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Explore the intersection of physics and advanced mathematics in this plenary lecture from the 35th Brazilian Mathematics Colloquium. Delve into the fascinating connections between two-dimensional physics, generalized geometry, and higher groupoids as presented by Marco Gualtieri from the University of Toronto. Discover how these mathematical frameworks provide powerful tools for understanding physical phenomena in lower dimensions, examining the geometric structures that emerge from physical theories and their representation through sophisticated algebraic constructs. Learn about the role of higher groupoids in organizing and categorizing geometric objects that arise naturally in two-dimensional physical systems, and understand how generalized geometry extends classical differential geometry to accommodate the mathematical needs of modern theoretical physics. Gain insights into cutting-edge research that bridges pure mathematics and theoretical physics, exploring how abstract mathematical concepts find concrete applications in understanding the fundamental nature of physical reality in reduced dimensions.
