Research activities of the group, including PhD students, papers, conferences, seminars and talks.


K Leschke Member of Scientific Committee PADGE 2017, Leuven




L. Hauswirth, M. Kilian, M. Schmidt, Mean-convex Alexandrov embedded constant mean curvature tori in the 3-sphere. Proc. London Math. Soc. (3), 112, 588-622, 2016

K. Leschke, K. Moriya: Applications of Quaternionic Holomorphic Geometry to minimal surfaces, Complex Manifolds. Volume 3, Issue 1, ISSN (Online) 2300-7443, DOI: 10.1515/coma-2016-0015, November 2016.

T. Hoffmann,  Sageman-Furnas, A 2×2 Lax Representation, Associated Family, and Bäcklund Transformation for Circular K-Nets A.O. Discrete Comput Geom (2016) 56: 472. (first online 28.06.2016)

T. Hoffmann, A. Sageman-Furnas, M. Wardetzky A Discrete Parametrized Surface Theory in ℝ3,
International Mathematics Research Notices, Volume 2017, Issue 14, 01.07.2017, Pages 4217–4258,

H. Kadhim, A. Rona, H. Obaida, K. LeschkeThe performance of a 1.5 stage axial turbine with a non-axisymmetric casing at off-design conditions, Proceedings of the 9th International Conference on Applied Energy, ICAE2017, paper 204, Cardiff, UK, 21-24 August 2017. Published by Elsevier in the Energy Procedia, ISBN: 1876-610

H. Obaida, H. Kadhim, A. Rona,  K. Leschke, P. Gostelow : A numerical study of secondary flows in a 1.5 stage axial turbine guiding the design of a non-axisymmetric hub, Proceedings of ASME Turbo Expo 2017, Turbomachinery Technical Conference and Exposition, GT2017-65251, Charlotte, NC, USA, 26-30 June 2017.

K. Hasegawa, K. MoriyaTwistor lifts and factorization for conformal maps from a surface to the Euclidean four-space. Adv. Appl. Clifford Algebr. 27, No. 2, 1243-1262 (2017).

A. Rona, K. Kadhim, J Gostelow, K Leschke, Mitigating secondary flows in a 1½ stage axial turbine by a guide groove casing, 23rd ISABE conference, by the International Society of Air-breathing Engines (ISABE), Manchester, UK, 03-08.09.2017. (ISABE), Manchester. 1-8 (8 pages). 03.09.2017

K. Moriya, The Schwarz lemma for super-conformal maps. Hermitian-Grassmannian submanifolds, 59–68, Springer Proc. Math. Stat., 203, Springer, Singapore, 2017.


H. Kadhim, A. Rona, P. Gostelow, K. Leschke. Optimization of the non-axisymmetric stator casing of a 1.5 stage axial turbine. International Journal of Mechanical Sciences, Vol. 136, pages 503–514, 2018.

D. Ye,  G. Tang,  T. Hoffmann. A unified discrete framework for intrinsic and extrinsic Dirac operators for geometry processing,  Symp. on Geom. Proc. (2018) (received best paper award)

F. Martin, J. Perez-Garcia, A. Savas-Halilaj and K. Smoczyk A characterization the of the grim reaper cylinder, Journal für reine und angewandte Mathematik, Volume 2019, Issue 746 (Jan 2019), pp. 209–234.

D. Hoffman, T. Ilmanen, F. Martin and B. WhiteGraphical translators for the mean curvature flow. Calculus of Variations and PDE’s, vol. 58, (2019), art. 117.


J. Lira and F. Martin. Translating solitons in Riemannian products. Journal of Differential Equations, Volume 266, Issue 12, 5 June 2019, Pages 7780-7812.


L. Ferrer, F. Martin, R. Mazzeo, M. Rodriguez. Properly embedded minimal annuli in H2xR. Math. Ann., Volume 375, Issue 1–2, (2019), pp 541–594.

K. Leschke, K. Moriya. Simple factor dressing and the Lopez-Ros deformation of minimal surfaces in Euclidean 3-space, Math. Z 291(3), 1015-1058, DOI 10.1007/s00209-018-2217-8, online.

K. Leschke, K. Moriya. The μ–Darboux transformation of minimal surfaces, manuscripta mathematica, August 2019.

M. Rabinovich, T. Hoffmann, O. Sorkine-Hornung, Modeling Curved Folding with Freeform Deformations, ACM Siggraph Asia, 2019.

