The major topic of this reading seminar is the Kähler Minimal Model Program and some analytic methods in birational geometry.

2025-Spring

Here is the list of topics that we discussed in the seminar:

(1) 2025.2.26 Horing-Peternell’s proof of Mori bend and break for Kahler 3-folds, Douady space,

(2) 2025.3.5 Horing-Peternell’s proof of cone theorem for Kahler 3-folds, Douady space

(3) 2025.3.12 Horing-Peternell’s proof of small contraction and divisorial contraction for Kahler 3-folds, Douady space

(4) 2025.3.19 Das-Hacon’s proof of exisntence of divisorial contraction for GDLT Kahler 3-folds,

(5) 2025.3.26 Das-Hacon’s proof of existence of divisorial contraction for GDLT Kahler 3-folds,

(6) 2025.4.2 Das-Hacon’s proof of existence of small contraction for GDLT Kahler 3-folds,

(7) 2025.4.9 Das-Hacon’s proof of existence of small contraction for GDLT Kahler 3-folds

(8) 2025.5.7 Cao-Horing’s proof of subadjunction, Ohsawa–Takegoshi L2 extension theorem,

(9) 2025.5.8 The Clemens-Schmid exact sequence,

(10) 2025.5.10 Demailly-Hacon-Paun extension,

(11) 2025.5.21 Cao Horing’s subadjunction,

(12) 2025.5.28 Hacon-Paun’s canonical bundle formula for Kahler variety, existence of universal deformation space,

(13) 2025.5.29 degeneration of Leray spectral sequence for smooth projective morphism,

(14) 2025.6.5 Betti moduli space,

(15) 2025.6.11 Hacon-Paun’s canonical bundle formula; equivalent characterization of existence of universal deformation space;

(16) 2025.6.12 Perverse sheaves; variational characterization of harmonic metric ,Donaldson theorem, Hitchin-Simpson’s theorem;

(17) 2025.8.1. A brief introduction of Andre-Oort conjecture, Ax-Shamuel conjecture and Zilber–Pink conjecture, unlikely intersection theory;

(18) 2025.8.3 Attractor Conjecture, Sheng-Xu-Zuo’s cyclic cover construction of Dolgachev Calabi-Yau variety.

2025-Fall

(1) 2025.9.19. Hacon-Popa-Schnell’s proof of Iitaka conjecture when the base is of maximal Albanese dimension,

(2)