Introduction to Bruhat-Tits Theory - Lecture 1

Embark on a comprehensive exploration of Bruhat-Tits theory in this first lecture of a mini-course delivered by Brian Conrad at the International Centre for Theoretical Sciences. Delve into the foundations of this important mathematical concept, which plays a crucial role in the study of algebraic groups and their applications. Learn about the historical context, key principles, and fundamental structures that form the basis of Bruhat-Tits theory. Gain insights into how this theory connects with other areas of mathematics, including number theory, geometry, and representation theory. Prepare to engage with advanced mathematical concepts and develop a deeper understanding of the intricate relationships between algebraic structures and geometric spaces. This lecture serves as an essential starting point for mathematicians, researchers, and graduate students interested in expanding their knowledge of modern algebraic and geometric theories.