Conference: Center for Mathematics at Notre Dame

圣母大学数学中心将在2023年开展一个关于双曲性和理性的项目，以及2024年开展一个关于交换代数及其与代数几何和代数组合学的相互作用的项目。2023年计划将于2023年6月12日至30日举行。第一周将是本科生暑期学校，主题与双曲性和合理性有关，第二周将是研究生/博士后暑期学校，为新研究人员介绍这一领域，第三周将是国际研究会议。2024年计划将是一个国际研究会议，将于2024年8月12日至19日举行。这两个项目的目标是让不同层次的数学家参与这些令人兴奋和快速发展的领域。暑期学校的目的是向各级学生介绍代数几何的重要思想，更具体地说，是双有理几何，在更深的层次比通常在他们的本科或研究生学习。这两个会议将为学生和各级研究人员提供充足的机会，以发展富有成效的专业关系。关于2023年夏季双曲性和理性会议的更多细节，双有理几何中的一个基本激励问题是理解正则丛的正性或负性如何影响几何，算术和分析品种。具有非常负的标准丛的簇被期望“看起来像”射影空间，而具有非常正的标准丛的簇被期望看起来与射影空间非常不同。会议将汇集研究问题双方的专家：研究法诺品种如何看起来像（和不像）投射空间的研究人员，以及研究一般类型的品种看起来与投射空间非常不同的研究人员。有关2023年主题计划的更多信息，请访问计划网站：https://sites.nd.edu/2023cmndthematicprogram/。有关2024年会议的更多细节将在圣母大学数学中心网站上提供：https://centerformath.nd.edu/.This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。

The Center for Mathematics at the University of Notre Dame will run a 2023 program on Hyperbolicity and Rationality and a 2024 program on Commutative Algebra and its Interaction with Algebraic Geometry and Algebraic Combinatorics. The 2023 program will take place June 12-30, 2023. The first week of will be an undergraduate summer school on topics relating to hyperbolicity and rationality, the second week will be a graduate/postdoc summer school to give new researchers an introduction to this field, and the third week will be an international research conference. The 2024 program will be an international research conference that will take place August 12-19, 2024. The goal of both programs is to allow mathematicians at different levels to engage with these exciting and fast-developing fields. The purpose of the summer schools is to introduce students at various levels to important ideas in algebraic geometry, and more specifically birational geometry, at a deeper level than is usual in their undergraduate or graduate studies. Both conferences will provide ample opportunities for students and researchers at all levels to develop productive professional relationships.In more detail regarding the summer 2023 conference on Hyperbolicity and Rationality, one fundamental motivating question in birational geometry is to understand how positivity or negativity of the canonical bundle impacts the geometry, arithmetic and analysis of varieties. Varieties with very negative canonical bundle are expected to "look like" projective space and varieties with very positive canonical bundle are expected to look very different from projective space. The conference will bring together experts who study both sides of the question: researchers who study how Fano varieties look like (and unlike) projective space, and researchers who study ways that varieties of general type look very different from projective space. More information about the 2023 thematic program is available on the program website: https://sites.nd.edu/2023cmndthematicprogram/. More details about the 2024 conference will be available from the Center for Mathematics at Notre Dame website: https://centerformath.nd.edu/.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.