1. Time & Venue

10-12 am on August 7, 8 at Room 515, Cosmology Building, NTU

10-12 am on August 10 at Room 505, Cosmology Building, NTU

2. Course Outline & Descriptions

The filtration method both appeared in the study of Diophantine approximation and the K-stability of Q-Fano varieties. In particular, the so-called beta-constant (the expected vanishing order) appeared in the recent result of Ru-Vojta concerning the height inequality for general divisors on a projective variety, as well as in the so-called Fujita-Li criterion for the K-stability of Q-Fano varieties. This short course intends to present the filtration method, as well as to explore potential connections between these different subjects.

Monday (Day 1): Bigness and ampleness of the line bundles; Kodaira's embedding theorem; The volume of L and its exrepssion through the Okounkov body,  the standard (simple) filtration, the beta constant (the expected vanishing order), the Duistermaat-Heckman measure associated to the filtration and its expected value, the Green-transform, the integral expression of the beta-constant, weight function on a vector space and its one-to-one corresponding to the weighted filtration.

Tuesday (Day 2): Introduction to Diophantine approximation, Roth's theorem and Schmidt's subspace theorem, the Hilbert and Chow weights, the theorem of Evertse and Ferretti and its proof, the proof of Ru-Vojta theorem using Autissier's filtration.

Thursday (Day 3): Fujita-Li's criterion for the K-stability of Q-Fano varieties. 

3. Registration

https://forms.gle/wmXsMUtrZMzE9ziJ6

4. Online Meeting Link

08/07  10:00-12:00  https://ntucc.webex.com/ntucc-en/j.php?MTID=m733ba27ab674be907be6f8289bea3be1

08/08  10:00-12:00  https://ntucc.webex.com/ntucc-en/j.php?MTID=m94cfabb77a3ccfd48a201300c5cd2fe7

08/10  10:00-12:00  https://ntucc.webex.com/ntucc-en/j.php?MTID=mded6c77fcb19cc858cbbf2877dd0e91e

5. Course Video

The Filtration Method in Diophantine Approximation and K- Stability

6. Course Note

Download here