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4. Martin Kilian

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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

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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]

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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]

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Conference Publications

	Year	Publication
	(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]

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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]

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Professional Activities

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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)

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Professional Associations

	Association	Function	From / To
	Irish Mathematical Society	Member	01-SEP-07 /

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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]

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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 /

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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

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Education

	Year	Institution	Qualification	Subject
	2000	University of Massachusetts, Amherst	PhD	Mathematics
	1994	TU Berlin	DIPLOMA	Mathematics, Philosophy

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Other Activities

	Description
	External PhD Examiner: Thomas Raujouan, Tours, 2019.
	External PhD Examiner: Daniel Holzwart, Hannover 2024
	External PhD Examiner: Tobias SImon, Mannheim 2018
	External Examiner PhD: Ross Ogilvie, University of Sydney, 2017.
	External Examiner MSc: S. Neugebauer, Mannheim 2008.
	External Examiner MSc: M. Knopf, Mannheim 2008.

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Teaching Activities

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Teaching Interests

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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