Mid-Atlantic Topology Symposium: New Directions

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一场名为“大西洋中部拓扑：新方向”的研讨会。这次会议的灵感来自于2015年春天在弗吉尼亚大学举行的一次类似的会议。私人投资主任打算建立这样一种会议的传统。代数拓扑学、几何学和范畴论正处于语言、技术和范式的代际转换之中，根植于几何、物理、范畴理论和数据分析中关于更高同伦理论结构的新思想。这些领域正在酝酿之中，年轻一代的研究人员将高等代数的新思想带到了几何、物理和应用数学的经典领域，定义了一个前沿。这次会议旨在帮助澄清这些密切相关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关于几何是什么的概念；作为回应，来自同伦和范畴理论的思想提供了新的代数方法来(重新)组织我们对这些问题的理解，以及如何处理它们。会议将集中于正在发展的几何和代数的新的全球语言，与以下领域的联系：1.算术几何(动机的新方法，例如，通过动机同伦理论；通过Hochschild和循环同调在K理论中的新技术；例如，通过各种协边假设(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的单价基础计划和计算机科学中关于同伦类型理论的相关工作，并涉及更高范畴理论的基础工作和应用)2.几何量子场论，例如，通过各种协边假设(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的单价基础计划和计算机科学中关于同伦类型理论的相关工作，并涉及更高范畴理论的基础工作和应用)2.几何量子场论，例如，通过各种协边假设(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的单价基础计划和计算机科学中关于同伦类型理论的相关工作，以及涉及更高范畴理论的基础工作和应用)2.几何量子场论，例如，通过各种协边假设(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的单价基础计划和计算机科学中关于同伦类型理论的相关工作，并涉及更高范畴理论的基础工作和应用)这些领域的人口统计学发言者名单强调初级研究人员和多样性，但对正在讨论的工作的力度毫不妥协。演讲者展示了在新方向上的开创性工作，这为代数和几何的新综合指明了道路。这次会议是让研究生和新的研究人员了解这些发展的机会，并可能对他们的职业生涯产生重大影响。演讲者名单和其他细节可在会议网站http://www.math.jhu.edu/matc/上找到

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/