Alexander Kasprzyk

Mirror symmetry and the classification of orbifold del Pezzo surfaces We state a number of conjectures that together allow one to classify a broad class of del Pezzo surfaces with cyclic quotient singularities using mirror symmetry. We prove our conjectures in the simplest cases. The conjectures relate mutation-equivalence classes of Fano polygons with Q-Gorenstein deformation classes of del Pezzo surfaces.

"Mirror symmetry and the classification of orbifold del Pezzo surfaces" by M. Akhtar, T. Coates, A. Corti, L. Heuberger, A. Kasprzyk, A. Oneto, A. Petracci, T. Prince, and K. Tveiten. In Proceedings of the AMS @amermathsoc.bsky.social . #AlgebraicGeometry

Vasco Portilheiro (UCL)12 April 2023"Barriers to Learning Symmetries"Given the success of equivariant models, there has been increasing interest in models wh... Vasco Portilheiro (UCL)

Vasco Portilheiro (UCL) speaking on "Barriers to Learning Symmetries" at our #MachineLearning #Math seminar back in April 2023. #MathSky

Restrictions on the singularity content of a Fano polygon We determine restrictions on the singularity content of a Fano polygon, or equivalently of certain orbifold del Pezzo surfaces. We establish bounds on the maximum number of 1/R(1,1) singularities in the basket of residual singularities. In particular, there are no Fano polygons without T-singularities and with a basket given by (i) {k x 1/R(1,1)} for k \in Z_{\geq 0} > 0 and R \geq 5, or (ii) {1/R_1(1,1), 1/R_2(1,1), 1/R_3(1,1)}.

The research discussed by Daniel Cavey appeared in the workshop proceedings "Algebraic and Geometric Combinatorics on Lattice Polytopes", edited by Takayuki Hibi and Akiyoshi Tsuchiya.
www.worldscientific.com/doi/abs/10.1...

Daniel Cavey (Nottingham)26 February, 2021"Restrictions on the Singularity Content of a Fano Polygon"Singularity content is a combinatorial property of a Fan... Daniel Cavey (Nottingham)

Daniel Cavey (Nottingham) speaking on "Restrictions on the Singularity Content of a Fano Polygon" at our #AlgebraicGeometry #Math seminar back in February 2021. #MathSky

Representations of Deligne-Mostow lattices into PGL(3,C) We classify representations of a class of Deligne-Mostow lattices into PGL(3,C). In particular, we show local rigidity for the representations (of Deligne-Mostow lattices with three-fold symmetry and of type one) where the generators we chose are of the same type as the generators of Deligne-Mostow lattices. We also show local rigidity without constraints on the type of generators for six of them and we show the existence of local deformations for a number of representations in three of them. We use formal computations in SAGE and Maple to obtain the results. The code files are available on GitHub.

"Representations of Deligne-Mostow lattices into PGL(3,C)" by E. Falbel, I. Pasquinelli, and A. Ucan-Puc. #ExperimentalMath #RepresentationTheory #MathSky

London Mathematical Society Two Grade II listed buildings, 4-storey yellow stock brick with a rusticated stucco base. No. 57 has an attic level with a garden at the rear. Staircases are intact and each room still retains its…

We are thrilled to be a part of this year's @opencity-uk.bsky.social, an annual celebration of London's architecture and urban landscape

Our historic home at De Morgan House will be open for visits on Sat 13 Sep

Booking is free and opens at 12pm on 20 Aug
programme.openhouse.org.uk/listings/5048

Passagemath is a really interesting project to, as I understand it, streamline the process of using Sage (starting with simple installation via pip, but also easing integration into your own #Python projects) and making it a part of the lively scientific Python community. #computeralgebra #mathsky

Classification of Fano 4-folds with Lefschetz defect 3 and Picard number 5 Let X be a smooth, complex Fano 4-fold, and \rho_X its Picard number. If X contains a prime divisor D with \rho_X - \rho_D > 2, then either X is a product of del Pezzo surfaces, or \rho_X = 5,6. In this setting, we completely classify the case where \rho_X = 5; there are 6 families, among which one is new. We also deduce the classification of Fano 4-folds with \rho_X >= 5 with an elementary divisorial contraction sending a divisor to a curve.

