Research Profile

Martin Kilian

Biography

As an undergraduate I studied Mathematics and Philosophy at TU Berlin, and wrote my Diploma thesis 'On the Riemann-Hilbert Problem' under the supervision of Ulrich Pinkall. I then moved to Amherst, Massachsuetts where I obtained a PhD in Mathematics in 2000 under the guidance of Franz Pedit. Then followed seven postdoctoral years with stops in Bennington, Amherst, Bath and Mannheim. I am a College Lecturer in Mathematics at UCC since 2007.   

Research Interests

My research area is in Differential Geometry and Global Analysis. More specifically I work in surface theory, focusing on variational problems such as minimal surfaces, constant mean curvature surfaces and Willmore surfaces. 

Publications

Peer Reviewed Journals

 YearPublication
(2016)'Mean-convex Alexandrov embedded constant mean curvature tori in the 3-sphere'
L. Hauswirth, M. Kilian, M.U. Schmidt (2016) 'Mean-convex Alexandrov embedded constant mean curvature tori in the 3-sphere'. Proceedings of the London Mathematical Society, 112 (3):588-622 [DOI] [Details]
(2015)'On mean-convex Alexandrov embedded surfaces in the 3-sphere'
L.Hauswirth, M.Kilian, M.U.Schmidt (2015) 'On mean-convex Alexandrov embedded surfaces in the 3-sphere'. Mathematische Zeitschrift, 281 (1):483-499 [DOI] [Details]
(2015)'Flows of constant mean curvature tori in the 3-sphere: The equivariant case'
M.Kilian, M.Schmidt, N.Schmitt (2015) 'Flows of constant mean curvature tori in the 3-sphere: The equivariant case'. Journal Fur Die Reine Und Angewandte Mathematik, 2015 (707):45-86   [DOI] [Details]
(2014)'On stability of equivariant minimal tori in the 3-sphere'
M.Kilian, M.U.Schmidt, N.Schmitt (2014) 'On stability of equivariant minimal tori in the 3-sphere'. Journal of Geometry and Physics, 85 :171-176   [DOI] [Details]
(2013)'Finite type minimal annuli in S2 x R'
L.Hauswirth, M. Kilian, M.Schmidt (2013) 'Finite type minimal annuli in S2 x R'. Illinois Journal of Mathematic, 57 (3):697-741 [Details]
(2013)'Constant mean curvature cylinders with irregular ends'
M.Kilian, N.Schmitt (2013) 'Constant mean curvature cylinders with irregular ends'. Journal of The Mathematical Society of Japan, 65 (3):775-786 [Details]
(2012)'Bubbletons are not embedded'
M Kilian; (2012) 'Bubbletons are not embedded'. Osaka Journal of Mathematics, 49 (3):653-663 [Details]
(2010)'On infinitesimal deformations of cmc surfaces of finite type in the 3-sphere'
M Kilian, M Schmidt; (2010) 'On infinitesimal deformations of cmc surfaces of finite type in the 3-sphere'. OCAMI Studies, 3 :231-248   [Details]
(2008)'Delaunay ends of constant mean curvature surfaces'
M Kilian, W Rossman, N Schmitt; (2008) 'Delaunay ends of constant mean curvature surfaces'. Compositio Math, 144 :186-220 [Details]
(2007)'Unitarization of monodromy representations and constant mean curvature trinoids in 3-dimensional space forms'
N Schmitt, M Kilian, S Kobayashi, W Rossman ; (2007) 'Unitarization of monodromy representations and constant mean curvature trinoids in 3-dimensional space forms'. Journal of The London Mathematical Society, 75 :563-581 [Details]
(2006)'Equivariant harmonic cylinders'
F E Burstall, M Kilian ; (2006) 'Equivariant harmonic cylinders'. Quart. J. Math, 57 :449-468 [Details]
(2005)'Dressing preserving the fundamental group'
J Dorfmeister, M Kilian; (2005) 'Dressing preserving the fundamental group'. Differential Geom. Appl, 23 :176-204 [Details]
(2005)'Constant mean curvature surfaces of any positive genus'
M Kilian, S Kobayashi, W Rossman, N Schmitt; (2005) 'Constant mean curvature surfaces of any positive genus'. J. London Math. Soc, 72 :258-272 [Details]
(2004)'Dressing CMC n-Noids'
M Kilian, N Schmitt, I Sterling; (2004) 'Dressing CMC n-Noids'. Math. Z, 246 (3):501-519 [Details]
(2004)'On the associated family of Delaunay surfaces'
M Kilian; (2004) 'On the associated family of Delaunay surfaces'. Proc. Amer. Math Soc, 132 (10):3075-3082 [Details]
(2001)'Bäcklund transform of a perturbed Delaunay unduloid'
M Kilian, N Schmitt; (2001) 'Bäcklund transform of a perturbed Delaunay unduloid'. Electronic Geometry Models,   [Details]
(2000)'New constant mean curvature surfaces'
M Kilian, I McIntosh, N Schmitt; (2000) 'New constant mean curvature surfaces'. Experiment. Math, 9 (4):595-611 [Details]

