Derived algebraic geometry is generalization of ordinary algebraic geometry, having homotopical idea as a new input. It has been known to have surprising applications, from solving classical problems in algebraic topology and number theory to providing new ways of thinking about representation theory and mathematical physics, to name a few.
The goal of this lecture series is to give an introductory overview of the subject. Our purpose is not to focus on a specific application in the subject, but to explain its philosophy and some of the main ideas by letting audience exposed to as many different characters in the subject as possible, without dealing with too much technical details.
Both the level and topics of lectures will crucially depend on participants' demand. Familiarity with basics of scheme theory, algebraic topology, and homological algebra would be helpful, if not required.