ICMS-Sofia and IMSA-Miami present Consortium Distinguished Lecture Series June 30, 2023, 15:30 (EEST, Sofia time), “Prof. Marin Drinov” Hall, Bulgarian Academy of Sciences 1, “15th November” Str., Sofia and via Zoom Michael R. Douglas, Harvard University, CMSA 3:30 pm (UTC+3) Lecture 1: Tameness and quantum field theory Abstract: I will discuss the notion of a space of quantum field theories, and explain various approaches to its definition and some of its expected properties. I will then cover joint work with Thomas Grimm and Lorenz Schlechter on tameness of quantum field theories.  This is based on the mathematical concept of o-minimal structures, which has been very powerful for proving finiteness results. Given a QFT or a space of QFTs, we define a corresponding structure, and conjecture [...]