Alexander M Kasprzyk
Publications

Quasiperiod collapse for duals to Fano polygons: an explanation arising from algebraic geometry, with Ben Wormleighton.

Appendix to Four dimensional Fano quiver flag zero, by Elana Kalashnikov. Appendix joint with Tom Coates and Elana Kalashnikov.
^{[arXiv]}

Equivalence classes for smooth Fano polytopes, with Akihiro Higashitani.

Laurent inversion, with Tom Coates and Thomas Prince.
^{[arXiv]}

Threedimensional lattice polytopes with two interior lattice points, with Gabriele Balletti.
^{[arXiv]}

On the maximum dual volume of a canonical Fano polytope, with Gabriele Balletti and Benjamin Nill.
^{[arXiv]}

Ehrhart polynomial roots of reflexive polytopes, with Gábor Hegedüs and Akihiro Higashitani.
^{[arXiv]}

Constructions of varieties and Gorenstein formats, with Gavin Brown and Lei Zhu.
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Singularity content, with Mohammad Akhtar.
^{[arXiv]}

Classifying terminal weighted projective space.
^{[arXiv]}

Normal forms of convex lattice polytopes, with Roland Grinis.
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Quantum periods for certain fourdimensional Fano manifolds, with Tom Coates, Sergey Galkin, and Andrew Strangeway.
^{[doi/arXiv]}
Experimental Mathematics (2018).

Fano 3folds in P^{2} x P^{2} format, Tom and Jerry, with Gavin Brown and Muhammad Imran Qureshi.
^{[MR/doi/arXiv]}
European Journal of Mathematics, 4 (2018), no. 1, 5172.

Minimality and mutationequivalence of polygons, with Benjamin Nill and Thomas Prince.
^{[MR/doi/arXiv]}
Forum of Mathematics, Sigma, 5 (2017), e18.

Mutations of fake weighted projective planes, with Mohammad Akhtar
^{[MR/doi/arXiv]}
Proceedings of the Edinburgh Mathematical Society, 59 (2016), no. 2, 271285.

Quantum periods for 3dimensional Fano manifolds, with Tom Coates, Alessio Corti, and Sergey Galkin.
^{[MR/doi/arXiv]}
Geometry & Topology, 201 (2016), 103256.

Mirror symmetry and the classification of orbifold del Pezzo surfaces, with Mohammad Akhtar, Tom Coates, Alessio Corti, Liana Heuberger, Alessandro Oneto, Andrea Petracci, Thomas Prince, and Ketil Tveiten.
^{[MR/doi/arXiv]}
Proceedings of the American Mathematical Society, 144 (2016), 513527.

Fourdimensional projective orbifold hypersurfaces, with Gavin Brown.
^{[MR/doi/arXiv]}
Experimental Mathematics, 25 (2016), no. 2, 176193.

Fourdimensional Fano toric complete intersections, with Tom Coates and Thomas Prince
^{[MR/doi/arXiv]}
Proceedings of the Royal Society Series A, 471:20140704 (2015).

Mutations of fake weighted projective spaces, with Tom Coates, Samuel Gonshaw, and Navid Nabijou
^{[MR/link/arXiv]}
Electronic Journal of Combinatorics, 21 (2014), no. 4, P4.14.

Seven new champion linear codes, with Gavin Brown
^{[MR/doi/arXiv]}
LMS Journal of Computation and Mathematics, 16 (2013), 109117.

Mirror symmetry and Fano manifolds, with Tom Coates, Alessio Corti, Sergey Galkin, and Vasily Golyshev
^{[MR/doi/arXiv]}
In "Proceedings of the 6th European Congress of Mathematics", European Mathematical Society, 2013, pp. 285300.

Small polygons and toric codes, with Gavin Brown
^{[MR/doi/arXiv]}
Journal of Symbolic Computation, 51 (2013), 5562.

Minkowski polynomials and mutations (appendices 6.5MB), with Mohammad Akhtar, Tom Coates, and Sergey Galkin
^{[MR/doi/arXiv]}
SIGMA, 8 (2012), 094, pp. 707.

Fano polytopes, with Benjamin Nill
^{[MR/doi]}
In "Strings, Gauge Fields, and the Geometry Behind  the Legacy of Maximilian Kreuzer", A. Rebhan, L. Katzarkov, J. Knapp, R. Rashkov, E. Scheidegger (eds.), World Scientific, 2012, pp. 349364.

Reflexive polytopes of higher index and the number 12, with Benjamin Nill
^{[MR/link/arXiv]}
Electronic Journal of Combinatorics, 19 (2012), no. 3, P9.

Computational birational geometry of minimal rational surfaces, with Gavin Brown and Daniel Ryder.
^{[arXiv]}

The boundary volume of a lattice polytope, with Gábor Hegedüs
^{[MR/doi/arXiv]}
Bulletin of the Australian Mathematical Society, 85 (2012), 84104.

Roots of Ehrhart polynomials of smooth Fano polytopes, with Gábor Hegedüs
^{[MR/doi/arXiv]}
Discrete and Computational Geometry, 46 (2011), no. 3, 488499.

Canonical toric Fano threefolds
^{[MR/doi/arXiv]}
Canadian Journal of Mathematics, 62 (2010), no. 6, 12931309.

On the combinatorial classification of toric log del Pezzo surfaces, with Maximilian Kreuzer and Benjamin Nill
^{[MR/doi/arXiv]}
LMS Journal of Computation and Mathematics, 13 (2010), 3346.

Bounds on fake weighted projective space
^{[MR/doi/arXiv]}
Kodai Mathematical Journal, 32 (2009), 197208.

A note on palindromic δvectors for certain rational polytopes, with Matt Fiset
^{[MR/link/arXiv]}
Electronic Journal of Combinatorics, 15 (2008), N18.

