# Arend Bayer

I am ''Professor of Algebraic Geometry'' 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.

## Various

Our EDGE (EDinburgh GEometry) seminar. Friends of MAXIMALS, our Algebra seminar.

A (probably slightly outdated) CV.

My research has been supported by an ERC starting grant 2013--2019, and since June 2019 by an ERC consolidator grant. I am part of an EPSRC programme grant Enhancing Representation Theory, Noncommutative Algebra and Geometry, jointly with Tom Bridgeland (Sheffield), Michael Wemyss (Glasgow) and my colleagues Iain Gordon and Agata Smoktunowicz.

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 Bulletin/Journal/Transactions of the London Mathematical Society. Please submit articles via the LMS journals webpage, where you can select me as responsible advisor if you wish.

I am editor for Selecta Mathematica. Instructions for submission (by email).

I am no longer editor for the Proceedings of the Royal Society of Edinburgh (Mathematics Section). Instead, Diane Maclagan recently joined the editorial board covering a similar range of topics.

## Research interests

Algebraic Geometry:

- Stability conditions in triangulated categories
- Wall-Crossing and birational geometry of moduli spaces
- Donaldson-Thomas invariants, (Stacky) Gromov-Witten invariants

## Graduate students

Current students:

Tzu-Yang Chou.
Hannah Dell.
Augustinas Jacovskis.

Former students:

Fatemeh Rezaee.
Sjoerd Beentjes (now Chancellor's Fellow at Univiersity of Edinburgh).

Soheyla Feyzbaksh (now at Imperial).

Rebecca Tramel.

## Post-docs mentored

Current post-docs:

Fei Xie, 2020--.

Giulia Gugiatti, 2020--21.

Qingyuan Jiang, 2019--.

Naoki Koseki, 2019--.

Shizhou Zhang, 2019--.

Former post-docs:

Diletta Martinelli, 2016--18.

Laura Pertusi. Autumn 2018.

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 (subscription needed) and zbMath (free).

Joint with Alex Perry: Kuznetsov's Fano threefold conjecture via K3 categories and enhanced group actions. arXiv:2202.04195.

Joint with Emanuele Macrì: The unreasonable effectiveness of wall-crossing in algebraic geometry. arXiv:2201.03654. To appear in the Proceedings of the ICM 2022.

Joint with Sjoerd Beentjes, Soheyla Feyzbakhsh, Georg Hein, Diletta Martinelli, Fatemeh Rezaee, Benjamin Schmidt: The desingularization of the theta divisor of a cubic threefold as a moduli space. arXiv:2011.12240. To appear in Geometry \& Topology.

Joint with Martí Lahoz, Emanuele Macrì, Howard Nuer, Alexander Perry, Paolo Stellari: Stability conditions in families. Pub. IHES, 2021. 1902.08184 .

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. Pure Appl. Math. Q. 13 (2017), no. 1 (Special Issue in Honor of Yuri I. Manin), 49-76.

Joint with Marti Lahoz, Emanuele Macrì, and Paolo Stellari: Stability conditions on Kuznetsov components. To appear in Annales ENS. arXiv:1703.10839.

A short proof of the deformation property of Bridgeland stability conditions. Math. Ann. 375, 1597–1613 (2019). arXiv:1606.02169.

Wall-crossing implies Brill-Noether. Applications of stability conditions on surfaces. arXiv:1604.08261. Proceedings of the AMS Summer Institute on Algebraic Geometry, Salt Lake City 2015. (Proc. Sympos. Pure Math., 97.1, AMS, 3-27).

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. Invent. Math. 206 (2016), no. 3, 869-933.

Joint with Tom Bridgeland: Derived automorphism groups of K3 surfaces of Picard rank 1. arXiv:1310.8266. Duke Math. Journal, Volume 166, Number 1 (2017), 75-124.

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

## Other mathematical writing

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

Reading, and Writing, Referee Reports, a contribution to the AMS Notices ``Early Career'' section.

## 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.