## 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, see https://scholar.google.com/citations?user=uriH1FgAAAAJ&hl=en&oi=ao## Publications

### Books

Year | Publication | |
---|---|---|

(2021) | Minimal Surfaces: Integrable Systems and Visualisation.m:iv Workshops, 2016–19 (2021) Minimal Surfaces: Integrable Systems and Visualisation. Switzerland: Springer. [DOI] [Details] |

### Peer Reviewed Journals

Year | Publication | |
---|---|---|

(2021) | 'On the elliptic sinh–Gordon equation with integrable boundary conditions' Kilian, Martin; Smith, G. (2021) 'On the elliptic sinh–Gordon equation with integrable boundary conditions'. Nonlinearity, 34 (8):5119-5135 [DOI] [Full Text] [Details] | |

(2020) | 'Properly embedded minimal annuli in S2 x R' L. Hauswirth, M. Kilian, M.U. Schmidt (2020) 'Properly embedded minimal annuli in S2 x R'. Journal of Integrable Systems, 5 (1):1-37 [DOI] [Details] | |

(2020) | 'Constant mean curvature trinoids with one irregular end' M.Kilian, E.Mota, N.Schmitt (2020) 'Constant mean curvature trinoids with one irregular end'. Tohoku Mathematical Journal, 72 :317-333 [Details] | |

(2020) | 'On closed finite gap curves in spaceforms II' S. Klein and M.Kilian (2020) 'On closed finite gap curves in spaceforms II'. Journal of Integrable Systems, 5 (1):1-25 [Details] | |

(2020) | 'On closed finite gap curves in spaceforms I' S.Klein and M.Kilian (2020) 'On closed finite gap curves in spaceforms I'. Symmetry Integrability and Geometry-Methods and Applications, SIGMA 16 (2020), 011, 29 pages [Details] | |

(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

Year | Publication | |
---|---|---|

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

### Published Reports

Year | Publication | |
---|---|---|

(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

Year | Title | Awarding Body | |
---|---|---|---|

2021 | Teaching Hero | T&L and USI | |

2003 | Postdoctoral Fellowship | EPSRC | |

2002 | Postdoctoral Fellowship | EDGE (European Commission FP 5) |

### Professional Associations

Association | Function | From / To | |
---|---|---|---|

Irish Mathematical Society | Member | 01-SEP-07 / |

### Conference Contributions

Year | Publication | |
---|---|---|

(2021) | Irish Geometry Seminar,M.Kilian (2021) Integrable systems methods for constant mean curvature surfaces. [Invited Seminars/Guest Lectures], Irish Geometry Seminar, NUI Galway , 13-APR-21. [Details] | |

(2019) | Integrable Systems & Harmonic Maps 2019,Martin Kilian (2019) On Finite Gap Curves. [Invited Lectures (Conference)], Integrable Systems & Harmonic Maps 2019, Technical University Vienna , 16-SEP-19 - 18-SEP-19. [Details] | |

(2019) | Minimal Surfaces, Integrable Systems and Visualization,Martin Kilian (2019) Properly embedded minimal annuli in S2 x R. [Invited Lectures (Conference)], Minimal Surfaces, Integrable Systems and Visualization, University of Leicester , 02-SEP-19 - 06-SEP-19. [Details] | |

(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

Committee | Function | From / To | |
---|---|---|---|

Teaching, Learning and the Student Experience (TLSE), School of Mathematical Sciences | Chair | 2020 / | |

Graduate Studies Committee, School of Mathematical Sciences | Chair | 2012 / 2016 | |

Graduate Studies Committee SEFS | Member | 2012 / 2016 | |

BComm Board of Studies | Member | 2009 / | |

BComm Int Board of Studies | Member | 2009 / |

### Employment

Employer | Position | From / To | |
---|---|---|---|

University College Cork | College Lecturer in Mathematics | 01-AUG-07 / | |

Universität Tübingen | Visiting Professor | 01-OCT-11 / 31-MAR-12 | |

Universitaet Mannheim | Research Officer | 01-AUG-05 / 31-JUL-07 | |

University of Bath | Research Officer | 01-FEB-02 / 31-JUL-05 | |

Amherst College | Visiting Assistant Professor | 01-SEP-01 / 31-DEC-01 | |

Bennington College | Visiting Assistant Professor | 01-SEP-00 / 31-AUG-01 |

### Education

Year | Institution | Qualification | Subject | |
---|---|---|---|---|

2000 | University of Massachusetts, Amherst | PhD | Mathematics | |

1994 | TU Berlin | DIPLOMA | Mathematics, Philosophy |

### Other Activities

Description | |
---|---|

External PhD Examiner : Thomas Raujouan, Tours, 2019. | |

External PhD Examiner: Tobias SImon, Mannheim 2018 | |

External Examiner PhD: Ross Ogilvie, University of Sydney, 2017. | |

External Examiner PhD: J. Zentgraf, Mannheim 2012. | |

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 Year | Student Name | Institution | Degree Type | Thesis Title | |
---|---|---|---|---|---|

2019 | Eduardo Mota | University College Cork | PHD | Constant Mean Curvature surfaces and Heun's Differential Equations | |

2014 | Alan McCarthy | University College Cork | PhD | Flat surfaces of finite type in the 3-sphere |