Higher dimensional complex geometry

Programme theme

Classification of surfaces, 3-folds and higher dimensional varieties. Calabi-Yau 3-folds, mirror symmetry. Moduli. Relations with other areas .

Classification: problems on existence and moduli of algebraic surfaces and 3-folds, including methods of projective and birational geometry, commutative algebra, toric geometry, etc. The minimal model program, flips and birational contractions. The proof of classification of 3-folds and log 3-folds. Biregular and birational geometry of Fano 3-folds.
CYs and mirror symmetry: CY 3-folds in classification, problems of existence, moduli and period maps. Kaehler cone, birational changes of models. Resolution of quotient singularities, McKay correspondence and stringy geometry. Special Lagrangian geometry and mirror symmetry. Relation with "physics".
Moduli: The heading covers two quite different topics: Moduli of varieties, e.g., Abelian varieties or K3s, and moduli of vector bundles, especially over curves, surfaces and special 3-folds.
Relations with other areas: there are very many of these, not all predictable. Lean towards interested British math community. Algebra, number theory, physics, gauge theory, symplectic geometry and other aspects of differential geometry, hyperKhler and related "special" geometries.

Click here to download the programme's final scientific report

Preprints

Title	Year	Programme	Publication Date
Vanishing Theorems, Boundedness and Hyperbolicity over Higher Dimensional Bases Authors: Sándor Kovács Download PDF	2001	HDG	21 October 2016
Are rational curves determined by tangent vectors? Authors: S Kebekus, Sándor Kovács Download PDF	2001	HDG	21 October 2016
The nef cone of toroidal compactifications of A$_4$ Authors: K Hulek, Gregory Sankaran Download PDF	2001	HDG	21 October 2016
Toric residues and mirror symmetry Authors: Evgueni Materov, Victor Batyrev Download PDF	2001	HDG	21 October 2016
On a classical correspondence between K3 surfaces Authors: C Madonna, Viacheslav Nikulin Download PDF	2001	HDG	21 October 2016
Two applications of instanton numbers Authors: E Gasparim Download PDF	2001	HDG	21 October 2016
Mixed toric residues and Calabi-Yau complete intersections Authors: Evgueni Materov, Victor Batyrev Download PDF	2001	HDG	21 October 2016

Workshops

Satellite

HDGW01

Warwick teach-in on 3-folds

7 January 2002 to 1 February 2002

HDGW02

HDG Euro conference

23 June 2002 to 29 June 2002

Seminars

Wednesday 6th February 2002
15:00 to 16:00	HDG Organisational Meeting	Room 2

Thursday 7th February 2002
14:00 to 15:30	Quantum cohomology of Grassmannians and a conjecture of Knutson	Room 2
16:00 to 17:00	Jaroslaw Antoni Wisniewski $\chi$ - connectedness of Hom and symplectic contractions of 4-folds	Room 2

Friday 8th February 2002
10:00 to 11:00	3-fold flips after Shokurov: an overview I	Room 2
11:30 to 12:30	3-fold flips after Shokurov: an overview II	Room 2
14:00 to 15:00	Torsion in the cohomology of a Lie group G, and G-bundles in algebraic geometry	Room 2

Thursday 14th February 2002
10:00 to 11:00	Seminar on flips	Room 2
11:30 to 12:30	Seminar on flips	Room 2
14:00 to 15:00	Seminar on flips	Room 2
15:30 to 16:30	Seminar on flips	Room 2

Thursday 21st February 2002
10:00 to 11:00	Seminar on flips: bounded lca saturated pbd algebras are finitely generated I	Room 2
11:30 to 12:30	Seminar on flips: bounded lca saturated pbd algebras are finitely generated II	Room 2
14:30 to 15:30	Stably rational irrational varieties: the Beauville et al. examples revisited	Room 2

Friday 22nd February 2002
10:00 to 11:00	Seminar on flips: canonical boundedness I	Room 2
11:30 to 12:30	Seminar on flips: canonical boundedness II	Room 2
14:30 to 15:30	Fujiki relation and fibre space structures on symplectic varieties	Room 2

Thursday 28th February 2002
10:00 to 11:00	Osamu Fujino Kyoto University Seminar on flips: approximation and stabilisation 1	Room 2
11:30 to 12:30	Osamu Fujino Kyoto University Seminar on flips: approximation and stabilisation 2	Room 2
14:30 to 15:30	Research lecture: the indeterminacy locus of the Prym map	Room 2

Friday 1st March 2002
10:00 to 11:00	Osamu Fujino Kyoto University Seminar on flips: approximation and stabilisation 3	Room 2
11:30 to 12:30	Osamu Fujino Kyoto University Seminar on flips: approximation and stabilisation 4	Room 2
14:30 to 15:30	Chad(mark) Schoen Research lecture: TBA	Room 2

