Facets of Algebraic Geometry

“代数几何的方方面面”会议将于2019年10月18日至20日在密歇根大学安娜堡分校举行。会议将集中讨论代数几何与组合学交界的丰富研究领域的最新发展和未来工作的有希望的方向。众所周知，代数几何的许多中心研究对象都具有复杂的组合结构。此外，来自代数几何、交点理论和变异上同调的复杂工具已经在纯组合问题上得到了深刻的结果。会议将汇集早期的职业生涯和建立高级数学家在组合代数几何工作。在主要会议之前，将有一天专门为年轻数学家组织的活动。会议将讨论的主题包括交换代数群的结构；现代舒伯特微积分，包括齐次空间的等变和非等变量子K理论，以及通过数值方法的计算方法；退化轨迹的chen类公式及其在曲线模空间上协同轨迹虚类计算中的应用曲线的Hurwitz空间和模空间上有效因子和无基点因子的模空间和锥上的交点理论代数几何和霍奇理论在拟阵和组合几何中的应用。在过去几年中，这些主题都取得了重大突破。该奖项反映了NSF的法定使命，并通过使用基金会的知识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 "Facets of Algebraic Geometry" will take place October 18-20, 2019 at the University of Michigan, Ann Arbor. The conference will focus on recent developments and promising directions for future work in the rich research areas of algebraic geometry near the interface with combinatorics. It is well-known that many of the central objects of study in algebraic geometry have intricate combinatorial structures. Furthermore, sophisticated tools from algebraic geometry, intersection theory, and the cohomology of varieties have led to deep results on purely combinatorial questions. The conference will bring together early career and established senior mathematicians working in combinatorial algebraic geometry. Preceding the main conference there will be a day devoted to activities organized by and for young mathematicians.The topics to be covered in the conference include the structure of commutative algebraic groups; modern Schubert calculus, including equivariant and non-equivariant quantum $K$-theory of homogeneous spaces, and computational approaches via numerical methods; Chern class formulas for degeneracy loci and applications of such formulas to virtual class computations of syzygetic loci on moduli spaces of curves; intersection theory on moduli spaces and cones of effective and basepoint free divisors on Hurwitz spaces and moduli space of curves; and applications of algebraic geometry and Hodge theory to matroids and combinatorial geometry. Each of these topics has had significant breakthroughs in the past few years. The conference website is https://sites.google.com/view/facetsofalgebraicgeometry/.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.