Petra Poklukar: On the real spectrum compactification of Teichmüller space

In this talk, I will present an approach to compactifying the Teichmüller space associated with a closed connected oriented surface of genus greater or equal to 2. I will present an algebraic model of the Teichmüller space which enables us to identify it with a real closed semi-algebraic set. With this identification, I will describe its real spectrum compactification which is realized using the real spectrum of an appropriate commutative ring. If time allows, I will also compare the real spectrum compactification of the Teichmüller space with the well-known Thurston compactification.