For further details see the article "Classification of Fano 4-folds with Lefschetz defect 3 and Picard number 5" by Cinzia Casagrande and Eleonora Romano, published in the Journal of Pure and Applied Algebra.
www.sciencedirect.com/science/arti...

Cinzia Casagrande (Torino)24 February, 2021"On Fano 4-folds with Lefschetz defect 3"We will talk about a classification result for some (smooth, complex) Fan... Cinzia Casagrande (Torino)

Cinzia Casagrande (Torino) speaking on "On Fano 4-folds with Lefschetz defect 3" at our #AlgebraicGeometry #Math seminar back in February 2021. #MathSky

16% of the UK population was born overseas (21/22 census)
12% of UK prisoners were born overseas
Therefore people born overseas are less likely to be in jail than people born in the UK.
That should be the headline.

AI-driven research in pure mathematics and theoretical physics - Nature Reviews Physics Advances in artificial-intelligence-assisted mathematical investigations suggest that human–machine collaboration will be an integral part of future theoretical research.

Yang-Hui He explored some of these ideas in more detail in a nice article for @natrevphys.nature.com in August last year.
www.nature.com/articles/s42...

Yang-Hui He (LIMS)5 April 2023"Universes as Bigdata: Physics, Geometry and Machine-Learning"The search for the Theory of Everything has led to superstring th... Yang-Hui He (LIMS)

Yang-Hui He (LIMS) speaking on "Universes as Bigdata: Physics, Geometry and Machine-Learning" at our #MachineLearning #Math seminar back in April 2023. #MathSky

Computation of the Taut, the Veering and the Teichmüller Polynomials Landry, Minsky and Taylor (LMT) introduced two polynomial invariants of veering triangulations—the taut polynomial and the veering polynomial. Here, we consider a pair of taut polynomials associated to one veering triangulation, the upper and the lower one, and analogously the upper and lower veering polynomials. We prove that the upper and lower taut polynomials are equal. In contrast, the upper and lower veering polynomials of the same veering triangulation may differ by more than a unit. We give algorithms to compute all these invariants. LMT related the Teichmüller polynomial of a fibered face of the Thurston norm ball with the taut polynomial of the associated layered veering triangulation. We use this result to give an algorithm to compute the Teichmüller polynomial of any fibered face of the Thurston norm ball.

"Computation of the Taut, the Veering and the Teichmüller Polynomials" by Anna Parlak. #ExperimentalMath #Manifolds #MathSky

Philip Engel, Olivier de Gaay Fortman, Stefan Schreieder
Matroids and the integral Hodge conjecture for abelian varieties
https://arxiv.org/abs/2507.15704

Local Normal Forms of Noncommutative Functions This article describes local normal forms of functions in noncommuting variables, up to equivalence generated by isomorphism of noncommutative Jacobi algebras, extending singularity theory in the style of Arnold’s commutative local normal forms into the noncommutative realm. This generalisation unveils many new phenomena, including an ADE classification when the Jacobi ring has dimension zero and, by taking suitable limits, a further ADE classification in dimension one. These are natural generalisations of the simple singularities and those with infinite multiplicity in Arnold’s classification. We obtain normal forms away from some exceptional Type E cases. Remarkably, these normal forms have no continuous parameters, and the key new feature is that the noncommutative world affords larger families. This theory has a range of immediate consequences to the birational geometry of 3-folds. The normal forms of dimension zero are the analytic classification of smooth 3-fold flops, and one outcome of NC singularity theory is the first list of all Type D flopping germs, generalising Reid’s famous pagoda classification of Type A, with variants covering Type E. The normal forms of dimension one have further applications to divisorial contractions to a curve. In addition, the general techniques also give strong evidence towards new contractibility criteria for rational curves.

The work discussed by Gavin Brown was published earlier this year in Forum of Math., Pi.
www.cambridge.org/core/journal...

