Publications – Balázs Szendrői's Homepage

Articles on algebraic geometry

(with Nsibiet E. Udo, Praise Adeyemo and Stavros Argyrios Papadakis) Ideals, representations and a symmetrised Bernoulli triangle, preprint September 2024.
(with Andrew Pollock) Translating between hypersurface models of degree one del Pezzo surfaces with a conic bundle structure, note June 2024.
(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, June 2023, accepted in Journal of Algebra.
(with Geoffrey Mboya) On K3 fibred Calabi-Yau threefolds in weighted scrolls, Rendiconti del Circolo Matematico di Palermo 73 (2024) 621-635.
(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.