Dr Katrin Leschke

I am a reader in Mathematics and a Royal Society Short Industry Fellow. I obtained my Diplom and PhD on topics in geometry at TU Berlin. Before joining the University of Leicester in 2007 I hold research positions at TU Berlin the University of Massachusetts in Amherst and the University of Augsburg where I was awarded my habilitation. My research expertise is in surface theory and integrable systems. I currently also work on applications of discrete geometry in machine learning, engineering and chemistry.

I am currently Postgraduate Tutor for Mathematics. I'm also a member of appeals panels and co-director of the VisLab. Elsewhere, I'm an elected member of the standing panel of European Women in Mathematics. I'm an elected member of the SLAM committee of the London Mathematical Society. I’m a member of AIDAM and the Creative Computing Research Group.

For more information about me and my research see the webpages https://sites.google.com/site/kleschke/, https://www.le.ac.uk/miv and https://gigda.ugr.es/pm2021/ 

My research is in surface theory and its applications. In papers with Burstall Ferus Pedit and Pinkall we generalise methods and statements known in complex algebraic geometry to complex quaternionic line bundles and derive this way new results in surface theory. The main idea of ""Quaternionic Holomorphic Geometry"" is to consider the 4 sphere as quaternionic projective space and use the conformal maps into the 4-sphere as the holomorphic functions of the theory.

I am leading an international network team working on minimal surfaces ""m:iv"" which investigates links between minimal surfaces integable systems and visualisation (originally funded by the Leverhulme Trust, now partially funded by the project Semi-Riemannian Geometry and geometric flows in mathematical physics).

I am a Royal Society Short Industry Fellow, looking at machine learning and discrete Geometry methods for monitoring of particle outfall.

Geometrically inspired discretisation of surfaces play an important role in providing fast and efficient numerical methods to solve PDEs. I'm currently investigating certain discrete curves and surfaces to find efficient tools to solve the underlying differential equations. My current engagement is built on a SPRINT collaboration on how to improve machine learning algorithms via geometric information given by discrete curves.

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D. Ferus, K. Leschke, F. Pedit, U. Pinkall, Quaternionic holomorphic geometry: Plücker formula, Dirac eigenvalue estimates and energy estimates of harmonic 2-tori, Invent. math., Vol. 146, pages 507-593, 2001.

F. Burstall, D. Ferus, K. Leschke, F. Pedit, U. Pinkall, Conformal Geometry of Surfaces in S4 and Quaternions , Lecture Notes in Mathematics 1772, 86 pages, Springer, Berlin, Heidelberg, 2002.

K. Leschke, F. Pedit, U. Pinkall, Willmore tori with nontrivial normal bundle, Math. Annalen, Volume 332, No. 2, pages 381-394, 2005.

K. Leschke, F. Pedit, Sequences of Willmore surfaces, Mathematische Zeitschrift, Springer, vol. 259 (2008), no. 1, pp. 113-122

C. Bohle, K. Leschke, F. Pedit, U. Pinkall, Conformal maps from a 2-torus into the 4-sphere, Crelle's journal, Vol 2012, Issue 671, pages 1-30

K. Leschke, P. Romon, Darboux transforms and spectral curves of Hamiltonian stationary Lagrangian tori, Calc. Var. PDE,  Vol 38, issue 1, (2010), pages 45-74. 

F. Burstall, J. Dorfmeister, K. Leschke, A. Quintino, Darboux transforms and simple factor dressing of constant mean curvature surfaces, Manuscripta Mathematica, Vol 140, Issue 1 (2013), pages 213-236

E. Carberry, K. Leschke, F.  Pedit, Darboux transforms and spectral curves of constant mean curvature surfaces revisited,  Annals of Global Analysis and Geometry, Volume 43, Issue 4 (2013), pages 299-329

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

J. Cho, K. Leschke, Y. Ogata, Generalised Bianchi permutability of isothermic surfaces. arXiv:2104.07185, Annals of Global Analysis and Geometry, 2022, DOI 10.1007/s10455-022-09833-5

My research area is in surface theory with applications in machine learning, Engineering, Informatics and Chemistry. The approach to problems is via Quaternionic Holomorphic Geometry which is an efficient tool to study surfaces in 3- and 4-space. Particular interest is in studying the underlying PDEs via integrable system methods, which allows for a reliable discretisation.

