Explore a homotopical approach to crystalline cohomology in this advanced mathematics lecture. Delve into the challenges of traditional methods for defining crystalline cohomology globally and discover an innovative variant that incorporates higher homotopies. Learn how this approach makes the lift canonical and simplifies the gluing process. Gain insights from the joint work of Kerz Moritz from the University of Regensburg and G. Tamme, presented at the Institut des Hautes Etudes Scientifiques (IHES). Enhance your understanding of advanced algebraic geometry and cohomology theories in this hour-long presentation.