Geometric Vertex Decomposition in Combinatorial Algebraic Geometry

Learn about geometric vertex decomposition in this advanced mathematics lecture that explores the inductive strategy for understanding simplicial complexes. Delve into the evolution from traditional vertex decomposition, introduced by Provan and Billera in 1980, to its geometric generalization developed by Knutson, Miller, and Yong in 2009. Explore how geometric vertex decomposition preserves combinatorial information when studying initial varieties and understand its relationships with algebro-geometric invariants and Frobenius splitting. Examine practical examples in combinatorially-natural settings and engage with current open problems in the field. The lecture includes insights from collaborative work with Andrew Berget, Emanuela De Negri, Elisa Gorla, Jenna Rajchgot, Lisa Seccia, Mayada Shahada, and Anna Weigandt, offering a comprehensive view of this advanced mathematical concept and its applications in algebraic geometry.