Thursday 7th March 2002
10:00 to 11:00	Osamu Fujino Kyoto University Seminar on flips: approximation and stabilisation 3	Room 2
11:30 to 12:30	Osamu Fujino Kyoto University Seminar on flips: approximation and stabilisation 4	Room 2
16:00 to 17:15	Research lecture: Nodes, mirror symmetry \& symplectic manifolds with c\_1=0	Room 1

Friday 8th March 2002
10:00 to 11:00	Florin Ambro University of Cambridge Seminar on flips: destabilisation and nonklt, case 1	Discussion Room
11:30 to 12:30	Florin Ambro University of Cambridge Seminar on flips: destabilisation and nonklt, case 2	Discussion Room
14:30 to 15:30	William Oxbury University of Durham Prym varieties of Weyl group actions	Room 2

Thursday 14th March 2002
10:00 to 11:00	Seminar on flips: destabilisation and nonklt case 3	Room 2
11:30 to 12:30	Seminar on flips: destabilisation and nonklt case 4	Room 2
14:30 to 15:30	Osamu Fujino Kyoto University Research seminar: a canonical bundle formula and its applications	Room 2

Friday 15th March 2002
10:00 to 11:00	Hiromichi Takagi Kyoto University Seminar on flips: the main result 1	Room 2
11:30 to 12:30	Hiromichi Takagi Kyoto University Seminar on flips: the main result 2	Room 2
14:30 to 15:30	Research seminar:	Room 2

Wednesday 20th March 2002
14:30 to 15:30	Florin Ambro University of Cambridge Research lecture: cone and contraction theorems for log varieties	Room 2
16:00 to 17:00	Research lecture: boundedness of log Fano pairs of bounded index	Room 2

Thursday 21st March 2002
10:00 to 11:00	Hiromichi Takagi Kyoto University Seminar on flips: the main result 3	Room 2
11:30 to 12:30	Hiromichi Takagi Kyoto University Seminar on flips: the main result 4	Room 2
14:30 to 15:30	Research lecture: graded rings and Fano 3-folds	Room 2
16:00 to 17:00	Akira Ishii Kyoto University Research lecture: on the McKay correspondence for quotient surface singularities	Room 2

Friday 22nd March 2002
14:30 to 15:30	Victor Batyrev Research lecture: toric residues and mirror symmetry	Room 2
16:00 to 17:00	Yujiro Kawamata University of Tokyo Research lecture: some examples of flops	Room 2

Thursday 25th April 2002
14:30 to 15:30	The CCS conjecture: renamed, revised and revisited	Room 2
16:30 to 17:30	Helena Verrill Leibniz Universität Hannover A pencil of Calabi-Yau threefolds coming from the A$_4$ root lattice	Room 2

Tuesday 30th April 2002
16:15 to 17:15	Chad(mark) Schoen The singular cohomology of certain 3-folds I	Room 2

Thursday 2nd May 2002
17:00 to 18:00	Gavin Brown University of Warwick Graded rings and Hilbert series in Magma II: the big K3 database	Room 1

Friday 3rd May 2002
14:30 to 15:30	Chad(mark) Schoen The singular cohomology of certain 3-folds II	Room 2

Wednesday 8th May 2002
16:15 to 17:15	Colin Ingalls Kyoto University Non-commutative surfaces 1	Room 2

Thursday 9th May 2002
16:00 to 17:00	Degenerations of Calabi-Yau varieties I	Room 2

Friday 10th May 2002
14:30 to 15:30	Gavin Brown University of Warwick Graded rings and Hilbert series in Magma III	Room 2
16:00 to 17:00	Colin Ingalls Kyoto University Non-commutative surfaces 2	Room 2

Thursday 16th May 2002
14:30 to 15:30	Justin Sawon University of Oxford Twisted Fourier-Mukai transforms for irreducible holomorphic symplectic manifolds	Room 2
16:00 to 17:00	Degenerations of Calabi-Yau varieties II	Room 2

Friday 17th May 2002
14:30 to 15:30	Rationally connected varieties over finite fields	Room 2
16:00 to 17:00	Colin Ingalls Kyoto University Noncommutative surfaces III	Room 2

Friday 24th May 2002
14:30 to 15:30	Deformations of Picard bundles	Room 2
16:00 to 17:00	Degenerations of Calabi-Yau III	Room 2

Thursday 30th May 2002
14:30 to 15:30	Gabor Megyesi Real enumerative geometry	Room 2
16:00 to 17:00	Vyacheslav Shokurov Johns Hopkins University TBA	Room 2

Friday 31st May 2002
14:00 to 15:30	Vasilii Iskovskikh Steklov Mathematical Institute, Russian Academy of Sciences Smooth super-rigid hypersurfaces according to Pukhlikov	Room 2

