Dr Katrin Leschke

I am an Associate Professor in Mathematics and was a Royal Society Short Industry Fellow (2022-2023). 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 Deputy Director for PGR in the College of Science and Engineering, besides other memberships in College panels.  Elsewhere, I am currently external examiner at the University of Manchester. I was an elected member of the standing panel of European Women in Mathematics and  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 personal webpage, https://www.le.ac.uk/miv  and https://gigda.ugr.es/pm2021/ 

My research is in smooth and discrete 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. 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 my Royal Society Short Industry Fellowship in 2022-2023 and a SPRINT collaboration on how to improve machine learning algorithms via geometric information, in particular, looking at machine learning and discrete Geometry methods for monitoring of particle outfall. 

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

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 include the following

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

I'm happy to supervise students with a commitment to mathematical research and strong background in smooth or discrete differential geometry, integrable systems, numerical analysis and PDEs. 

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)

Mathematics Gender issues in STEM Visualisation.

Arts and Science.

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.

Chair of Editorial Panel

Minimal surfaces: Integrable Systems and Visualisation, m:iv workshops, 2016-2019, Springer

Member of Scientific Committee

• The 13th MSJ-SI "Differential Geometry and Integrable Systems"(part 2), Takamatsu.

• RIMS Workshop (Type A) – Applications of Harmonic Maps and Higgs Bundles to Differential Geometry, Research Institute for Mathematical Sciences, Kyoto.

• RIMS Symposium – The 4th International Workshop Geometry of Submanifolds and Integrable Systems, Osaka.

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

Keynotes/Plenary Talks

• 2023Periodic Darboux transforms, Recent Advances in the theory of submanifolds, Istituto Nazionale di Alta Mata, Rome.

• 2023 Periodic Darboux transforms, The 3^rd Shot of the 13^th MSJ-SI “Differential Geometry and Integrable System”, International Conference, Osaka.

• 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

Recent Grants

PI: Construction of isothermic tori via tori via discrete integrable systems: from discrete to smooth, LMS RIP

PI: Construction of isothermic tori via tori via discrete integrable systems: from discrete to smooth, RIMS

PI: Royal Society Short Industry Fellow, Discrete Geometry informed deep learning for reliable Particulate Fallout Monitoring in Rocket Launchers

PI: Minimal surfaces: integrable systems and visualisation, Leverhulme Trust

I: Semi–Riemannian Geometry and Geometric Flows in Mathematical ,Ministerio de Ciencia e Innovacion, Spain.

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