I am a Royal Society Research Professor in Pure Mathematics at the University of Sheffield. Here is my CV.
I work in algebraic geometry with a particular focus on homological methods and interactions with topological string theory.
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Publications
Publications
Fourier-Mukai transforms for elliptic surfaces, J. reine ang. math. 498, 115-133 (1998).
Equivalences of derived categories and Fourier-Mukai transforms, Bull. Lond. Math. Soc. 31, 1, 25-34 (1999).
with Antony Macioica, Fourier-Mukai transforms for quotient varieties, J. Geom. Phys. 122, 119-127 (1999).
with Antony Maciocia, Complex surfaces with equivalent derived categories, Math. Zeit. 236, 4, 677-697 (2001).
with Antony Maciocia, Fourier-Mukai transforms for K3 and elliptic fibrations, J. Alg. Geom. 11, 629-657 (2002).
with Alastair King and Miles Reid, The McKay correspondence as an equivalence of derived categories, J. Amer. Math. Soc. 14, 535-554 (2001).
Flops and derived categories, Invent. Math. 147, 613-632 (2002)
T-structures on some local Calabi-Yau varieties, J. of Algebra. 289, 453-483 (2005).
Stability conditions on a non-compact Calabi-Yau threefold, Comm. Math. Phys. 266, 3, 715-733 (2006).
with Srikanth Iyengar, A criterion for regularity of local rings, C. R. Math. Acad. Sci. Paris 342, 10, 723-726 (2006).
Derived categories of coherent sheaves, International Congress of Math. vol. 2, 563-582 (2006).
Stability conditions on triangulated categories, Annals of Math. 166 (2), 317-345 (2007).
Stability conditions on K3 surfaces, Duke Math. J. 141 (2), 241-291 (2008).
Spaces of stability conditions, Algebraic geometry – Seattle 2005. Part 1, 1-21 (2009).
Stability conditions and Kleinian singularities, International Math. Research Notices, 21, 4142-4157 (2009).
Aspinwall, P et al., Dirichlet branes and mirror symmetry, Clay Math. Monographs, x+681 pp. (2009).
with David Stern, Helices on del Pezzo surfaces and tilting Calabi-Yau algebras, Adv. Math. 224, 1672-1716 (2010).
Hall algebras and curve-counting invariants, J. Amer. Math. Soc. 24, 969-998 (2011).
An introduction to motivic Hall algebras, Adv. Math. 229, 102-138 (2012).
with Valerio Toledano Laredo, Stability conditions and Stokes factors, Invent. Math. 187 (1), 61-98 (2012).
with Valerio Toledano Laredo, Stokes factors and multilogarithms, J. reine ang. math. 682, 89-128 (2012).
Quantum groups via Hall algebras of complexes, Annals of Maths. 177 (2), 739-759 (2013).
with Ivan Smith, Quadratic differentials as stability conditions, Publ. Math. IHES. 121, 155-278 (2015).
with Arend Bayer, Derived automorphism groups of K3 surfaces of Picard number 1, Duke Math. J. 166 (1), 75-124 (2017).
with Yu Qiu and Tom Sutherland, Stability conditions and the A2 quiver, Adv. Math. 365, 107049, 33 pp, (2020).
Hall algebras and Donaldson-Thomas invariants, Algebraic geometry: Salt Lake City 2015, Proc. Sympos. Pure Math. 75-100 (2018).
Scattering diagrams, Hall algebras and stability conditions, Algebr. Geom. 4 (5), 523-561 (2017).
Riemann-Hilbert problems from Donaldson-Thomas theory, Invent. Math. 216 (1), 69-124 (2019).
Riemann-Hilbert problems and the resolved conifold, J. Differential Geom. 115 (3), 395-435 (2020).
with Dylan Allegretti, The monodromy of meromorphic projective structures, Trans. Amer. Math. Soc. 373(9), 6321-6367 (2020).
with Anna Barbieri and Jacopo Stoppa, A quantized Riemann-Hilbert problem in Donaldson-Thomas theory, IMRN, no. 5, 3417–3456 (2022).
with Davide Masoero, On the monodromy of the deformed cubic oscillator, Math. Ann. 385 (2023), no. 1-2, 193–258.
Geometry from Donaldson-Thomas invariants, Integrability, quantization and geometry II, 1-66, Proc. Sympos. Pure Math. 103.2, AMS (2021).
with Ian Strachan, Complex hyperkahler structures from Donaldson-Thomas invariants, Lett. Math. Phys. 111 no. 2, paper no. 54 (2021).
Tau functions from Joyce structures, SIGMA 20 (2024) 26pp., arXiv:2303.07061.
Joyce structures on spaces of quadratic differentials, to appear Geometry and Topology (2025), arXiv:2203.17148.
Joyce structures and their twistor spaces, Adv. Math. 462 (2025), 40 pp., arXiv:2407.18229.
with Iván Tulli, Resurgence and Riemann-Hilbert problems for elliptic Calabi-Yau threefolds, Comm. Math. Phys. 406 (2025), arXiv:2407.06974.
with Fabrizio Del Monte and Luca Giovenzana, Invariant stability conditions on certain Calabi-Yau threefolds, arXiv:2412.08531.
with Fabrizio Del Monte, Joyce structures and poles of Painlevé equations, arXiv:2505.03429.
with Helge Ruddat, Clusters, twistors and stability conditions, arXiv:2505.03433.
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