Conference: Tensor Invariants in Geometry and Complexity Theory

“几何和复杂性理论中的张量不变量”会议将于2024年5月13日至17日在奥本大学举行。本次会议旨在汇集早期职业研究人员和专家来研究张量不变量，它们在纯代数和微分几何中的出现，以及它们在代数复杂性理论和量子信息中的应用。该研讨会将邀请经验丰富的专家和有前途的年轻研究人员进行演讲。该活动旨在促进新的研究联系并发起新的合作。会议将使与会者接触到涉及各种科学学科的最新研究成果。这些活动将支持纯数学和每个科学重点领域（代数和微分几何、代数复杂性、量子信息）的“下游”应用的进一步发展。会议以几何中的不变量为中心，分为三个主题：代数与微分几何、张量与复杂性、量子计算与量子信息。几何学长期以来一直是数学的基石，而不变量是其中的关键。在代数和微分几何方面，组织者邀请专家就射影几何和微分几何之间的联系等主题发表演讲。在这些领域的考虑，例如关于尺寸和定义割线变量方程的问题，已经在几何和计算复杂性和量子信息等领域的应用中产生了强大的工具。同样，组织者还邀请了代数复杂性和量子信息领域的应用领域专家。纯数学和应用数学的这种自然并置将导致新的和有趣的联系，并有助于启动新的研究合作。除了由经验丰富的专家进行的日常谈话外，会议还将邀请年轻的研究人员参加海报会议，并提供交流机会，包括工作组活动，以帮助早期职业研究人员结识该领域的其他人，这将为新的（和正在进行的）研究合作提供机会。预计这些合作将在会议结束后很长时间内继续进行。该奖项反映了美国国家科学基金会的法定使命，并通过基金会的智力价值和更广泛的影响审查标准进行评估，认为值得支持。

The conference Tensor Invariants in Geometry and Complexity Theory will take place May 13-17, 2024 at Auburn University. This conference aims to bring together early-career researchers and experts to study tensor invariants, their appearance in pure algebraic and differential geometry, and their application in Algebraic Complexity Theory and Quantum Information. The workshop will feature talks from both seasoned experts and promising young researchers. The event is designed to facilitate new research connections and to initiate new collaborations. The conference will expose the participants to state-of-the-art research results that touch a variety of scientific disciplines. The activities will support further development of both pure mathematics and the "down-stream" applications in each area of scientific focus (Algebraic and Differential Geometry, Algebraic Complexity, Quantum Information). The conference is centered on invariants in geometry, divided into three themes: Algebraic and Differential Geometry, Tensors and Complexity, and Quantum Computing and Quantum Information. Geometry has long been a cornerstone of mathematics, and invariants are the linchpins. Regarding Algebraic and Differential Geometry, the organizers are inviting expert speakers on topics such as the connections between projective and differential geometry. Considerations in these areas, such as questions about dimensions and defining equations of secant varieties, have led to powerful tools both within geometry and applications in areas such as computational complexity and quantum information. Likewise, the organizers are inviting application-area experts in Algebraic Complexity and Quantum Information. This natural juxtaposition of pure and applied mathematics will lead to new and interesting connections and help initiate new research collaborations. In addition to daily talks by seasoned experts, the conference will include young researchers in a Poster Session and provide networking opportunities, including working group activities, to help early career researchers meet others in the field, which will provide opportunities for new (and ongoing) research collaborations. It is anticipated that these collaborations will continue long after the meeting is over. The conference webpage is: https://webhome.auburn.edu/~lao0004/jmlConference.html.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.