Emphasis Year in Noncommutative Geometry

该奖项将在2018年至2019年期间部分支持西北大学https://sites.math.northwestern.edu/~tamarkin/Emphasis/at的“非对易几何强调年”计划。这项计划将包括“拓扑循环同调的最新发展”小型研讨会(https://sites.math.northwestern.edu/~tamarkin/Emphasis/Topcyc)和“非对易几何的现代趋势”(https://sites.math.northwestern.edu/~tamarkin/Emphasis/Tsyganfest).会议迷你研讨会将于2018年11月3日至4日周末举行，大会将于2019年5月20日至24日(周一至周五)举行。这两项活动都将在伊利诺伊州埃文斯顿的西北大学举行。这个项目的目标是促进与非对易几何相关领域的研究人员之间的互动。迷你讲习班和会议将为研究人员提供传播他们的想法和拓宽他们的视野的机会。他们还将为研究生和博士后提供与非对易几何相关领域的资深专家互动的机会。非对易几何与数学和数学物理的许多分支相联系，非对易几何的主要思想是通过“非对易流形”上的函数的代数来研究几何。在这样的“非对易流形”上，相关的对象不再是点的空间，而是一个可能是非对易的结合代数。该计划的主题将包括：非对易Hodge理论、(拓扑)循环/Hochschild同调、K理论、指数理论、形变量子化、Riemann-Hilbert对应和微局部范畴。该奖项反映了NSF的法定使命，并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，被认为值得支持。

This award will partially support the program "Noncommutative Geometry Emphasis year" https://sites.math.northwestern.edu/~tamarkin/Emphasis/at Northwestern University in the academic year 2018-2019. This program will include the mini-workshop "Recent developments in Topological Cyclic Homology" (https://sites.math.northwestern.edu/~tamarkin/Emphasis/Topcyc) and the conference "Modern Trends in Non-commutative Geometry" (https://sites.math.northwestern.edu/~tamarkin/Emphasis/Tsyganfest). The mini-workshop will be held on the weekend Nov 3-4, 2018 and the conference will be held during the week May 20-24 (Monday-Friday) in 2019. Both events will take place at Northwestern University in Evanston IL. The goal of this program is to promote interaction between researchers working in areas related to non-commutative geometry. The mini-workshop and the conference will provide opportunities for researchers to disseminate their ideas and to broaden their perspectives. They will also provide opportunities for graduate students and postdocs to interact with senior experts in the areas related to noncommutative geometry. Noncommutative geometry is connected to many branches of mathematics and mathematical physics and the main idea of noncommutative geometry is to study geometry via algebras of functions on "noncommutative manifolds". On such a "noncommutative manifold", the relevant object is no longer the space of points, but rather an associative algebra, which may be noncommutative. The topics of the program will include: noncommutative Hodge theory, (topological) cyclic/Hochschild homology, K-theory, index theory, deformation quantization, Riemann-Hilbert correspondence and microlocal categories.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.