Gavin Brown (Warwick)23 February, 2021"Some normal forms for flops"I describe ongoing work with Michael Wemyss to understand crepant contractions from smooth... Gavin Brown (Warwick)

Gavin Brown (Warwick) speaking on "Some normal forms for flops" at our #AlgebraicGeometry #Math seminar back in February 2021. #MathSky

More coverage from the BBC! Give it a watch to learn what is at stake in our industrial actions.

Compulsory redundancies are NOT necessary for the future of our university! In fact, it undermines it.

Buildings don't teach and campuses don't do research. We do.

#StopTheCuts #SaveHE

Staff ‘demoralised’ by lack of career progression amid cost cuts Promotion freezes at UK universities exacerbate frustrations caused by mass redundancies and low pay rises, with academics warning it could force more people out of the sector

A lack of career progression within UK universities is “demoralising” staff and threatening to push people out of the sector, it has been warned, as institutions respond to the financial crisis by freezing promotions and concentrating hiring on lower-level positions
#academicsky #edusky

Weronika Buczy\'nska, Jaros{\l}aw Buczy\'nski, Maciej Ga{\l}\k{a}zka
Grassmann cactus variety and socle dimension
https://arxiv.org/abs/2507.21586

Quantum periods for 3-dimensional Fano manifolds The quantum period of a variety X is a generating function for certain Gromov–Witten invariants of X which plays an important role in mirror symmetry. We compute the quantum periods of all 3–dimensional Fano manifolds. In particular we show that 3–dimensional Fano manifolds with very ample anticanonical bundle have mirrors given by a collection of Laurent polynomials called Minkowski polynomials. This was conjectured in joint work with Golyshev. It suggests a new approach to the classification of Fano manifolds: by proving an appropriate mirror theorem and then classifying Fano mirrors. Our methods are likely to be of independent interest. We rework the Mori–Mukai classification of 3–dimensional Fano manifolds, showing that each of them can be expressed as the zero locus of a section of a homogeneous vector bundle over a GIT quotient V//G, where G is a product of groups of the form GL_n(C) and V is a representation of G. When G=GL_1(C)^r, this expresses the Fano 3–fold as a toric complete intersection; in the remaining cases, it expresses the Fano 3–fold as a tautological subvariety of a Grassmannian, partial flag manifold, or projective bundle thereon. We then compute the quantum periods using the quantum Lefschetz hyperplane theorem of Coates and Givental and the abelian/non-abelian correspondence of Bertram, Ciocan-Fontanine, Kim and Sabbah.

"Quantum periods for 3-dimensional Fano manifolds" by Tom Coates, Alessio Corti, Sergey Galkin and Alexander Kasprzyk. In Geometry & Topology. #AlgebraicGeometry #ComputerAlgebra #HPC

Trainable and explainable simplicial map neural networks Simplicial map neural networks (SMNNs) are topology-based neural networks with interesting properties such as universal approximation ability and robustness to adversarial examples under appropriate conditions. However, SMNNs present some bottlenecks for their possible application in high-dimensional datasets. First, SMNNs have precomputed fixed weight and no SMNN training process has been defined so far, so they lack generalization ability. Second, SMNNs require the construction of a convex polytope surrounding the input dataset. In this paper, we overcome these issues by proposing an SMNN training procedure based on a support subset of the given dataset and replacing the construction of the convex polytope by a method based on projections to a hypersphere. In addition, the explainability capacity of SMNNs and effective implementation are also newly introduced in this paper.

For further details see the article "Trainable and explainable simplicial map neural networks" by Eduardo Paluzo-Hidalgo, Rocio Gonzalez-Diaz, and Miguel Gutiérrez-Naranjo, published in Information Sciences last year.
www.sciencedirect.com/science/arti...

Eduardo Paluzo-Hidalgo (Seville)29 March 2023"An introduction to Simplicial-map Neural Networks"In a recently accepted project RexasiPro, we deal with a crit... Eduardo Paluzo-Hidalgo (Seville)

Eduardo Paluzo-Hidalgo (Seville) speaking on "An introduction to Simplicial-map Neural Networks" at our #MachineLearning #Math seminar back in March 2023. #MathSky

Seshadri constants and K-stability of Fano manifolds We give a lower bound of the δ-invariants of ample line bundles in terms of Seshadri constants. As applications, we prove the uniform K-stability of infinitely many families of Fano hypersurfaces of arbitrarily large index, as well as the uniform K-stability of most families of smooth Fano threefolds of Picard number one.

