Higher Algebra in Geometry by Hiro Lee Tanaka on July 31, 2023

8 days of introductory lectures on Higher Algebra (infinity categories) were given by Dr. Hiro Lee Tanaka (Texas State University). Recent developments on infinity-category theory and their applications have received attraction from various areas of mathematics, including geometric topology, symplectic geometry, and algebraic geometry. The lectures were targeted to students and researchers interested in applications of infinity-categorical tools.

The first day was devoted to non-specialists, where Dr. Tanaka introduced the concept of associativity and homotopies, and explained how they naturally lead us to the ideas of infinity-categories. From the second day, Dr. Tanaka introduced the basic concepts of infinity-cagetories together with familiar examples. In the second week, some of the works of Dr. Tanaka were given as applications of the ideas of inifity-categories.

His aim was to show us that these concepts are not mere abstractions, but are accessible and usefully applicable to concrete questions of geometry. The participants also shared their own works and interests after the lectures, and lively discussions took place.

Reported by Taketo Sano