Thursday 6th June 2002
16:00 to 17:00	Sorin Popescu Exterior algebra methods for syzygies	Room 2

Friday 7th June 2002
14:30 to 15:30	Two applications of instanton numbers	Room 2
16:00 to 17:00	Marco Andreatta Lifting extremal rays from ample sections	Room 2

Wednesday 12th June 2002
16:00 to 17:00	Nikolaos Tziolas University of Warwick Threefold divisorial contractions that contract a divisor onto a curve	Room 2

Thursday 13th June 2002
14:30 to 15:30	Gregory Sankaran University of Bath Divisors on moduli of abelian fourfolds: the scenic route	Room 2
16:00 to 17:00	Tie Luo University of Texas at Arlington Differential forms on varieties of general type	Room 2

Friday 14th June 2002
14:30 to 15:30	Adjunction techniques and the regulator after Collino	Room 2
16:00 to 17:00	Viacheslav Nikulin University of Liverpool On a classical correspondence between K3 surfaces	Room 2

Tuesday 18th June 2002
14:50 to 15:50	Seán Keel Japan Atomic Energy Agency & University of Texas at Austin Oort's conjecture for the moduli space of abelian varieties	Discussion Room
16:00 to 17:00	Anvar Mavlyutov Deformations of Calabi-Yau hypersurfaces	Room 1

Wednesday 19th June 2002
14:30 to 15:30	The Mori cones of moduli spaces of pointed curves	Room 1
16:00 to 17:00	Kieran Gregory O'Grady Degenerations of holomorphic symplectic varieties	Room 1

Thursday 20th June 2002
14:30 to 15:30	Rob Lazarsfeld University of Michigan Asymptotic invariants of base-loci and in vitro linear series	Room 2
16:00 to 17:00	Eugene Victor Flynn University of Liverpool Covering collections of curves and visibility of Sha	Room 2

Friday 21st June 2002
14:30 to 15:30	Hyperk\"ahler metrics on cotangent bundles of K\"ahler manifolds	Room 2
16:00 to 17:00	Anatoly Libgober University of Illinois at Chicago Elliptic genera of orbifolds	Room 2

Monday 1st July 2002
14:30 to 15:30	Takehiko Yasuda University of Tokyo Twisted jet and orbifold cohomology	Room 2

Thursday 4th July 2002
14:30 to 15:30	When is every coherent sheaf a quotient of some vector bundle? (a positive result for orbifolds)	Room 2

Friday 5th July 2002
16:00 to 17:00	Anda Degeratu Duke University The topology of crepant resolutions of Calabi-Yau orbifolds	Room 2

Tuesday 9th July 2002
16:00 to 17:00	D-brane categories on higher dimensional tori	Room 2

Thursday 11th July 2002
14:30 to 15:30	Daniel Ryder University of Warwick Elliptic and K3 fibrations birational to Fano 3-fold hypersurfaces I	Room 2

Friday 12th July 2002
14:30 to 15:30	Daniel Ryder University of Warwick Elliptic and K3 fibrations birational to Fano 3-fold hypersurfaces II	Room 2

Speakers

Florin Ambro University of Cambridge
Marco Andreatta
Victor Batyrev
Gavin Brown University of Sydney
Anda Degeratu Duke University
Eugene Victor Flynn University of Liverpool
Osamu Fujino Kyoto University
Colin Ingalls Kyoto University
Akira Ishii Kyoto University
Vasilii Iskovskikh Steklov Mathematical Institute, Russian Academy of Sciences
Yujiro Kawamata University of Tokyo
Seán Keel Japan Atomic Energy Agency & University of Texas at Austin
Rob Lazarsfeld University of Michigan
Anatoly Libgober University of Illinois at Chicago
Tie Luo University of Texas at Arlington
Anvar Mavlyutov
Gabor Megyesi
Viacheslav Nikulin University of Liverpool
Kieran Gregory O'Grady
William Oxbury University of Durham
Sorin Popescu
Daniel Ryder University of Warwick
Gregory Sankaran University of Bath
Justin Sawon University of Oxford
Chad(mark) Schoen
Vyacheslav Shokurov Johns Hopkins University
Hiromichi Takagi Kyoto University
Nikolaos Tziolas University of Warwick
Helena Verrill Leibniz Universität Hannover
Jaroslaw Antoni Wisniewski
Takehiko Yasuda University of Tokyo

Show All

Programme theme

Preprints

Vanishing Theorems, Boundedness and Hyperbolicity over Higher Dimensional Bases

Are rational curves determined by tangent vectors?

The nef cone of toroidal compactifications of A$_4$

Toric residues and mirror symmetry

On a classical correspondence between K3 surfaces

Two applications of instanton numbers

Mixed toric residues and Calabi-Yau complete intersections

Workshops

Warwick teach-in on 3-folds

HDG Euro conference

Seminars

Speakers

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