Conference Publications

 YearPublication
(2000)3rd European Congress of Mathematicians
M Kilian, N Schmitt; (2000) Surfaces, flows and holonomy . In: Sebastià Xambó-Descamps, Santiago Zarzuela eds. 3rd European Congress of Mathematicians [Details]

Published Reports

 YearPublication
(2010)Flows of equivariant constant mean curvature tori in the 3-sphere.
M Kilian; (2010) Flows of equivariant constant mean curvature tori in the 3-sphere. European Mathematical Society, Oberwolfach Report. [Details]
(2007)Constant mean curvature surfaces with Delaunay ends.
M Kilian; (2007) Constant mean curvature surfaces with Delaunay ends. European Mathematical Society, Oberwolfach Report. [Details]

Professional Activities

Honours and Awards

 YearTitleAwarding Body
2003Postdoctoral Fellowship EPSRC
2002Postdoctoral Fellowship EDGE (European Commission FP 5)

Professional Associations

 AssociationFunctionFrom / To
Irish Mathematical Society Member01-SEP-07 /

Conference Contributions

 YearPublication
(2017)Variational Methods in Submanifold Theory,
Martin Kilian (2017) Dressing curves. [Invited Lectures (Conference)], Variational Methods in Submanifold Theory, University of York , 30-MAY-17 - 02-JUN-17. [Details]
(2017)Irish Geometry Conference,
Martin Kilian (2017) On finite gap curves. [Invited Lectures (Conference)], Irish Geometry Conference, Maynooth University , 25-MAY-17 - 26-MAY-17. [Details]
(2015)Workshop on Differential Geometry and Exterior Differential Systems,
M Kilian (2015) Finite type curves and beyond. [Invited Lectures (Conference)], Workshop on Differential Geometry and Exterior Differential Systems, University College Cork , 13-OCT-15 - 13-OCT-15. [Details]
(2014)Workshop on Kähler Geometry and Geometric Analysis,
M Kilian (2014) Recent results in integrable surface geometry. [Invited Lectures (Conference)], Workshop on Kähler Geometry and Geometric Analysis, NUI Cork , 12-MAY-14 - 14-MAY-14. [Details]
(2014)Irish Geometry Conference,
M Kilian (2014) On elastic Hopf-tori. [Invited Lectures (Conference)], Irish Geometry Conference, NUI Galway , 09-MAY-14 - 10-MAY-14. [Details]
(2013)Variational Problems and Geometric PDE's,
M Kilian (2013) Elastic curves and Willmore Hopf-Tori. [Invited Lectures (Conference)], Variational Problems and Geometric PDE's, Granada University , 17-JUN-13 - 21-JUN-13. [Details]
(2013)Workshop on Advances in Surface Theory,
M Kilian (2013) On moduli spaces in integrable surface geometry. [Invited Lectures (Conference)], Workshop on Advances in Surface Theory, University of Leicester , 12-JUN-13 - 14-JUN-13. [Details]
(2012)Navigating the space of surfaces,
Martin Kilian; (2012) Constrained Willmore tori of spectral genus one. [Invited Lectures (Conference)], Navigating the space of surfaces, Hausdorff Institute, Bonn , 26-MAR-12 - 30-MAR-12. [Details]
(2010)Progress in Surface theory,
Martin Kilian; (2010) Flows of equivariant constant mean curvature tori in the 3-sphere. [Invited Lectures (Conference)], Progress in Surface theory, Oberwolfach , 02-MAY-10 - 08-MAY-10. [Details]
(2010)Irish Geometry Conference,
Martin Kilian; (2010) Flows of equivariant cmc tori in the 3-sphere. [Invited Lectures (Conference)], Irish Geometry Conference, Maynooth , 14-MAY-10 - 15-MAY-10. [Details]
(2009)British Mathematical Colloquium,
Martin Kilian; (2009) Flows of cmc surfaces. [Invited Lectures (Conference)], British Mathematical Colloquium, Galway , 06-APR-09 - 09-APR-09. [Details]
(2008)Advances in surface theory,