Topics for research supervision

• Integrable systems of Minimal surfaces via isothermic spectral data
• Discrete Minimal Surfaces
• Discrete Isothermic Surfaces
• Applications of surface theory to machine learning 

I am a Fellow of the HEA and received my Habilitation at the University of Augsburg.

I have obtained a wide range of pedagogic experience by teaching at undergraduate and postgraduate level in Germany the USA and the UK. I consider teaching as an integral part of my work: experiences in teaching enhance my views in research and conversely new approaches in research lead to more meaningful teaching. My teaching expertise lies in the area of geometry and visualisation but I also made significant contributions to the curriculum of the Calculus and Analysis stream.

Modules

• Linear Algebra 1 (MA1112)
• Calculus and Analysis I (MA1012)
• Geometry and Visualisation (MA3152)
• Curves and Surfaces (MA3152)
• Proofs and Number Systems (MA1103)
• Complex Analysis (MA3121)
• Minimal surfaces (MA7155)
• Investigations in Mathematics (MA2510)
• BSc/MMath Project (MA3156, MA4505)
• Analytic Geometry (MA0001 - DUT)
• Vector Calculus (MA2032 - DUT)
• Mathematics in Business (MA1254)

I'm an elected member of the SLAM committee of the London Mathematical Society and the Standing Committee of the European Women in Mathematics. I’m a member of AIDAM and the Creative Computing Research Group.

I was main organiser of the following workshops/conferences:

m:iv Autumn 2019 Workshop September 2019

m:iv Summer 2018 Workshop July 2018 (with Tim Hoffmann).

m:iv Winter 2018 Workshop January 2018 (with Francisco Martin).

LMS Northern Regional Meeting June 2017 (with Ian McIntosh) and Workshop on ""Variational Methods in Submanifold Theory"" May 2017 (with Ian McIntosh).

m:iv Spring 2017 Workshop March 2017 (with Martin Kilian).

LMS Midlands Regional Meeting June 2013 (with Ian McIntosh).

Workshop on ""Advances in Surface Theory"" June 2013 (with Ian McIntosh).

Differential Geometry Workshop at the BMC 2011 (with Mark Haskins).

I was the Chair of the Editorial Panel for the book

T. Hoffmann M. Kilian K. Leschke F. Martin editors Minimal surfaces: Integrable Systems and Visualisation Springer Proceedings in Mathematics.

Member of Scientific Committee

• LMS/IMA Joint Meeting 2021 - Maths in Human Society online Organising Committee.
• PADGE 2017 Leuven.

Keynotes/Plenary Talks

• 2022 Periodic Discrete Darboux transforms, RIMS Symposium, Kyoto.
• 2019 Isothermic surfaces, Lecture series, Differential Geometry and its discretisations, OCAMI Osaka.
• 2018 Darboux transforms of CMC surfaces revisited, Geometry of Submanifolds and Integrable Systems, OCAMI Osaka.
• 2016 Quaternionic Holomorphic Geometry, Complex Geometry and Lie groups, Nara Women’s University Nara.
• 2011 Darboux transforms and simple factor dressing, Differential Geometry section of the meeting of the Mathematical Society of Japan, Matsumoto.
• 2009 Quaternionic holomorphic geometry, I-III OCAMI-KNUGRG Joint Differential Geometry Workshop Submanifold Geometry and Lie Group Theory, Osaka.
• Invited Research visits to Japan, Spain and Germany.

Referee

Research proposals: Research Foundation Flanders London Mathematical Society Austrian Research Council

Journals: LMS journals Math. Annalen, Journal of Geometry and Physics, International Journal of Mathematics Journal of Physics A: Mathematical and Theoretical, Annals of Global Analysis and Geometry

Leschke K: Maths meets Arts LMS newsletter issue 488 pages 31-35 2020

Leschke K C. Aligianni L. Allatson J. Hibberd A. Johnston The Arts of the Finite Topology Conjecture 2020 BRIDGES short film festival

K. Leschke M. Simmons and J. Hibberd. Maths Garden.

Maths Meets Arts Festival. You can see all events on YouTube.

Leschke K. Not adding up. Pan European Networks: Science and Technology 9 pages 130-131 2014.

Work of women mathematicians at the University to be celebrated.

Diplom TU Berlin 1994

PhD TU Berlin 1997

Habilitation University of Augsburg 2007

Fellow of Higher Education Academy 2016