Facets of Algebraic Geometry

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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.