Research

Papers:

Symmetry breaking in geometry (with Andreas Fuchs and Udo Hertrich-Jeromin). Preprint available at https://arxiv.org/abs/2206.13401.

Discrete Weierstrass-type representations (with Denis Polly and Masashi Yasumoto). Accepted for publication in Discrete & Computational Geometry. Preprint available at https://arxiv.org/abs/2105.06774.

Channel linear Weingarten surfaces in space forms (with Udo Hertrich-Jeromin and Denis Polly). Accepted for publication in Beit. Algebra Geom. Preprint available at https://arxiv.org/abs/2105.00702.

Constrained elastic curves and surfaces with spherical curvature lines (with Joseph Cho and Gudrun Szewieczek). Accepted for publication in Indiana Univ. Math. J. Preprint available at https://arxiv.org/abs/2104.11058.

Discrete $\Omega$-nets and Guichard nets (with Francis Burstall, Joseph Cho, Udo Hertrich-Jeromin and Wayne Rossman). Accepted for publication in Proc. Lond. Math. Soc. Preprint available at https://arxiv.org/abs/2008.01447.

Lie applicable surfaces and curved flats (with Francis Burstall). manuscripta math 168, 525-533, (2022), https://doi.org/10.1007/s00229-021-01304-8.

Quartic differentials and harmonic maps in conformal surface geometry (with Francis Burstall and Emilio Musso). Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XXIII (2022), 1507-1524. Preprint available at https://arxiv.org/abs/2007.03992.

Discretization of isothermic surfaces in Lie sphere geometry (with Joseph Cho, Kosuke Naokawa, Yuta Ogata, Wayne Rossman and Masashi Yasumoto), in progress.

G-Deformations of maps into projective space, Boll. Unione Mat. Ital. 13(2), 275-292 (2020), https://doi.org/10.1007/s40574-020-00218-9. Preprint available at https://arxiv.org/abs/1712.06945.

Weierstrass-type representations, Geom. Dedicata 204(1), 299-309 (2020), https://doi.org/10.1007/s10711-019-00456-y

Channel surfaces in Lie sphere geometry (with Gudrun Szewieczek), Beit. Algebra Geom. 59(4), 779-796 (2018), https://doi.org/10.1007/s13366-018-0394-6.

Characterizing singularities of a surface in Lie sphere geometry (with Wayne Rossman, Kentaro Saji and Keisuke Teramoto), Hokkaido Math. J. 48(2), 281-308 (2019). https://doi.org/10.14492/hokmj/1562810509.

Lie applicable surfaces, Comm. Anal. Geom. 28(6), 1407-1450 (2020). https://dx.doi.org/10.4310/CAG.2020.v28.n6.a5

Polynomial conserved quantities of Lie applicable surfaces (with Fran Burstall, Udo Hertrich-Jeromin and Wayne Rossman), manuscripta math. 158 (3), 505-546 (2019). https://doi.org/10.1007/s00229-018-1033-0

Maximal surfaces in Minkowski 3-space with non-trivial topology and corresponding CMC 1 surfaces in de Sitter 3-space (with Shoichi Fujimori and Samah Gaber Mohamed), Kobe J. Math. 33, 1-12 (2016).

PhD Thesis: Special Surface Classes. Available at https://researchportal.bath.ac.uk/en/studentTheses/special-surface-classes.

Talks:

Constrained elastic curves and spherical curvature lines, Selected Topics in Mathematics - Online Edition (2021).

Constrained elastic curves and spherical curvature lines, Probability, Differential Geometry and Mathematical Physics Seminar, Texas Tech University (2021).

Spherical curvature lines, The 27th Osaka City University International Academic Symposium, Osaka City University (2021).

Spherical curves in Lie sphere geometry, PRIN seminar, Politecnico di Torino (2020).

Discrete Weierstrass-type representations, Discrete Harmonic Analysis and Differential Geometry Days, Politecnico di Torino (2020).

Quartic differentials and harmonic maps in conformal surface geometry, Differential Geometry Workshop 2020 - Online, University of Vienna (2020).

Constrained elastica and spherical curvature lines, closing workshop of the project "Geometric Shape Generation", Tokyo Institute of Technology (2020).

Discrete Weierstrass type representations, Workshop and School on Geometric Analysis and Discrete Geometry, KIAS (2020).

Discrete Omega surfaces, Workshop and School on Geometric Analysis and Discrete Geometry, KIAS (2020).

Weierstrass type representations, Pure mathematics seminar, University of Leicester (2020).

Spherical curvature lines, ISHM2019, TU Wien (2019).

Weierstrass type representations, ICIAM 2019, Valencia (2019).

Discrete differential geometry, DISMA seminar, Politecnico di Torino (2019).

Discrete Omega surfaces, Discrete differential geometry - integrable discretisation workshop. Politecnico di Torino (2019).

Omega surfaces: breaking news, Geometry Seminar, TU Wien (2018).

Weierstrass type representations, Autumn School “Geometric shape generation”, TU Wien (2018).

Omega surfaces, Korea University (2018).

Weierstrass-type representations, Micro-workshop on surface representations, Kobe University (2018).

Omega-surfaces and Weierstrass-type representations, 4th Croatian Conference on Geometry and Graphics, Vodjnan (2018).

Weierstrass-type representations: a recipe for black holes, Geometry Seminar, TU Wien (2018).

Spherical Curvature Lines: A Lie Sphere Geometry Story, Geometry Seminar, TU Wien (2017).

Channel surfaces in Lie sphere geometry, The 9th KOOK-TAPU Joint Seminar on Knots and Related Topics, Osaka City University (2017).

Deformability and integrable systems, International Workshop on Differential Geometric Aspects of Integrable Systems, Kobe University (2017).

Singularities and Lie sphere transformations, Conference on Geometry Theory and Applications, Pilsen (2017).

Ribaucour transformations of channel surfaces- work in progress (joint with Gudrun Szewieczek), Geometry Seminar, TU Wien (2017).

Lie applicable surfaces, Geometry Seminar, TU Wien (2017).

Characterising singularities in Lie sphere geometry, Germs be ambitious, Hokkaido University (2016).

Characterising singularities in Lie sphere geometry, Topology, singularity theory, and their applications, Aoyama Gakuen University (2016).

Lie sphere transformations and singularities on surfaces, Transformations and Singularities, Tokyo Institute of Technology (2016).

Transformations of Omega Surfaces, Transformations and Singularities, TU Wien (2014).

Bubble Trouble, Postgraduate Seminar Series, University of Bath (2014).

Weierstrass representations and creating CMC surfaces with holes, Geometry Seminar, University of Bath (2012).

Spacelike CMC-1 surfaces with genus in 3-dimensional de Sitter space S^{2,1}, Geometry Symposium, Kyushu University (2012).

Lie Sphere Geometry, Geosock Seminar, Osaka City University (2012).

Lie geometry of linear Weingarten surfaces with singularities, Singularity Theory and Geometry Conference, Nagano (2012).

Workshops:

Integrable discretization, Politecnico di Torino (2019).

Weierstrass-type representations, Autumn school "Geometric shape generation", TU Wien (2018).