数全球语言，与以下领域有关：1.算术几何（新的方法动机，例如，通过motivic同伦理论;新技术在K理论通过Hochschild和循环同调;同伦理论方法自守形式，与应用到经典同伦理论）2.几何量子场论，例如，通过各种配边假设（通过手征同调和相关的非对易环谱）3.范畴理论（例如，通过Voevodsky的univalent基金会项目和计算机科学中同伦类型理论的相关工作，并涉及基础工作和高等范畴理论的应用，这些领域的人口和智力发展带来了新的研究人员进入该领域的多样化人口，组织者希望会议将促进和鼓励这种发展。发言者名单强调初级研究人员和多样性，但不妥协所讨论的工作的强度。演讲者在新的方向上开创性的工作，这指向了一个新的综合代数和几何的方式。这次会议是一个机会，让研究生和新的研究人员接触到这些发展，并可能对他们的职业生涯产生重大影响。发言者名单和其他细节可以在会议网站上找到http：www.math.jhu.edu/matc/