- Topics: Volume and log canonical centers.
- Speaker: Swaraj Pande (University of Michigan).
July 9th "Boundedness of Pluricanonical Maps of Varieties of General Type" Sections 4-5. (Notes)
- Topics: Lifting log canonical centers.
- Speaker: Devlin Mallory (University of Michigan).
July 16th "Boundedness of Pluricanonical Maps of Varieties of General Type" Sections 3. (Notes)
- Topics: Lifting sections from log canonical centers.
- Speaker: Sridhar Venkatesh (University of Michigan).
July 23rd "On the existence of flips" Sections 1-3. (Notes, Recording)
- Topics: Reduction to finite generation of the restricted algebra.
- Speaker: Tai-Hsuan Chung (UCSD).
July 30th "On the existence of flips" Sections 4. (Notes, Recording)
- Topics: Reduction to limiting algebras.
- Speaker: Justin Lacini (The University of Kansas).
August 13th "On the existence of flips" Sections 6. (Notes, Recording)
- Topics: Finite generation of the limiting algebra.
- Speaker: Jacob Keller (UCSD).
August 13th "Cox rings and Mori Dream Spaces". (Notes, Recording)
- Topics: Introduction to the theory of Mori dream spaces.
- Speaker: Joaquin Moraga (Princeton University).
August 20th "Logarithmic bounds on Fujita's conjecture". (Notes, Recording)
- Topics: Effective cutting down of log canonical centers.
- Speaker: Justin Lacini (The University of Kansas).
August 27th "Varieties of general type with small volume". (Notes, Recording)
- Topics: Constructing general type varieties with small volume.
- Speaker: Chengxi Wang (UCLA).
Fall 2021:
September 3rd: "On the termination of flips". (Notes, Recording)
- Topics: Overview of the termination of flips.
- Speaker: Joaquin Moraga (Princeton University).
September 10th: "Introduction to BCHM". (Notes, Recording)
- Topics: Introduction to BCHM.
- Speaker: Fernando Figueroa (Princeton University).
September 17th: "Sketch of the proof of BCHM". (Notes, Recording)
- Topics: Sketch of the proof of BCHM.
- Speaker: Jennifer Li (Princeton University).
September 24th: "BCHM: Preliminaries, Part 1". (Notes, Recording)
- Topics: Preliminaries 1: Nakayama-Zariski decomposition, Adjunction, Stable Base Locus, and Type of Models.
- Speaker: Sridhar Venkatesh (University of Michigan).
October 1st: "BCHM: Preliminaries, Part 2". (Notes, Recording)
- Topics: Preliminaries 2: Rational curves of low degree, Effective base point free Theorem, MMP with scaling, and Shokurov's polytopes.
- Speaker: Joaquin Moraga (Princeton University).
October 8th: "BCHM: Special Termination and Log Terminal Models". (Notes, Recording)
- Topics: Special Termination and Log Terminal Models.
- Speaker: Dori Bejleri (Harvard University).
October 15th: "BCHM: Non-Vanishing Theorem". (Notes, Recording)
- Topics: Non-Vanishing Theorem.
- Speaker: Justin Lacini (University of Kansas).
October 22nd: "BCHM: Finiteness of Models and Finite Generation". (Notes, Recording)
- Topics: Finite of Models and Finite Generation.
- Speaker: Emelie Arvidsson (IAS).
October 29th: "BCHM: Proof of the Corollaries". (Notes, Recording)
- Topics: Applications to Moduli, Fano varieties, and Birational Geometry.
- Speaker: Joaquin Moraga (Princeton University).
November 5th: "The Sarkisov Program". (Notes, Recording)
- Topics: The Sarkisov Program.
- Speaker: Joaquin Moraga (Princeton University).
November 12th: "Jumping on the nef cone for Fano varieties". (Notes, Recording)
- Topics: Jumping on the nef cone for Fano varieties.
- Speaker: Fumiaki Suzuki (UCLA).
November 19th: "On the number of minimal models for log smooth 3-folds". (Notes, Recording)
- Topics: Minimal models for log smooth 3-folds
- Speaker: Talon Stark (UCLA).
November 26th: "Birational automorphisms of varieties of general type". (Notes, Recording)
- Topics: Automorphisms and birational automorphisms of varieties of general type.
- Speaker: Joaquin Moraga (Princeton University).
December 2nd: "Descending chain condition of volumes". (Notes, Recording)
- Topics: Descending chain condition of volumes.
- Speaker: Junyao Peng (Princeton University).
