This is an online learning seminar series on Birkar's multiple work on Fano varieties, singularities, and related topics. The focus will be on main results, key ideas, applications, and open problems. The aim is to help researchers and students learn about this very exciting area of algebraic geometry and to stimulate further work. The seminar will be held online via Zoom.

Zoom Meeting ID: 262 865 5007

Passcode: YMSC

Recording: https://cloud.tsinghua.edu.cn/d/7d67fef3f26343b1be34/

Talk 1: 7 March, 4pm (all times are Beijing time)

 Introduction to Fano varieties and singularities

 Speaker: Caucher Birkar (Tsinghua)

Talk 2: 14 March, 4pm

 Pairs, singularities, MMP, generalised pairs

 Speaker: Junpeng Jiao (Tsinghua)

Talk 3: 21 March, 4pm

Complements: main results, applications, open problems [1]

 Speaker: Caucher Birkar (Tsinghua)

Talk 4: 28 March, 2pm

 Complements: sketch of proofs of main results of [1]

 Speaker: Joaquin Moraga (UCLA)

Talk 5: 4 April, 4pm

 BAB: main results, applications, open problems [1]

 Speaker: Caucher Birkar (Tsinghua)

Talk 6: 11 April, 4pm

 BAB: sketch of proofs of main results of [2]

 Speaker: Jihao Liu (Northwestern)    

Talk 7: 18 April, 4pm      

 Boundedness of Fano fibrations: main results and sketch of some proofs of [3]

 Speaker: Chen Jiang (Fudan)

Talk 8: 25 April, 4pm

 Singularities on Fano fibrations: main results, applications, open problems [4]

 Speaker: Caucher Birkar (Tsinghua)

Talk 9: 2 May, 4pm

 Toroidalisation of fibrations and toric models of toroidal fibrations (sections 3,4,5 of [4])

 Speaker: Santai Qu (USTC)

Talk 10: 9 May, 4pm

 Multiplicities along lc places (sections 7,8 of [4])

 Speaker: Jia Jia (Tsinghua)

Talk 11: 16 May, 4pm

 Proofs of main results of [4] (section 9 of [4])

 Speaker: Bingyi Chen (Tsinghua)

Talk 12: 23 May, 4pm

 Proofs of other results of [4] (sections 10,11 of [4])

 Speaker: Zou Yu (Tsinghua)

References:

[1] C. Birkar, Anti-pluricanonical systems on Fano varieties.

[2] C. Birkar, Singularities of linear systems and boundedness of Fano varieties.

[3] C. Birkar, Boundedness of Fano type fibrations.

[4] C. Birkar, Singularities on Fano fibrations and beyond.