Special Lecture by Thomas Scanlon at KIAS (Korea Institute for Advanced Study)
On the morning of August 31, after the conference, Professor Thomas Scanlon will give special lectures (10:00-11:00, 11:15-12:15).
The venue is room no. 1423, KIAS in Seoul. You may find more details from the list here.
Please feel free to ask if you have any questions about the lecture. mt.in.seoul2023@gmail.com
Lecture 1: Functional transcendence for Mahler functions from the model theory of difference fields
Abstract: Starting in the 1930s, Mahler studied functions f(x) which satisfy functional relations of the form R(x,f(x),f(x^q)) = 0 for some rational function R and positive rational number q ≠ 1, showing, for example, that under certain explicit conditions algebraic relations involving values of these functions are controlled by functional equations. When the equation take the form f(x^q) = P(f(x)) where P∈ℂ(x)[Y] is a polynomial over the field of rational functions we show f is algebraically independent from functions satisfying difference equations of the form R(x,g(x), g(x^r), ... , g(x^{r^m}) = 0 where R is a rational function and r is multiplicatively independent from q. We address this problem by giving an exhaustive account of a class of definable sets relative to the model companion of the theory of difference fields. (This is an account of joint work with Alice Medvedev and Khoa Dang Nguyen.)
Lecture 2: Definable quotient spaces and complex geometry
Abstract: Various quotients of homogeneous spaces by the action of discrete groups play important roles in such subjects as the theory of quadratic forms, the study of modular functions, Hodge theory, and homogeneous dynamics, amongst others. Strictly speaking the map from such a homogeneous space to the quotient cannot be definable in an o-minimal structure, but as various other authors (e.g. Bakker, Klingler, Tsimerman, Peterzil, Starchenko, etc.) have observed, by making suitable restrictions it can be fruitfully analyzed using o-minimality and the quotient spaces themselves may be treated as definable objects. I will discuss how to develop this theory and some basic open questions and will then show how this formalism may be used to prove some general theorems around the Zilber-Pink conjectures. (This is an account of joint work with Jonathan Pila and separately with Sebastian Eterović.)
Getting from Main gate of the campus to KIAS by bus
Exit through the main gate of Yonsei University and head away from the campus, walking straight until you reach Sinchon subway station. It will take about 10 minutes.
Once at the station, turn right at gate number 2. You’ll notice a bus station situated in the middle of the crosswalk.
Board bus number 273 and remain on it until you reach the <KAIST. Hongneung Elementary School> station. The ride will last approximately 1 hour.
After alighting, you’ll find KIAS located across the road. Go to Room 1423.