Toric Fano threefolds with terminal singularities
^{[MR/doi/arXiv]}
Tohoku Mathematical Journal, 58 (2006), no. 1, 101121.

Toric Fano varieties and convex polytopes
^{[MR/link]}
PhD Thesis, 2006, University of Bath. My supervisor was Professor G K Sankaran.
Electronic resources

The Graded Ring Database, with Gavin Brown.
An online database of graded rings in algebraic geometry, including classifications of toric varieties, polarised K3 surfaces, and Fano 3folds and 4folds.

Convex polytopes and polyhedra, with Gavin Brown and Jaroslaw Buczynski.
A Magma computational algebra package for working with convex polytopes and polyhedra.

Toric varieties, with Gavin Brown and Jaroslaw Buczynski.
A Magma computational algebra package for working with toric varieties.

Fano varieties and extremal Laurent polynomials, with Tom Coates, Alessio Corti, Sergey Galkin, and Vasily Golyshev.
A collaborative research blog on the topic of Fano varieties, extremal Laurent polynomials, and mirror symmetry.
Data and databases

Webbased searchable databases

A printable list of the terminal Fano polytopes in three dimensions is available in pdf format, in ps format, and as plain text. The C source code for generating the list is available here.

Tables of the lowindex LDPpolygons are here. Plain text copies of the raw data are available here.

Plain text copies of the classification of terminal and canonical weighted projective space in dimension 4 (along with source code) are available here. The web page also contains the classification of all 1point lattice simplices in dimension 4.

Plain text copies of the classification of terminal Gorenstein weighted projective space in dimensions 5 to 10 (along with the source code used to generate them) can be downloaded here.

Magma code to generate the databases of canonical and CalabiYau 3folds can be downloaded here.

Magma code to recreate the classification of lreflexive polygons is available here.

Magma code to calculate classifications of wellformed, quasismooth hypersurfaces in weighted projective space, along with the resulting fourfold classifications are available for download here.
Organisation of seminars and conferences

The East Midlands Seminar in Geometry (EmSG) is an algebraic geometry seminar based at the Universities of Nottingham, Loughborough, Leicester, and Sheffield. The EmSG meets approximately six times per year.

Cluster Algebras and Algebraic Geometry,1114 July 2018. University of Nottingham. A workshop exploring some of the connections between cluster algebras and algebraic geometry. Organised by my then postdoc student Andrea Petracci.

Interactions with Lattice Polytopes, 1416 September 2017. OttovonGuerickeUniversität Magdeburg, Magdeburg, Germany. A workshop on lattice polytopes and their interactions with toric geometry, mirror symmetry, integer optimisation, commutative algebra, etc.

Experimental Classification of Fano Varieties, 1618 August 2017. Universität Tübingen. A small workshop on the various methods of computational and experimental classification of Fano varieties, with a focus on Mirror Symmetry and complexity one torus actions.

3CinG Workshop on Computational Algebra, 1821 April 2017. King's College, Cambridge. A workshop to discuss current and future applications of computational algebra in mathematics, with a particular focus on geometry.

Mirror Symmetry and Pencils of CalabiYau Motives, 1415 February 2015. Huxley Building, Imperial College London. A workshop to discuss recent progress in mirror symmetry for higherdimensional Fano manifolds, the construction of pencils of CalabiYau motives, and connections with arithmetic geometry and the theory of differential equations.

Magma workshop on Computational Algebraic Geometry, 810 September 2010. School of Mathematics, Loughborough University. A practical workshop to discuss possibilities for extending facilities in Algebraic Geometry in existing computational algebra systems such as Magma.

Graduate workshop on K3 surfaces and multigraded rings, 68 April 2009. Mathematics Institute, University of Warwick. With talks from Juergen Hausen (Tuebingen), Daniel Ryder (Bristol), Katrin Wendland (Augsburg), and graduate participants.

Whilst at UNB I helped organise several geometry seminars. I was also the UNB organiser for the summer 2007 ASCI seminar series.

GAeL XIV, 611 March 2006. Stephan Banach Centre, Bedlewo, Poland. With principal talks from Frederic Campana (Nancy), Brendan Hassett (Rice), and Claire Voisin (Paris VI).

Between October 2003 and October 2005 I organised the Calf (junior COW). For information on current Calf events, please go here. For a historical record of the events I organised, go here.
In the press

Math in the Media: A monthly magazine from the AMS
"Beautiful pictures and animations reminiscent of flowers or folding cloth grace recent posts of this blog, in which most entries take the form of a technical conversation between specialists Tom Coates, Alessio Corti, Sergei Galkin, Vasily Golyshev, and Al Kasprzyk..."

Physics World: Nature's building blocks brought to life
"The scientists are looking for shapes, known as "Fano varieties", which are basic building blocks and cannot be broken down into simpler shapes. They find Fano varieties by looking for solutions to a variety of string theory, a theory that seeks to unify quantum mechanics with gravity..."

Science: Elementary mathematics
"An international group of mathematicians hopes to do for math what Dmitri Mendeleev’s periodic table did for chemistry by identifying the shapes in three, four, and five dimensions that cannot be divided into other shapes..."

New Scientist: Atoms ripple in the periodic table of shapes
"This rippling structure may look like a piece of origami, or an intricate scarf. In fact, it is geometry's answer to the atom because it can't be broken down into smaller components. Inspired by string theory, there is now a way to classify these atoms by their properties – and hunt down their higher dimensional cousins..."

Cosmos: Mathematicians propose periodic table of shapes
"Mathematicians have embarked on a threeyear project to create their own version of the periodic table that will provide a vast directory of all the possible shapes in the universe across three, four and five dimensions..."