December 9th: "Existence of log canonical closures - Preliminaries". (Notes, Recording)
- Topics: Existence of log canonical closures - Preliminaries.
- Speaker: Sridhar Venkatesh (University of Michigan).
December 16th: "Existence of log canonical closures - Abundance for slc pairs". (Notes, Recording)
- Topics: Existence of log canonical closures - Abundance for slc pairs.
- Speaker: Fernando Figueroa (Princeton University).
December 24th: "Base point free and Termination of Flips". (Notes, Recording)
- Topics: Existence of log canonical closures - Base point free and Termination of Flips.
- Speaker: Joaquin Moraga (Princeton University).
December 31th: "Existence of log canonical closures - Proof of the Corollaries". (Notes, Recording)
- Topics: Existence of log canonical closures - Proof of the Corollaries.
- Speaker: Joaquin Moraga (Princeton University).
Spring 2022:
January 7th: "Finiteness of B-representations". (Notes, Recording)
- Topics: Finiteness of B-representations: Preliminaries.
- Speaker: Joaquin Moraga (Princeton University).
January 14th: "Semi-log canonical abundance". (Notes, Recording)
- Topics: Semi-log canonical abundance.
- Speaker: Joaquin Moraga (Princeton University).
January 21st: "Overview of the canonical bundle formula". (Notes, Recording)
- Topics: Overview of the canonical bundle formula.
- Speaker: Enrica Floris (University of Poitiers).
January 28th: "The work of Fujino-Mori on the canonical bundle formula". (Notes, Recording)
- Topics: The canonical bundle formula and nefness of the moduli part.
- Speaker: Fabio Bernasconi (EPFL).
February 4th: "The work of Ambro on the canonical bundle formula". (Notes, Recording)
- Topics: The canonical bundle formula and Shokurov's boundary property.
- Speaker: Joaquin Moraga (Princeton University).
February 11th: "The generalized canonical bundle formula". (Notes, Recording)
- Topics: The generalized canonical bundle formula.
- Speaker: Stefano Filipazzi (EPFL).
February 18th: "Ascending chain condition for log canonical thresholds". (Notes, Recording)
- Topics: Introduction and Sketch of the Proof: ACC for lct's.
- Speaker: Joaquin Moraga (Princeton University).
February 25th: "Ascending chain condition for log canonical thresholds". (Notes, Recording)
- Topics: Conventions and adjunction.
- Speaker: Fernando Figueroa (Princeton University).
March 4th: "Ascending chain condition for log canonical thresholds". (Notes, Recording)
- Topics: Global-to-local, Upper bound for volumes, and birational boundedness.
- Speaker: Joaquin Moraga (Princeton University).
March 11th: "Ascending chain condition for log canonical thresholds". (Notes, Recording)
- Topics: Numerically trivial pairs, proof of theorems, and proof of corollaries.
- Speaker: Junyao Peng (Princeton University).
March 18th: "Accumulation points for log canonical thresholds". (Notes, Recording)
- Topics: Accumulation points for numerical thresholds and log canonical thresholds.
- Speaker: Sridhar Venkatesh (University of Michigan).
March 25th: "Finiteness of local fundamental groups". (Notes, Recording)
- Topics: Finiteness of the regional fundamental group of klt singularities.
- Speaker: Lukas Braun (University of Freiburg).
April 1st: "Jordan property for Cremona groups". (Notes, Recording)
- Topics: Jordan property for Cremona groups.
- Speaker: Konstantin Loginov (HSE).
April 8th: "Boundedness of varieties of general type". (Notes, Recording)
- Topics: Introduction to the boundedness of varieties of general type.
- Speaker: Joaquin Moraga (Princeton University).
April 15th: "Boundedness of varieties of general type". (Notes, Recording)
- Topics: Preliminaries to the boundedness of varieties of general type.
- Speaker: Fernando Figueroa (Princeton University).
April 22nd: "Boundedness of varieties of general type". (Notes, Recording)
- Topics: Preliminaries to the boundedness of varieties of general type.
- Speaker: Emelie Arvidsson (IAS).
April 29th: "Boundedness of varieties of general type: MMP in families and invariance of plurigenera". (Notes, Recording)
- Topics: MMP in families and invariance of plurigenera.
- Speaker: Chuyu Zhou (EPFL).
Summer 2022:
May 6th: "Boundedness of varieties of general type: Abundance in families". (Notes, Recording)
- Topics: Abundance in families.
