Differential Equations and Topology in Algebraic Varieties

Explore the intricate connections between differential equations and topology in this 48-minute lecture by Piotr Achinger at the Banach Center. Delve into the topology of algebraic varieties, De Rham cohomology, and the relationship between differential equations and monodromy. Examine the monodromy representation and its significance. Investigate the Riemann-Hilbert problem, also known as Hilbert's 21st problem, and its implications. Study regular singularities, focusing on Fuchs' contributions. Conclude with an analysis of Deligne's Riemann-Hilbert correspondence, bridging the gap between these mathematical disciplines.

DIFFERENTIAL EQUATIONS & TOPOLOGY
Topology of algebraic varieties
De Rham cohomology
Differential equations and monodromy
The monodromy representation
The Riemann-Hilbert problem (Hilbert 21)
Regular singularities (Fuchs)
Deligne's Riemann-Hilbert correspondence