Teaching

• Classification of compact, connected surfaces (2024)
• The knot equivalence problem (2024)
• The classification of compact surfaces (2024)
• The separation axioms (2023)
• From regular surfaces to Einstein manifolds (2022)
• Projective geometry and its applications (2022)
• De Rham cohomology (2020 & 2021)
• Morse theory and Reeb's sphere theorem (2020)
• Isometric immersions of the flat torus in three-dimensional Euclidean space (2019)
• Introducing hyperbolic geometry (2019)
• Parallel transport and holonomy (2017)
• Hopf-Rinow theorem (2017)
• Genus of knots (2016)
• Hyperbolic tesselation and Poincaré's polygon theorem (2016)
• Geodesics and the Hopf-Rinow theorem (2015)
• Gauss' linking number and Calugareanus' theorem (2015)
• The Gauss-Bonnet theorem for compact surfaces (2015)
• Surfaces of constant mean curvature (2015)
• Smooth manifolds and the Poincaré-Hopf theorem (2015)
• Minimal surfaces in space and the strong halfspace theorem (2014)
• Frobenius' theorem (2014)
• Classification of topological manifolds and the \( 3 \)-dimensional Poincaré homology sphere (2014)
• Hilbert's theorem for surfaces in space (2014)
• Knot theory: the Conway polynomial in two variables (2013)
• Symplectic geometry, moment maps and the Marsden-Weinstein quotient (2012)
• Minimal surfaces in \(\mathbb{R}^3\): Weierstrass representations and Costa's surface (2012)

• Hyperkähler metrics and cotangent bundles (2023)
• Geometry of flying saucers (2022)
• Exceptional holonomy and group actions (2021)
• Almost Abelian Lie algebras and balanced Hermitian structures (2021)
• Complex symplectic reduction and oxidation (2020)
• Special Kähler structures on surfaces (2019)
• Evolution of smooth, strictly convex curves undergoing homogeneous expansion curvature flows (2018)
• Classification of non-compact toric symplectic manifolds via manifolds with corners (2018)
• Strominger's system on complex Lie groups (2017)
• Projective special real geometries (2016)
• Hermitian structures and cohomogeneity one spaces of dimension \(4\) and \(6\) (2016)
• Lie algebra with a stably Ricci diagonal basis (2015)
• Seifert surfaces and alternating links (2015)
• Invariants for Legendre links in \(\mathbb{R}^3\) (2014)

See my research page.