- Speaker: Priyankur Chaudhuri (University of Maryland).
May 13th: "Boundedness of varieties of general type: Boundedness of Moduli". (Notes, Recording)
- Topics: Boundedness of Moduli.
- Speaker: Myeonhu Kim (Princeton University).
May 20th: "Survey on boundedness of varieties of general type, part 1". (Notes, Recording)
- Topics: ACC for numerically trivial pairs and boundedness of volumes.
- Speaker: Justin Lacini (University of Kansas).
May 27th: "Survey on boundedness of varieties of general type, part 2". (Notes, Recording)
- Topics: ACC for log canonical thresholds and boundedness.
- Speaker: Joaquin Moraga (Princeton University).
June 3rd: "Introduction to Dual Complexes". (Notes, Recording)
- Topics: Introduction to Dual Complexes.
- Speaker: Joaquin Moraga (Princeton University).
June 10th: "Dual complexes of Calabi-Yau pairs: Topology and Arithmetic". (Notes, Recording)
- Topics: Dual complexes of Calabi-Yau pairs.
- Speaker: Mirko Mauri (University of Michigan).
June 17th: "Dual complexes of Calabi-Yau pairs: Topology and Arithmetic". (Notes, Recording)
- Topics: Dual complexes and non-archimedean geometry.
- Speaker: Enrica Mazzon (University of Michigan).
June 24th: "Calabi-Yau pairs with maximal intersection and no toric model". (Notes, Recording)
- Topics: Calabi-Yau pairs and toric geometry.
- Speaker: Anne-Sophie Kaloghiros (University of Poitiers).
July 1st: "Introduction to the Theory of complements". (Notes, Recording)
- Topics: Introduction to the theory of complements.
- Speaker: Joaquin Moraga (UCLA).
July 8th: "The first main theorem of complements". (Notes, Recording)
- Topics: From global to local.
- Speaker: Talon Stark (UCLA).
July 15th: "The second main theorem of complements". (Notes, Recording)
- Topics: Lifting complements from divisors.
- Speaker: Chengxi Wang (UCLA).
July 22nd: "The second main theorem of complements". (Notes, Recording)
- Topics: Complements and the canonical bundle formula.
- Speaker: Louis Esser (UCLA).
July 29th: "Anti-pluricanonical systems on Fano varieties: Introduction". (Notes, Recording)
- Topics: Effective birationality and BAB.
- Speaker: Joaquin Moraga (UCLA).
August 5th: "Anti-pluricanonical systems on Fano varieties: Preliminaries I". (Notes, Recording)
- Speaker: Jose Yanez (University of Utah).
August 12th: "Anti-pluricanonical systems on Fano varieties: Preliminaries II". (Notes, Recording)
- Topics: Preliminaries II.
- Speaker: Erik Paemurru (University of Miami).
August 19th: "Anti-pluricanonical systems on Fano varieties: Effective Adjunction". (Notes, Recording)
- Topics: Adjunction to divisors and higher codimension centers.
- Speaker: Sridhar Venkatesh (University of Michigan).
August 26th: "Anti-pluricanonical systems on Fano varieties: Effective Birationality I". (Notes, Recording)
- Topics: Lemmata for Effective Birationality.
- Speaker: Myeonhu Kim (Princeton University).
September 2nd: "Anti-pluricanonical systems on Fano varieties: Effective Birationality II". (Notes, Recording)
- Topics: Proof of Effective Birationality.
- Speaker: Fernando Figueroa (Princeton University).
September 9th: "Anti-pluricanonical systems on Fano varieties: Boundedness of complements on Fano varieties". (Notes, Recording)
- Topics: Canonical bundle formula and complements.
- Speaker: Junyao Peng (Princeton University).
September 16th: "Anti-pluricanonical systems on Fano varieties: Existence of bounded complements". (Notes, Recording)
- Topics: Existence of bounded complements.
- Speaker: Joaquin Moraga (UCLA).
Fall 2022:
September 23rd: "Anti-pluricanonical systems on Fano varieties: Boundedness of exceptional Fano varieties". (Notes, Recording)
- Topics: Boundedness of Exceptional Fano Varieties.
- Speaker: Joaquin Moraga (UCLA).
September 30th: "Anti-pluricanonical systems on Fano varieties: Boundedness of relative complements". (Notes, Recording)
- Topics: Boundedness of Relative Complements.
- Speaker: Fernando Figueroa (Princeton - UCLA).
