所属学科： 基础数学,应用数学
开始日期： 2014-07-21
结束日期： 2014-07-25
所在国家： 中华人民共和国
所在城市： 天津市 南开区
具体地点： 南开大学
主办单位： 南开大学陈省身数学研究所
联系人： Wenhua Zhao
联系电话： 001-309-438-7367
传真： 001-309-438-5866
E-MAIL： wzhao@ilstu.edu
会议网站： https://cas.illinoisstate.edu/sites/aagjc/
会议背景介绍：
Affine Algebraic Geometry (AAG) is a new subbranch of Algebraic Geometry, which since 2000 has obtained its own Mathematics Subject Classification. It was motivated by some “notorious” open problems such as the Jacobian Conjecture; the Tame Generators Problem; the Cancellation problem; the Embedding Problem and several linearization problems. To treat these problems, a variety of techniques and approaches have been developed, which has already led to some remarkable successes: the solution of the Markus Yamabe Problem (the Jacobian Problem for differential equations), the solution of the Tame Generators problem (Nagata’s Conjecture), a proof of the linearization of $\mathbb C^*$ actions on $\mathbb C^3$ and very recently the solution of the Cancellation problem in positive characteristic.
The study of the Jacobian conjecture revealed the connections of the conjecture with many seemingly unrelated mathematics areas such as the Burgers and Heat PDEs, harmonic polynomials, non-commutative symmetric functions, the polynomial moment problem, etc. It also led recently to the study of a new notion, namely, Mathieu subspace, which generalizes the notion of an ideal. The new theory of Mathieu subspaces provides a much more general framework in which various open problems, including the Jacobian, can be studied.
The field of AAG is a rapidly growing research area that attracts senior researchers as well as young graduate students. During this short-school/conference most of the topics described above will be discussed by several of the world’s experts. It will give young researchers an excellent chance to see the state of the art of research in these very active and challenging areas. The short-school/conference is also aimed to promote the future collaborations of mathematicians from China with mathematicians from other countries in these areas.
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