Martin Kilian; (2008) The Lawson Conjecture. [Invited Lectures (Conference)], Advances in surface theory, Kloster Schoental , 05-MAR-08 - 05-MAR-08. [Details]
(2008)Uniqueness results in the theory of minimal surfaces,
Martin Kilian; (2008) Proof of the Lawson conjecture. [Invited Lectures (Workshops)], Uniqueness results in the theory of minimal surfaces, Université 7 Paris, France , 26-MAR-08 - 27-MAR-08. [Details]
(2008)Irish Mathematical Society, September Meeting 2008,
Martin Kilian; (2008) On the Lawson conjecture. [Invited Lectures (Conference)], Irish Mathematical Society, September Meeting 2008, CIT, Cork, , 01-SEP-08 - 02-SEP-08. [Details]
(2008)Advances in Surface Theory II,
Martin Kilian; (2008) Proof of the Lawson conjecture. [Invited Lectures (Conference)], Advances in Surface Theory II, Kloster Schöntal, Germany , 06-MAR-08 - 06-MAR-08. [Details]
(2008)Geometry Day, Granada,
Martin Kilian; (2008) On CMC tori in the 3-sphere. [Invited Lectures (Conference)], Geometry Day, Granada, Universidad de Granada, Spain , 21-FEB-08 - 21-FEB-08. [Details]
(2008)Riemann surfaces, harmonic maps and visualization; 16th Osaka City University International Academic Symposium 2008,
Martin Kilian (2008) On the Lawson conjecture. [Invited Lectures (Conference)], Riemann surfaces, harmonic maps and visualization; 16th Osaka City University International Academic Symposium 2008, Osaka City University, Japan , 15-DEC-09 - 20-DEC-09. [Details]
(2007)Progress in Surface theory,
Martin Kilian; (2007) CMC surfaces with Delaunay ends. [Invited Lectures (Conference)], Progress in Surface theory, Oberwolfach, Germany , 03-MAY-07 - 03-MAY-07. [Details]
(2006)LMS Symposium,
Martin Kilian; (2006) On CMC tori in the 3-sphere. [Invited Lectures (Conference)], LMS Symposium, Durham University, UK , 20-AUG-06 - 20-AUG-06. [Details]
(2005)Advances in surface theory,
Martin Kilian; (2005) Equivariant harmonic maps. [Invited Lectures (Conference)], Advances in surface theory, Kloster Benediktbeuern, Germany , 27-JAN-05 - 27-JAN-05. [Details]
(2004)Variational Problems on surfaces,
Martin Kilian; (2004) CMC cylinders and Mathieu's equation. [Invited Lectures (Conference)], Variational Problems on surfaces, Granada, Spain , 06-FEB-04 - 06-FEB-04. [Details]
(2003)Differential Geometry of submanifolds and integrable systems,
Martin Kilian; (2003) Dressing and monodromy. [Invited Lectures (Conference)], Differential Geometry of submanifolds and integrable systems, Kobe, Japan , 12-JUL-03 - 12-JUL-03. [Details]
(2003)EDGE Midterm meeting,
Martin Kilian; (2003) Dressing CMC n-noids. [Invited Lectures (Conference)], EDGE Midterm meeting, Pisa, Italy , 25-JAN-03 - 25-JAN-03. [Details]
(2002)Yorkshire Differential Geometry Day,
Martin Kilian; (2002) Constant mean curvature surfaces. [Invited Lectures (Conference)], Yorkshire Differential Geometry Day, Leeds, UK , 23-SEP-02 - 23-SEP-02. [Details]
(2002)Harmonic maps, minimal surfaces and geometric flows,
Martin Kilian; (2002) Constant mean curvature surfaces. [Invited Lectures (Conference)], Harmonic maps, minimal surfaces and geometric flows, Brest, France , 11-JUL-02 - 11-JUL-02. [Details]
(2002)EDGE Conference,
Martin Kilian; (2002) Dressing CMC surfaces. [Invited Lectures (Conference)], EDGE Conference, Edinburgh, UK , 02-AUG-02 - 02-AUG-02. [Details]
(2000)Harmonic maps and curvature properties of submanifolds II,
Martin Kilian; (2000) Constant mean curvature cylinders. [Invited Lectures (Conference)], Harmonic maps and curvature properties of submanifolds II, Leeds, UK , 04-DEC-00 - 04-DEC-00. [Details]

