Frobenius and Differential Operators to Measure Singularities

Explore a 46-minute mathematics lecture that delves into the application of Frobenius maps for classifying and measuring singularities in algebraic geometry. Learn about Kunz's 1969 discovery of using the Frobenius map to determine smooth versus singular varieties, and examine the F-pure threshold concept introduced by Takagi and Watanabe in 2004. Understand the geometric properties of this numerical invariant through the lens of differential operators, presented as collaborative research with Alessandro De Stefani from Università di Genova and Ilya Smirnov from Basque Center for Applied Mathematics.