October 7th: "Singularities of Linear Systems and Boundedness of Fano varieties". (Notes, Recording)
- Topics: Overview of the proof of BAB.
- Speaker: Caucher Birkar (Tsinghua University).
October 14th: "Singularities of Linear Systems and Boundedness of Fano varieties". (Notes, Recording)
- Topics: Log canonical thresholds of Anti-pluricanonical Systems.
- Speaker: Joaquin Moraga (UCLA).
October 21st: "Singularities of Linear Systems and Boundedness of Fano varieties". (Notes, Recording Part I, Recording Part II)
- Topics: Log canonical thresholds of bounded pairs.
- Speaker: Joaquin Moraga (UCLA).
October 28th: "Singularities of Linear Systems and Boundedness of Fano varieties". (Notes, Recording)
- Topics: Boundedness of Fano varieties
- Speaker: Lu Qi (Princeton University).
Novemeber 4th: "Termination of flips and Weak Zariski Decompositions". (Notes, Recording)
- Topics: Termination of flips and Weak Zariski Decompositions.
- Speaker: Nikolaos Tsakanikas (MPIM).
Novemeber 11th: "Termination of flips and Weak Zariski Decompositions". (Notes, Recording)
- Topics: Termination of flips and Weak Zariski Decompositions II.
- Speaker: Vladimir Lazić (Universitat des Saarlandes).
Novemeber 18th: "Termination of pseudo-effective 4-fold flips". (Notes, Recording)
- Topics: Termination of pseudo-effective 4-fold flips.
- Speaker: Joaquin Moraga (UCLA).
Novemeber 25th: "Minimal log discrepancies I: Exceptional Singularities". (Notes, Recording Part I,Recording Part II)
- Topics: Minimal log discrepancies I: Exceptional Singularities.
- Speaker: Joaquin Moraga (UCLA).
December 2nd: "Minimal log discrepancies II: Regularity one". (Notes, Recording)
- Topics: Minimal log discrepancies II: Regularity one.
- Speaker: Joaquin Moraga (UCLA).
December 9th: "Coregularity I: Log canonical thresholds". (Notes, Recording)
- Topics: Coregularity and log canonical thresholds.
- Speaker: Fernando Figueroa (Princeton University).
December 16th: "Coregularity II: Index". (Notes, Recording)
- Topics: Index of log Calabi-Yau pairs of coregularity zero.
- Speaker: Junyao Peng (Princeton University).
December 23th: "Coregularity III: Complements". (Notes,Recording)
- Topics: Complements and coregularity of Fano varieties.
- Speaker: Joaquin Moraga (UCLA).
References:
- Kollár-Mori "Birational Geometry of Algebraic Varieties".
- Hacon-Kovacs "Classification of Higher Dimensional Algebraic Varieties".
- Lazarsfeld "Positivity in Algebraic Geometry Part 1 & 2".
- "Shokurov's Rational Connectedness Conjecture" by Hacon and McKernan (Arxiv).
- "Boundedness of Pluricanonical Maps of Varieties of General Type" by Hacon and McKernan (Arxiv).
- "On the existence of flips" by Hacon and McKernan (Arxiv).
- "Iteration of Cox rings of klt singularities" by Braun and Moraga (Arxiv).
- "Logarithmic bounds on Fujita's conjecture" by Ghidelli and Lacini (Arxiv).
- "Varieties of general type with small volume" by Totaro and Wang (Arxiv).
- "Existence of minimal models for varieties of log general type" by Birkar, Cascini, Hacon, and McKernan (Arxiv).
- "Flops connect minimal models" by Kawamata (ArXiv).
- "The Sarkisov program" by Hacon and McKernan (ArXiv).
- "Deformations of canonical pairs and Fano varieties" by De Fernex and Hacon (ArXiv).
- "Jumping of the nef cone for Fano varieties" by Totaro (ArXiv).
- "Existence of log canonical closures" by Hacon and Xu (ArXiv).
- "A travel guide to the canonical bundle formula" by Floris and Lazic (ArXiv).
- "A canonical bundle formula" by Fujino and Mori (Link).
- "Shokurov's boundary property" by Ambro (ArXiv).
- "On a generalized canonical bundle formula and generalized adjunction" by Filipazzi (ArXiv).
- "ACC for log canonical thresholds" by Hacon, McKernan, and Xu (ArXiv).
- "The local fundamental group of a Kawamata log terminal singularity is finite" by Braun (ArXiv).
- "Jordan property for Cremona groups" by Prokhorov and Shramov (ArXiv).