Committees

 CommitteeFunctionFrom / To
Graduate Studies Committee, School of Mathematical Sciences Chair2012 / 2016
Graduate Studies Committee SEFS Member2012 / 2016
BComm Board of Studies Member2009 /
BComm Int Board of Studies Member2009 /

Employment

 EmployerPositionFrom / To
University College Cork College Lecturer in Mathematics01-AUG-07 /
Universität Tübingen Professurvertretung01-OCT-11 / 31-MAR-12
Universitaet Mannheim Wissenschaftlicher Mitarbeiter01-AUG-05 / 31-JUL-07
University of Bath Research Officer01-FEB-02 / 31-JUL-05
Amherst College Visiting Assistant Professor01-SEP-01 / 31-DEC-01
Bennington College Visiting Assistant Professor01-SEP-00 / 31-AUG-01

Education

 YearInstitutionQualificationSubject
2000University of Massachusetts, Amherst PhDMathematics
1994TU Berlin DIPLOMAMathematics, Philosophy

Other Activities

 Description

External Examiner PhD: J. Zentgraf, Mannheim 2012.

External Examiner PhD: R. Ogilvie, University of Sydney, 2017.

External Examiner MSc: S. Neugebauer, Mannheim 2008.

External Examiner MSc: M. Knopf, Mannheim 2008.

Teaching Activities

Teaching Interests

  • 2014 UCC: Topology, Linear Algebra, Business Math I, Diff Geom II, Math for Engineers II;  
  • 2013 UCC: Topology, Linear Algebra, Business Math I, Diff Geom I; 
  • 2012 UCC: Topology, Linear Algebra, Business Math I, Diff Geom II;  
  • 2011 Tuebingen: Manifolds, Seminar on H-surfaces; 
  • 2010 UCC: Diff Geom I, Analysis I, Business Math I, Topology; 
  • 2009 UCC: Diff Geom I, Math for Engineers II, Business Math I, Transformation Geometry;  
  • 2008 UCC: Analysis I, Math for Engineers II, Topology, Transformation Geometry; 
  • 2007 UCC: Analysis I, Topology, Transformation Geometry; 
  • 2005 - 2006 Mannheim: Diff. equations, Surfaces I & II;  
  • 2002 - 2005 Bath: Analysis I, Diff. equations & control; 
  • 2001 Amherst College: Calculus I, III;  
  • 2000 Bennington College: Calculus I, II, III, Graph Theory, Course in C++; 
  • 1996 - 1999 UMASS: Calculus I, II, III; 

Recent Postgraduates

 Graduation YearStudent NameInstitutionDegree TypeThesis Title
2014Alan McCarthy PhDFlat surfaces of finite type in the 3-sphere

Modules Taught

 Term (ID))TitleLinkSubject
2018Introduction to Differential Geometry MA3063Introduction to Differential Geometry
2018Topics in Differential Geometry MA4063Topics in Differential Geometry
2018Introductory Mathematics for Business I MA1100Introductory Mathematics for Business I

Contact details

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School of Biological, Earth and Environmental Sciences

An Scoil Eolaíochtaí Bitheolaíocha, Domhaneolaíocha agus Comhshaoil

University College Cork, Distillery Fields, North Mall, Cork, Ireland T23 N73K

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