Explore a comprehensive lecture on vanishing theorems in positive characteristics, focusing on the work of Hélène Esnault and Eckart Viehweg. Delve into the complexities of Kodaira and Kawamata-Viehweg vanishing theorems, examining their applicability in Complex geometry and their limitations in fields of positive characteristics. Investigate the unexpected failures of these theorems for certain classes of varieties, including log Fano varieties, and analyze the relationship between the dimension of Fano varieties and the characteristic of the base field. Learn about recent research conducted by the speaker, Emelie Arvidsson, in collaboration with Fabio Bernasconi and Justin Lacini, proving that the Kawamata-Viehweg vanishing theorem holds on log del Pezzo surfaces over perfect fields of characteristic p>5. Gain insights into this advanced topic in algebraic geometry through this hour-long presentation delivered at the Institut des Hautes Etudes Scientifiques (IHES) by Emelie Arvidsson from the University of Utah. Read more