Arend Bayer

I am Reader at the School of Maths at The University of Edinburgh, where I have been since 2012. You can read more about our research group on the Edinburgh Hodge Institute webpage.

Email: My official school page has more contact information.

I am currently coordinating the EDGE (EDinburgh GEometry) seminar.

A (probably slightly outdated) CV.

Since December 2013, my research is supported by an ERC starting grant.

My research has been recognized by the 2015 University of Cambridge Adams prize, shared with Tom Coates, by the 2016 Whitehead prize awarded by the London Mathematical Society, and the 2016 Whittaker prize by the Edinburgh Mathematical Society.

Editorial work

I am editorial advisor for the journals of the London Mathematical Society (Bulletin, Journal, Proceedings, Transactions). Please submit articles via the LMS journals webpage, where you can select me as responsible advisor if you wish.

I am editor for the Proceedings of the Royal Society of Edinburgh (Mathematics Section). Instructions for submission.

I have recently become editor for Selecta Mathematica. Instructions for submission (by email).

Research interests

Algebraic Geometry:

Graduate students

Current students:
Sjoerd Beentjes.
Soheyla Feyzbaksh.
Fatemeh Rezaee.

Former students:
Rebecca Tramel.

Post-docs mentored

Current post-docs:
Diletta Martinelli, 2016-.

Former post-docs:
Chunyi Li, 2013-16.
Ciaran Meachan, 2013-15.
Matthew Woolf, 2013-14.
Seun-Jo Jung, visiting from KIAS 2016-17.
Alice Rizzardo, 2016-17.

Publications and preprints

You can find all my papers on the arXiv, on google scholar, and after a while on MathSciNet.

Joint with Martí Lahoz, Emanuele Macrì, Howard Nuer, Alexander Perry, Paolo Stellari: Stability conditions in families and familes of Hyperkaehler varieties. In preparation. Summary of results available in our Oberwolfach report.

Complement of spherical objects on K3 surfaces. Appendix to On Entropy of spherical twists by Genki Ouchi. arXiv:1705.01001.

Joint with Chunyi Li: Brill-Noether theory for curves on generic abelian surfaces. arXiv:1704.03546.

Joint with Marti Lahoz, Emanuele Macrì, and Paolo Stellari: Stability conditions on Kuznetsov components. arXiv:1703.10839.

A short proof of the deformation property of Bridgeland stability conditions. arXiv:1606.02169.

Wall-crossing implies Brill-Noether. Applications of stability conditions on surfaces. arXiv:1604.08261. To appear in the Proceedings of the 2015 AMS Summer Institute on Algebraic Geometry, University of Utah.

Joint with Alastair Craw and Ziyu Zhang: Nef divisors for moduli spaces of complexes with compact support. arXiv:1602.00863. Selecta Mathematica New Series (2016), published online November 2016.

Joint with Emanuele Macrì and Paolo Stellari: The space of stability conditions for abelian threefolds, and some Calabi-Yau threefolds. arXiv:1410.1585. Inventiones Math., published online May 2016.

Joint with Tom Bridgeland: Derived automorphism groups of K3 surfaces of Picard rank 1. arXiv:1310.8266. Duke Math. Journal, published online September 2016.

Joint with Brendan Hassett and Yuri Tschinkel: Mori cones of holomorphic symplectic varieties of K3 type. arXiv:1307.2292. Annales scientifiques de l'Ecole Normale Superieure, 48(4), 941--950.

Joint with Emanuele Macrì: MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations.arXiv:1301.6968. Inventiones mathematicae 198 (2014), no. 3, 505--590.

Joint with Emanuele Macrì: Projectivity and birational geometry of Bridgeland moduli spaces.arXiv:1203.4613. Journal of the AMS 27 (2014), 707-752.

Joint with Aaron Bertram, Emanuele Macrì and Yukinobu Toda: Bridgeland Stability conditions on Threefolds II: An application to Fujita's conjecture. arXiv:1106.3430. Journal of Algebraic Geometry 23 (2014), 693-710.

Joint with Emanuele Macrì and Yukinobu Toda: Bridgeland Stability conditions on Threefolds I: Bogomolov-Gieseker type inequalities. arXiv:1103.5010. Journal of Algebraic Geometry 23 (2014), 117-163.

Joint with Emanuele Macrì: The space of stability conditions on the local projective plane. arXiv:0912.0043. Some related SAGE code. Duke Math. J. 160 (2011) no. 2, 263-322.

Polynomial Bridgeland stability conditions and the large volume limit. arXiv:0712.1083. Geometry & Topology 13 (2009), no. 4, 2389-2425.

Joint with Charles Cadman: Quantum Cohomology of [C^N/mu_r]. arXiv:0705.2160. Compos. Math. 146 (2010), no. 5, 1291-1322.

Joint with Yuri I. Manin: Stability conditions, wall-crossing and weighted Gromov-Witten invariants. arXiv:math.AG/0607580. Mosc. Math. J. 9 (2009), no. 1, 3-23.

Semisimple quantum cohomology and blowups. Int. Math. Res. Not. 2004, no. 40, 2069--2083. math.AG/0403260.

Joint with Yuri I. Manin: (Semi)simple Exercises in Quantum Cohomology. The Fano Conference, 143--173, Univ. Torino, Turin, 2004. math.AG/0103164

Lecture notes

Here are brief lecture notes on Bridgeland stability conditions intended for graduate students interested in the topic.


My PhD thesis on "Semisimple Quantum Cohomology, deformations of stability conditions and the derived category", written under supervision of Yuri I. Manin.

My diploma thesis on "Semisimple Frobenius Manifolds and Quantum Cohomology", also supervised by Yuri I. Manin.

My essay (for the exams of "Part III" in Cambridge) on "Mirror Symmetry for the Elliptic Curve", written under supervision by Alessio Corti.