School of Science

Research

Centre for Geometry and Applicatons

Geometry lies at the heart of modern science. It unifies diverse branches of mathematics such as algebra, analysis and number theory, and connects to applications in theoretical physics, computer science, statistics, and more.

Loughborough University has a strong tradition of research in Geometry and related areas. The new Centre for Geometry and Applications will build on this through an extensive programme of activities: international conferences, world-leading academic visitors, and new links with industrial partners utilising applications of geometry.

 

Research interests

Algebraic Geometry: Higher dimensional birational geometry; Positivity; Fano varieties; K3 surfaces and Calabi-Yau threefolds; Toric geometry; Secant varieties

Differential Geometry: Projective geometry; Lie sphere geometry; Web geometry; Generalised conformal geometry; Submanifold geometry; Special holonomy

Integrable systems: Hamiltonian and non-holonomic mechanics; Lagrangian fibrations; Soliton equations; Symmetry methods; Dispersionless integrability; Hamiltonian formalism; Algebraic reduction method; Frobenius manifolds; Discrete and quantum integrable systems; Special functions; Algebro-geometric approach to integrability

Members

Associate members

Current postdocs

Completed

  • Dr Matteo Casati

Current research students

Completed

  • Katie Spalding (2018): Growth and integrability in multivalued dynamics (supervisor A. Veselov)
  • Jonathan Moss (2016): Linear degeneracy in multidimensions (supervisor E. Ferapontov)
  • Andrea Savoldi (2016): On Poisson structures of hydrodynamic type and their deformations (supervisors E. Ferapontov and  P. Lorenzoni)
  • William Haese-Hill  (2015): Spectral properties of integrable Schroedinger operators with singular potentials (supervisors M. Hallnas and A. Veselov)
  • Ilia Roustemoglou (2015): Classification of integrable differential/difference equations in 2+1 dimensions (supervisors E. Ferapontov and V. Novikov)
  • Veronika Schreiber (2014): Special vector configurations in geometry and integrable systems (supervisor A. Veselov);
  • Dragomir Tsonev (2013): Realisation of holonomy algebras on pseudo-Riemannian manifolds by means of Manakov operators (supervisor A. Bolsinov)
  • Graham Kemp (2013): Algebra and geometry of Dirac magnetic monopole (supervisor A. Veselov)
  • Adrian Hemery (2012): The spectral properties and singularities of monodromy-free Schrodinger operators  (supervisor A Veselov);
  • Nikola Stoilov (2012): Hamiltonian systems of hydrodynamic type in 2+1 dimensions (supervisor E. Ferapontov)
  • Pumei Zhang (2012): Algebraic aspects of compatible Poisson structures (supervisor  A. Bolsinov)
  • Anton Izosimov (2012): Singularities of bihamiltonian systems and the multidimensional rigid body (supervisor A. Bolsinov)
  • Pavel Burovskiy (2009): On the integrability of three-dimensional second order quasilinear PDEs (supervisors E. Ferapontov and A. Veselov)
  • Lenos Hadjikos (2009): Integrable equations of the dispersionless Hirota type (supervisors E. Ferapontov and K. Khusnutdinova)
  • David Marshall (2008): Differential-geometric approach to the integrability of hydrodynamic chains (supervisors E. Ferapontov and K. Khusnutdinova)

 

2018 

  • H. Ahmadinezhad, I. Cheltsov, J. Schicho, On a conjecture of Tian. Mathematische Zeitschrift  288 (2018), no. 1-2, 217–241.
  • H. Ahmadinezhad, T. Okada, Birationally rigid pfaffian Fano 3-folds, Algebraic Geometry , (2018) Volume 5, Issue 2, 160-199.
  • B Doubrov, E. Ferapontov, B. Kruglikov, V. Novikov, On integrability in Grassmann geometries: integrable systems associated with fourfolds in Gr(3, 5). Proc. Lond. Math. Soc. 3 (2018), 1-32.
  • B Doubrov, E. Ferapontov, B. Kruglikov, V. Novikov, Integrable systems in 4D associated with sixfolds in Gr(3, 5). Int. Math. Res. Not. IMRN  (2018), DOI:10.1093/imrn/rnx308.

 

2017

  • H. Ahmadinezhad, On pliability of del Pezzo fibrations and Cox rings. J. Reine Angew. Math. 723 (2017) 101-125.
  • A. Bolsinov, Some remarks about Mishchenko-Fomenko subalgebras. J. Algebra 483 (2017), 58-70.
  • V. Knibbeler, S. Lombardo, J.A. Sanders, Higher-dimensional automorphic Lie algebras. Found. Comput. Math. 17 (2017), no. 4, 987-1035.
  • A. Hone, V. Novikov, J.P. Wang, Two-component generalizations of the Camassa-Holm equation. Nonlinearity 30 (2017), no. 2, 622-658. 

