Lefschetz, Hodge and Combinatorics - An Account of a Fruitful Cross-Pollination

Explore the profound connections between algebraic topology and combinatorics through this comprehensive lecture series delivered by Karim Alexander Adiprasito at the Institut des Hautes Etudes Scientifiques. Delve into the intricate relationships between Lefschetz theorems and Hodge theory as they apply to combinatorial structures, examining how classical results from algebraic geometry illuminate discrete mathematical objects. Discover how the cross-pollination between these seemingly disparate fields has led to breakthrough insights in both areas, with particular emphasis on how topological methods can solve combinatorial problems and vice versa. Learn about the modern applications of these classical theories to contemporary research in combinatorial geometry, polytopes, and discrete structures. Follow the development of key concepts across six detailed lectures that build systematically from foundational principles to cutting-edge research applications, demonstrating the power of interdisciplinary mathematical thinking in advancing our understanding of both algebraic topology and combinatorics.