Publications

Articles on algebraic geometry

• (with Lukas Bertsch and Ádám Gyenge) Euler characteristics of affine ADE Nakajima quiver varieties via collapsing fibers, preprint October 2023.
• (with Austin Conner, Mateusz Michalek and Michael Schindler) Polynomial systems admitting a simultaneous solution, preprint June 2023.
• (with Geoffrey Mboya) On K3 fibred Calabi-Yau threefolds in weighted scrolls, published online, Rendiconti del Circolo Matematico di Palermo (2023).
• (with Praise Adeyemo) Refined Ehrhart series and bigraded rings, Studia Sci. Math. Hung 60 (2023), 97–108.
• (with Jon Hauenstein and Laurent Manivel) On the equations defining some Hilbert schemes, Vietnam Journal of Mathematics 50 (special issue dedicated to Bernd Sturmfels’ 60th birthday, 2022), 487-500.
• (with Alastair Craw, Søren Gammelgaard and Ádám Gyenge) Quot schemes for Kleinian orbifolds, SIGMA 17 (special volume on the occassion of Lothar Göttsche’s 60th birthday, 2021) 099.
• (with Alastair Craw, Søren Gammelgaard and Ádám Gyenge) Punctual Hilbert schemes for Kleinian singularities as quiver varieties, Algebraic Geometry 8 (2021), 680-704.
• (with Ben Davison and Jared Ongaro) Enumerating coloured partitions in 2 and 3 dimensions, Math. Proc. Cam. Phil. Soc. 169 (2020) 479-505.
• (with Ádám Gyenge and András Némethi) Euler characteristics of Hilbert schemes of points on simple surface singularities, European Journal of Mathematics 4 (2018), 439-524.
• (with Ádám Gyenge and András Némethi) Euler characteristics of Hilbert schemes of points on surfaces with simple singularities, International Mathematics Research Notices, Volume 2017, 4152-4159.
• (with Alberto Cazzaniga, Andrew Morrison and Brent Pym) Motivic Donaldson–Thomas invariants of some quantized threefolds, Journal of Noncommutative Geometry 11 (2017) 1115-1139.
• Cohomological Donaldson–Thomas theory, Proceedings of String-Math 2014, AMS, 2016.
• (with Ben Davison, Davesh Maulik and Joerg Schuermann) Purity for graded potentials and quantum cluster positivity, Compositio Mathematica 151 (2015) 1913-1944; preprint version.
• (with Chris Brav, Vittoria Bussi, Delphine Dupont and Dominic Joyce) Symmetries and stabilization for sheaves of vanishing cycles, J. Singularities 11 (2015) 85-151. 
• (with Kai Behrend and Jim Bryan) Motivic degree zero Donaldson-Thomas invariants, Inv. Math. 192 (2013) 111-160.
• Nekrasov’s partition function and refined Donaldson–Thomas theory: the rank one case, SIGMA (2012) 088, 16pp.
• (with Andrew Morrison, Sergei Mozgovoy and Kentaro Nagao) Motivic Donaldson-Thomas invariants of the conifold and the refined topological vertex, Adv. Math. 230 (2012) 2065-2093.
• (with Imran Qureshi) Calabi-Yau threefolds in weighted flag varieties, Adv. High Energy Phys 2012 (2012) 547317, 14pp.
• (with Imran Qureshi) Constructing projective varieties in weighted flag varieties, Bull. Lon. Math. Soc. 43 (2011) 786-798.
• (with Alexandru Dimca) The Milnor fibre of the Pfaffian and the Hilbert scheme of four points on C³ , Math. Res. Lett. 16 (2009) 1037-1055.
• (with Philip Candelas, Xenia de la Ossa and Yang-Hui He) Triadophilia: a special corner in the landscape, Adv. Theor. Math. Phys. 12 (2008), featured in New Scientist.
• Non-commutative Donaldson-Thomas invariants and the conifold, Geometry and Topology 12 (2008) 1171-1202.
• Sheaves on fibered threefolds and quiver sheaves, Comm. Math. Phys. 278 (2008), 627-641.
• (with Anita Buckley) Orbifold Riemann-Roch for threefolds with an application to Calabi-Yau geometry, J. Algebraic Geom. 14 (2005), 601-622.
• Contractions and monodromy in homological mirror symmetry, in: Strings and geometry (ed. Douglas, Gauntlett and Gross), AMS, 2004. 
• Artin group actions on derived categories of threefolds, J. Reine Angew. Math. 572 (2004) 139-166.
• On an example of Aspinwall and Morrison, Proc. Am. Math. Soc. 132 (2004), 621-632.
• On the ample cone of an ample hypersurface, Asian Journal of Mathematics 7 (2003), 1-6.
• Enhanced gauge symmetry and generalized braid group actions, Communications in Mathematical Physics 238 (2003), 35-51. 
• On a conjecture of Cox and Katz, Math. Zeitschrift 240 (2002), 233-241.
• Diffeomorphisms and families of Fourier-Mukai transforms in mirror symmetry, in: Applications of Algebraic Geometry to Coding Theory, Physics and Computation, NATO Scinence Series, pp. 317-337, Kluver 2001.
• Calabi-Yau threefolds with a curve of singularities and counterexamples to the Torelli problem II, Math. Proc. Cam. Phil. Soc 129 (2000), 193-204.
• Calabi-Yau threefolds with a curve of singularities and counterexamples to the Torelli problem, Int. J. Math. 11 (2000), 449-459.
• Some finiteness results for Calabi-Yau threefolds, J. London Math. Soc. 60 (1999), 689-699.