  • O. Dumitrescu, E. Postinghel, Vanishing theorems for linearly obstructed divisors. J. Algebra 477 (2017), 312-359.
  • A. Prendergast-Smith, A special Cayley octad, Trans. Amer. Math. Soc. (2017).
  • A.M. Salagean, M. Mandache-Salagean, Counting and characterising functions with `fast points’ for differential attacks. Cryptography and Communications 9 (2)  (2017), 217-239.
  • A. Matsuo, A. Veselov, Universal formula for the Hilbert series of minimal nilpotent orbits. Proc. Amer. Math. Soc. 145 (2017), no. 12, 5123-5130.
  • A. Sergeev, A. Veselov,Orbits and invariants of super Weyl groupoid. Int. Math. Res. Not. IMRN (2017), no. 20, 6149-6167.
  • A. Sergeev, A. Veselov, Symmetric Lie superalgebras and deformed quantum Calogero-Moser problems. Adv. Math. 
304 (2017), 728-768.

 

2016

  • H. Ahmadinezhad, F. Zucconi, Mori dream spaces and birational rigidity of Fano 3-folds. Adv. Math. 292 (2016) 410-445.
  • H. Ahmadinezhad, A.S. Kaloghiros, Non-rigid quartic 3-folds, (2016)  Compositio Mathematica, 152(5) (2016) 955-983.
  • A.M. Salagean, R. Winter, M. Mandache-Salagean, R. Phan, Higher order differentiation over finite fields with applications to generalising the cube attack. Designs, Codes and Cryptography 84 (3) (2016) 425-449.

 

2015

  • A. Bolsinov, V. Matveev, T. Mettler, S. Rosemann, Four-dimensional Kahler metrics admitting c-projective vector fields. J. Math. Pures Appl. (9) 103 (2015), no. 3, 619-657.
  • A. Bolsinov, V. Matveev, Local normal forms for geodesically equivalent pseudo-Riemannian metrics. Trans. Amer. Math. Soc. 367 (2015), no. 9, 6719-6749.
  • A. Bolsinov, A. Borisov, I. Mamaev, Geometrisation of Chaplygin’s reducing multiplier theorem. Nonlinearity 28 (2015), no. 7, 2307-2318.
  • E. Ferapontov, V. Novikov, I. Roustemoglou, On integrability of discrete Hirota type equations in 3D. Int. Math. Res. Not. IMRN  (2015), no. 13, 4933-4974.
  • M. Brambilla, O. Dumitrescu, E. Postinghel, On a notion of speciality of linear systems in Pn. Trans. Amer. Math. Soc. 
367 (2015), no. 8, 5447-5473.
  • E. Postinghel, F. Sottile, N. Villamizar, Degenerations of real irrational toric varieties. J. Lond. Math. Soc. 92 (2015), no. 2, 223-241.
  • I. Coskun, A. Prendergast-Smith, Eckhard loci on hypersurfaces. Comm. Algebra 43 (2015), no. 8, 3083-3101.
  • A. Sergeev, A. Veselov, Jack-Laurent symmetric functions. Proc. Lond. Math. Soc. (3) 111 (2015), no. 1, 63-92.
  • K. Schobel, A. Veselov, Separation coordinates, moduli spaces and Stasheff polytopes. Comm. Math. Phys. 337 (2015), no. 3, 1255-1274.

 

2014

  • A. Bolsinov, D. Tsonev, On a new class of holonomy groups in pseudo-Riemannian geometry. J. Differential Geom. 97 (2014), no. 3, 377-394.
  • A. Bolsinov, A. Izosimov, Singularities of bi-Hamiltonian systems. Comm. Math. Phys. 331 (2014), no. 2, 507-543.
  • E. Ferapontov, B. Kruglikov, Dispersionless integrable systems in 3D and Einstein-Weyl geometry. J. Differential Geom. 97 (2014), no. 2, 215-254.
  • F. Baronio, M. Conforti, A. Degasperis, S. Lombardo, M. Onorato, S. Wabnitz, Vector rogue waves and baseband modulation instability in the defocusing regime. Phys. Rev. Lett. 113 (3) (2014), 034101.
  • I. Coskun, A. Prendergast-Smith, Fano manifolds of index n-1 and the cone conjecture. Int. Math. Res. Not. IMRN  (2014), no. 9, 2401-2439.

External

  • EPSRC EP/S004130/1: Dr Postinghel (PI), £203,354
  • EPSRC EP/N031369/1: Prof Ferapontov (PI), £280,335
  • Heilbronn Institute focused research grant: Dr Ahmadinezhad £5,485
  • Russian Science Foundation Grant: Dr Bolsinov, £250,000.

Internal

  • GRAnD mini-CDT: Dr Ahmadinezhad (PI)
  • IAS semester theme on Geometry: Dr Ahmadinezhad (PI) £25,000.

Past Funding (since September 2017)

  • INdAM Marie Curie Fellow Dr Casati, 2016-2018: £9,000
  • LMS Regional Meetings and Workshop: Prof Veselov £5,000
  • LMS scheme 2 grant for Prof Vitolo: Prof Ferapontov £970
  • Institute of Advanced Studies (IAS) grant for Prof Vitolo: Prof Ferapontov £750
  • Royal Society mobility grant: Dr Salagean, £6,000

 

Seminars

Events coordinated by the Centre

Lecture series

Visitors

  • Prof  C. Ciliberto (Rome), February 2019
  • Dr.  C. Urech (Imperial College), June 2018