L. Hauswirth, M Kilian, M Schmidt, Singularities of Whitham flows for hyperelliptic spectral curves, https://arXiv:1709.02330

K. MoriyaHolomorphic structures for surfaces in Euclideann n-space

E. S. Gama, F. MartinTranslating solitons of the mean curvature flow asymptotic to hyperplanes in Rn+1. Preprint

J. H. de Lira, F. MartinTranslating solitons in Riemannian products. Preprint

M. Kilian, E. Mota, N. Schmitt Constant Mean Curvature Trinoids with one Irregular End arXiv:1808.05491

M. Kilian,  S. Klein On closed finite gap curves in spaceforms I . arXiv:1801.07032

M. Kilian, G. Smith; Sur un système intégrable à bord arXiv:1807.02729 Submitted

L. Ferrer, F. Martin, R. Mazzeo, M. RodriguezFamilies of minimal surfaces in H2xR foliated by arcs and their Jacobi fields. Preprint, 2019

K. Leschke: Links between the integrable systems of CMC surfaces, isothermic surfaces and constrained Willmore surfaces. Preprint 2019

M. Rabinovich, T. Hoffmann, O. Sorkine-Hornung. The Shape Space of Discrete Orthogonal Geodesic Nets. Preprint.

D. Hoffman, F. Martin and B. WhiteScherk-like Translators for Mean Curvature Flow. Preprint, 2019.

D. Hoffman, T. Ilmanen, F. Martin, B. WhiteNotes on Translating Solitons of the Mean Curvature Flow. Preprint, 2019

J. Cho, K. Leschke, Y. Ogata, Generalised Bianchi permutability.. In preparation.

K. Leschke, Darboux transforms of minimal surfaces. In preparation.

T. Hoffmann, A. O. Sageman-Furnas, M. Wardetzky, Discrete Bonnet pairs and a conformal theory of quad-graphs, in preparation.

Springer Proceedings in Mathematics

T. Hoffmann, M. Kilian, K. Leschke, F. Martin, K. Moriya, editors, Springer Proceedings in Mathematics. In preparation.


PhD Students:

L. Collard: (K Leschke) Thesis title: "Characterising the Properties of Metastable Phases in Aerosols", University of Leicester (2018)

H. Kadhim (K Leschke co-supervisor with A Rona, Engineering). Thesis title: "Effect of non-axisymmetric casing design on flow and performance of an axial turbine", University of Leicester (2018)

J. García (F Martin) Thesis title: “Translating solitons of the mean curvature flow” December 2016 University of Granada.

E. Gama. (F Martin) Thesis title: “Problems related with the mean curvature: MCF and minimal surfaces”. University of Granada, 2019

H. Obaida (K Leschke co-supervisor with A Rona, Engineering), Thesis title: "Cryogenic cycle power turbines optimised by hub contouring". University of Leicester,(2017)

B. Koenig (T Hoffman) Thesis title: "A geometric construction for the associated family of S-isothermic CMC sufaces" July 2017, Technical University Munich.

J. Torres (F. Martin), University of Granada

Z. Ye (T Hoffmann), TU Munich.

E. Mota (M Kilian) Thesis title: 'Constant Mean Curvature Surfaces and Heun’s Differential Equations' , 2019, UCC.


Undergraduate Research Bursary (LMS):

Aneesah Parkar (K Leschke) Deformations of the Gyroid,


Postdocs & Visiting Researchers

Benoit Daniel (Nancy, France) - visiting Granada, July 2017

Tom Ilmanen (ETH, Zurich) - visting Granada, April 2017

Jorge Lira (UFC, Brazil) - visiting Granada, January 2017

Alessandro Carlotto (ETH, Zurich) - visiting Granada, September 2016

Michael Rabinovich (ETH, Zurich) - visiting Munich, November 2016

Sebastian Klein, Postdoc, Cork.

Keomkyo Seo, (Sookmyung University, Korea). January 2018.

Graham Smith (UFRJ, Brazil) visited UCC in January 2018

Laurent Hauswirth (MLV, France) visited UCC in May 2018

Esko Heinonen, University of Helsinki (Finland), Postdoc, Granada.

Fran Burstall, University of Bath, visited UCC in September 2018

Esko Heinonen Postdoc (fellowship of the Finnish Academy of Science) (UGR) 2019

Conference/Workshop presentations

K Leschke "A complex associated family for isothermic surfaces", Quaternionic Differential Geometry and its Related Topics ", Ochanomizu University, Tokyo, 6-9.9.2016

T Hoffman "Discrete curvatures and discrete integrable systems", Lecture series at the Autumns school at Graz, Austria, 27.09-06.10.2016.