Books

• Aspinwall, Bridgeland, Craw, Douglas, Gross, Kapustin, Moore, Segal, Szendroi, Wilson, Dirichlet branes and mirror symmetry, Clay Mathematics Monographs, AMS, 2009. 
• Reid and Szendrői, Geometry and topology, textbook at 2nd/3rd year undergraduate level, CUP, 2005.

Network science and big data

• Danny Parsons, David Stern, Balázs Szendrői and Elizabeth David-Barrett, Interdisciplinary data workshops: Combining Statistical Consultancy Training with Practitioner Data Literacy. In: Burrill, G.F., de Oliveria Souza, L., Reston, E. (eds) Research on Reasoning with Data and Statistical Thinking: International Perspectives. Advances in Mathematics Education. Springer, 2023.
• (with Ágnes Czibik, Elizabeth Dávid-Barrett, Mihály Fazekas, Danny Parsons, David Stern and Roger Stern) Assessing Tanzania’s National Procurement Data Infrastructure, policy paper, Government Transparency Institute, 2017.
• (with Gábor Csányi) Fractal/small-world dichotomy in real-world systems, Phys.Rev.E. 70, 016122 (2004).
• (with Gábor Csányi) Polynomial epidemics and clustering in contact networks, Proc. R. Soc. Lon. B (Suppl. Biology Letters) 271, S364-S366, DOI 10.1098/rsbl.2004.0188. 
• (with Gábor Csányi) Structure of a large social network, Phys.Rev.E. 69, 036131 (2004).

Talks, expository material, reviews, etc

• (with Jean-Pierre Bourguignon) Gene Calabi at 100 – Memorable encounters with Eugenio Calabi, EMS Magazine, 2023.
• (with Chiara Bonadiman, Jared Ongaro and Diletta Martinelli) Live and remote: Nairobi workshops in algebraic geometry, EMS Magazine 124, 38-31, 2022.
• Adventures with Algebra and Geometry in East Africa, talk at a remote meeting of the Calouste Gulbenkian Foundation, November 2021.
• Global aspects of Calabi-Yau moduli space, talk at a meeting of the Simons Collaboration on Special Holonomy in Geometry, Analysis, and Physics, June 2020.
• Hilbert schemes of points on singular surfaces: combinatorics, geometry, and representation theory, COVID remote talk in Vienna, London and Leicester, April-June 2020.
• Developing mathematics in East Africa, Newsletter of the London Mathematical Society, July 2018.
• Grothendieck és matematikája, 2015.
• Nekrasov’s partition function and refined Donaldson–Thomas theory, talk at StringMath 2012, Bonn.
• Physics on a circle and geometry, talk at the 1st Strathmore University Mathematics Conference, Nairobi, August 2011.
• A special corner in the landscape, talk at String Phenomenology 2008, UPenn, May 2008.
• Dimer models and local non-commutative algebraic gemetry, talk at the LMS Invited Lectures, Imperial College, April 2008.
• The structure of a large social network, presentation at Theory Group, Microsoft Research, February 2004.
• MathSciNet reviews (requires MathSciNet subscription)
• Review of Rational and nearly rational varieties by Kollar, Smith and Corti, Bull. London Math. Soc. 39 (2007) 698-700.
• Cubic curves: a short survey, talk at ICAMMP 2004, Sylhet, Bangladesh, January 2005.
• The unbearable lightness of deformation theory – A tutorial introduction, a Calf talk, 18 November 1999.
• Reflexive polytopes and Calabi-Yau threefolds, an expository article on mirror symmetry, 1996. 
• Modular forms, a short introduction, 1993. 

Thesis

• Calabi-Yau threefolds and the Torelli problem, PhD thesis University of Cambridge 1999, avaliable upon request.