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: arend.bayer@ed.ac.uk. 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A (probably slightly outdated) CV.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.

I am honoured to share the 2015 Adams prize with Tom Coates.

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.

Research interests

Algebraic Geometry:

Graduate students

Rebecca Tramel.
Soheyla Feyzbaksh.
Sjoerd Beentjes.

Post-docs mentored

Ciaran Meachan.
Chunyi Li.
Matthew Woolf.

Publications and preprints

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

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.

Joint with Alastair Craw and Ziyu Zhang: Nef divisors for moduli spaces of complexes with compact support. arXiv:1602.00863.

Joint with Emanuele Macrì and Paolo Stellari: The space of stability conditions for abelian threefolds, and some Calabi-Yau threefolds. arXiv:1410.1585. To appear in Inventiones Math.

Joint with Tom Bridgeland: Derived automorphism groups of K3 surfaces of Picard rank 1. arXiv:1310.8266. To appear in Duke Math. Journal.

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.

Theses

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.