K. Moriya, "The Weierstrass representation for surfaces in Euclidean space of arbitrary dimension"Geometry section, MSJ Autumn Meeting 2016, at Kansai University, Japan

K Leschke "Soap films, quaternions and geometry", "LMS Prospects in Mathematics", University of York, York, 16-17.12.2016

F  Martin "Translating solitons of the mean curvature flow", Analysis & PDE seminar at Stanford University, February 27, 2017

K Leschke"Introduction to Quaternionic Holomorphic Geometry" Valenciennes.

M Kilian "On Finite Gap Curves" Irish Geometry Conference, NUI Maynooth, Ireland, 26.05.2017

M Kilian "Dressing Curves", "Variational Methods in Submanifold Geometry", University of York, UK, 31.05.2017.

F Martin "Properly embedded minimal annuli in H^2xR"31st Brazilian Colloquium of Mathematics, IMPA, Rio de Janeiro, Brazil. 29.07- 05.08.2017.

K Leschke"Transformation of Minimal Surfaces", Higgs bundles, harmonic maps and integrable Systems", Hannover, 14-18.8.2017

K Moriya, "The Schwarz lemma for conformal maps from the open unit disk into the Euclidean four-space". Geometry of Submanifolds and Integrable Systems, Osaka City University, Japan, 2018-03-26--2018-03-30

K Moriya, "
Complex structures of vector bundles and harmonic maps into a sphere", Submanifolds at Yuzawa 2017, Yuzawa Grand Hotel, Japan, 2017-11-30--2017-12-02

T Hoffmann, "Curvature and integrable surface theory", Paris,  2017

K Moriya, "The spinor representation of conformal mappings of surfaces", Deepening and Development of Submanifold Geometry, Research Institute for Mathematical Sciences, Kyoto University, Japan, 2018-06-25--2018-06-27

K Moriya, "
The spinor representation of a surface in an Euclidean space of arbitrary dimension", m:iv mini-workshop at University of Leicester, UK, 15th August 2018

K Leschke, "Darboux transforms of CMC surfaces revisited", Geometry of Submanifolds and Integrable Systems, OCAMI, Osaka, 2018

F Martin, "Minimal Surfaces and Mean Curvature Flow". A Conference in Honor of Brian White. Stanford, July 6-8, 2018.

F Martin, "Translating graphs for the MCF in Euclidean space". Tsukuba, 2018

T Hoffmann, "Minicourse A discrete surface theory in R3", TU Wien, 2018

K Leschke, "Darboux transforms of minimal surfaces", YDGD,  Leeds, 2018

K Leschke "Isothermic surfaces”,  Key note lectures, Differential Geometry and its discretisation, OCAMI, Osaka 2019.

K Leschke "Transformations of minimal surfaces, Japan-UK winter school, Leeds, January 2019

F Martin "Scherk-like Translators for Mean Curvature Flow”, Geometric Analysis and Partial Differential Equations seminar, University of Cambridge, U.K May 3, 2019.

F Martin "Scherk-like Translators for Mean Curvature Flow”. Problèmes variationnels et géométrie des sous-variétés, Variational Problems and the Geometry of Submanifolds, 27-31 May, 2019. C.I.R.M., Luminy, France.

F Martin "New examples of translating solitons of the Mean Curvature Flow”.  Geometry Day Granada-Fortaleza, Universidad Federal do Ceara, Fortaleza, Brazil July 24, 2019.

K Leschke “Links between the integrable systems of a CMC surface” m:iv 2019, Leicester

T Hoffmann “On discrete geodesics” m:iv 2019, Leicester

F Martin “New examples of translating solitons fo the Mean Curvature Flow” m:iv 2019, Leicester

M Kilian “Properly embedded minimal annuli in S2xR” m:iv 2019, Leicester

K Leschke “Isothermic Positons”,   ISHM2019: Integrable systems and harmonic maps, Vienna 2019

M Kilian "On closed finite gap curves", ISHM 2019: Integrable systems and harmonic maps, Vienna 2019

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The Leverhulme Trust

Leverhulme Trust logo

The Leverhulme Trust awarded Dr Katrin Leschke at the University of Leicester a 3 year international research network grant that started 1st September 2016

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