- "Boundedness of varieties of log general type" by Hacon, McKernan, and Xu (ArXiv).
- "Boundedness of moduli of varieties of general type" by Hacon, McKernan, and Xu (ArXiv).
- "The dual complex of singularities" by de Fernex, Kollár, and Xu (ArXiv).
- "The dual complex of Calabi-Yau pairs" by Kollár and Xu (ArXiv).
- "Some examples of Calabi-Yau pairs with maximal intersection and no toric model" by Anne-Sophie Kaloghiros (ArXiv).
- "The first main theorem on complements: from global to local" by Prokhorov and Shokurov (ArXiv).
- "Toward the second main theorem on complements: from local to global" by Prokhorov and Shokurov (ArXiv).
- "Anti-pluricanonical systems on Fano varieties" by Birkar (ArXiv).
- "On the existence of minimal models for log canonical pairs" by Lazić and Tsakanikas (ArXiv).
- "On the termination of flips for log canonical generalized pairs" by Chen and Tsakanikas (ArXiv).
- "Termination of pseudo-effective 4-fold flips" by Moraga (ArXiv).
- "On minimal log discrepancies and Kollár components" by Moraga (ArXiv).
- "Minimal log discrepancies of regularity one" by Moraga (ArXiv).
- "Log canonical thresholds and coregularity" by Figueroa, Moraga, and Peng (ArXiv).
- "Index of coregularity zero log Calabi-Yau pairs" by Filipazzi, Mauri, and Moraga (ArXiv).
- "Complements and coregularity of Fano varieties" by Figueroa, Filipazzi, Moraga, and Peng (ArXiv).
- "Coregularity of Fano varieties" by Moraga (ArXiv).
Participants:
- The following is a non-exhaustive list of participants of the seminar.
- As the seminar has been extensive, many of the participants attended partially.
- 1.- Fernando Figueroa Zamora, Princeton University.
- 2.- Myeonhu Kim, Princeton University.
- 3.- Sridhar Venkatesh, University of Michigan.
- 4.- Priyankur Chaudhuri, University of Maryland.
- 5.- Talon Stark, UCLA.
- 6.- Junyao Peng, Princeton University.
- 7.- Mirko Mauri, University of Michigan.
- 8.- Stefano Filipazzi, EPFL.
- 9.- Enrica Floris, Universite de Poitiers.
- 10.- Fabio Bernasconi, EPFL.
- 11.- Mohan Swaminathan, Princeton University.
- 12.- James Myer, CUNY.
- 13.- Jennifer Li, UMass.
- 14.- Lena Ji, Princeton University.
- 15.- Patrick Lei, Columbia University.
- 16.- Nicolas Vilches, Columbia University.
- 17.- Devlin Mallory, Universify of Michigan.
- 18.- Eduardo Alves Da Silva, IMPA.
- 19.- Sheng Tan, Purdue University.
- 20.- Cesar Hilario, IMPA.
- 21.- Erroxe Etxabarri Alberdi, Loughborough University.
- 22.- Daniela Paiva, IMPA.
- 23.- Mahrud Sayrafi, University of Minnesota.
- 24.- Madison Delmoe, The University of Arizona.
- 25.- Nancy Wang, University of Michigan.
- 26.- Tai Hsuan Chung UCSD.
- 27.- Yueqiao Wu, University of Michigan.
- 28.- Hernan Falla Luza, Universidad Federal Fluminense.
- 29.- Shelby Cox, University of Michigan.
- 30.- Friedrich Carl Simon Schirren, Universita degli studi Roma Tre.
- 31.- Jose Yanez, University of Utah.
- 32.- Bradley Dirks, University of Michigan.
- 33.- Chengxi Wang, UCLA.
- 34.- Zengrui Han, Rutgers University.
- 35.- Dori Bejleri, Harvard University.
- 36.- Amina Adburrahman, Princeton University.
- 37.- Emelie Arvidsson, EPFL.
- 38.- Justin Lacini, The University of Kansas.
- 39.- Harold Blum, Stony Brook.
- 40.- Chuyu Zhou, EPFL.
- 41.- Swaraj Pande, University of Michigan.
- 42.- Inder Kaur, IMPA.
- 43.- Marta Benozzo, LSGNT.
- 44.- Pascale Voegtli, LSGNT.
- 45.- John Sheridan, Princeton University.
- 46.- Alessandro Passantino, Universita di Pavia.
- 47.- Enhao Feng, Boston College.
- 48.- Erik Paemurru, ICMS.