The work discussed by Hamid Abban was published in Duke Math Journal, in a paper joint with Ziquan Zhuang.
projecteuclid.org/journals/duk...

Hamid Ahmadinezhad (Loughborough)25 February, 2021"Seshadri constants, induction, and K-stability"I will talk about an inductive approach to proving K-stabil... Hamid Ahmadinezhad (Loughborough)

Hamid Abban (Loughborough) speaking on "Seshadri constants, induction, and K-stability" at our #AlgebraicGeometry #Math seminar back in February 2021. #MathSky

Covert 19th century political intrigues of Tenerife nobility revealed by cryptanalyzing an encrypted letter This article presents a cryptanalysis of a 19th-century encrypted manuscript discovered in the archives of Conde de Siete Fuentes in Tenerife, Canary Islands, Spain. The manuscript, preserved by th...

Covert 19th century political intrigues of Tenerife nobility revealed by cryptanalyzing an encrypted letter www.tandfonline.com/doi/full/10....

New Representations for all Sporadic Apéry-Like Sequences, With Applications to Congruences We find new representations, in terms of constant terms of powers of Laurent polynomials, for all the 15 sporadic Apéry-like sequences discovered by Zagier, Almkvist-Zudilin and Cooper. The new representations lead to binomial expressions for the sequences, which, as opposed to previous expressions, do not involve powers of 3 or 8. We use these to establish the supercongruence B_{np^k} \cong B_{np^{k-1}} mod p^{2k} for all primes p \geq 3 and integers n, k \geq 1, where B_n is a sequence discovered by Zagier, known as Sequence B. Additionally, for 14 of the 15 sequences, the Newton polytopes of the Laurent polynomials contain the origin as their only interior integral point. This property allows us to prove that these sequences satisfy a strong form of the Lucas congruences, extending work of Malik and Straub. Moreover, we obtain lower bounds on the p-adic valuation of these sequences via recent work of Delaygue.

"New Representations for all Sporadic Apéry-Like Sequences, With Applications to Congruences" by Ofir Gorodetsky. #ExperimentalMath #AperyNumbers #MathSky

Registration and Programme - RSECon25 Join us for the ninth annual Research Software Engineering conference RSECon25, at the University of Warwick, Coventry, UK, from 9–11 September 2025. Learn, share, and build connections across the…

This Thursday (31st) is your last chance to buy in-person tickets for #RSECon25 . Held at
@uni-of-warwick.bsky.social 9-11 September and organised by @society-rse.org this is a wonderful opportunity connect with the vibrant Research Software Engineering academic community.

FUJITA DECOMPOSITION AND MASSEY PRODUCT FOR FIBERED VARIETIES | Nagoya Mathematical Journal | Cambridge Core FUJITA DECOMPOSITION AND MASSEY PRODUCT FOR FIBERED VARIETIES - Volume 247

The research discussed by Francesco Zucconi was published in the Nagoya Mathematical Journal.
www.cambridge.org/core/journal...

Francesco Zucconi (Udine)18 February 2021"Fujita decomposition and Massey product for fibered varieties"Let f:X \mapsto B be a semistable fibration where X i... Francesco Zucconi (Udine)

Francesco Zucconi (Udine) speaking on "Fujita decomposition and Massey product for fibered varieties" at our #AlgebraicGeometry #Math seminar back in February 2021. #MathSky

38th BTM The meeting will begin on Tuesday 9th September at 13:00 and will close around noon on Thursday 11th September. All talks will be held in Abacws.

Cardiff is hosting the 38th British Topology Meeting from 9th - 11th September 2025. The registration is now open! Come along if you are looking for some interesting talks about all things topological. Details can be found here: sites.google.com/view/btm38 #MathSky #topology #AcademicSky