Publications

1. Classification of homogeneous hypersurfaces in some noncompact symmetric spaces of rank two, Annali di Matematica 202, 2915–46 (2023)

Preprints

1. Homogeneous codimension-one foliations on reducible symmetric spaces of noncompact type. arXiv:2112.02189 [math.DG]

2. Automorphisms of real semisimple Lie algebras and their restricted root systems. arXiv:2208.01131 [math.DG]

3. Sections of polar actions (with Juan Manuel Lorenzo Naveiro). arXiv:2111.05280 [math.DG]

4. The spinor and Weierstrass representations of surfaces in space. arXiv:2210.15558 [math.DG]

Notes

These are notes of varying levels of quality and precision that I write for my own use every now and then.

• A convenient formula for the second fundamental form in symmetric spaces (file).

• Maximal flats and the isotropy representation/action of a symmetric space (file).

• Universal Riemannian covering and isometries & applications to symmetric spaces (file).

• Hausdorff distance, convergence, measure, and dimension (file).

Talks at conferences and workshops

1. Homogeneous complex hypersurfaces in complex flag manifolds, 10 November 2023 at Riemannian Topology Meeting (University of Fribourg)

2. Diagram symmetries of symmetric spaces of noncompact type, 19 July 2022 at Differential Geometry and its Applications (satellite conference of vICM 2022; University of Hradec Králové) (slides)

3. Homogeneous hypersurfaces in the noncompact complex two-plane Grassmannian, 29 March 2022 at the Workshop on Manifolds with Symmetries (University of Stuttgart) (slides)

4. Homogeneous codimension-one foliations on symmetric spaces of noncompact type, 17 February 2022 at the workshop "Geometry of symmetric spaces and group actions" (slides)

Talks at seminars

1. Totally geodesic submanifolds and root subsystems, 3 May 2024 at Seminario Vidal-Abascal (University of Santiago de Compostela)

2. Noncompact Hermitian symmetric spaces and homogeneous complex hypersurfaces, 2 May 2024 at Seminario Vidal-Abascal (University of Santiago de Compostela)

3. Homogeneous complex hypersurfaces in noncompact Hermitian symmetric spaces, 2 November 2023 at the Submanifold Geometry Seminar (University of Stuttgart)

4. Homogeneous complex hypersurfaces in Hermitian symmetric spaces, 25 April 2023 at the Seminar of the Institute of Geometry and Topology (University of Stuttgart) and 16 May 2023 at the KCL Geometry Seminar

5. Compact homogeneous Einstein manifolds, 5 January 2023 at the Geometry and Topology Seminar (Technion, Haifa)

6. The nilpotent construction problem, 25 April 2022 at the Pure Maths Seminar (University of East Anglia, Norwich)

7. Symmetric spaces of noncompact type II: Roots and Dynkin diagrams, 9 February 2022 at Symmetric Spaces Seminar (part of an introductory series on symmetric spaces of noncompact type) (slides; recording)

8. The index of symmetry of a Riemannian manifold, 26 January 2022 at Symmetric Spaces Seminar (slides; recording)

9. Quaternion-Kähler manifolds, 21 October 2021 at KCL/UCL Junior Geometry Seminar (notes)

10. Conformal immersions and spinor representations, 4 September 2021 at IUM Spectral Geometry Seminar (IUM, Moscow)

11. The story of isoparametric hypersurfaces in space forms, 23 March 2021 at UCL Postgraduate Seminar (notes)

12. Totally geodesic submanifolds of symmetric spaces, 10 February 2021 at Oxford Junior Geometry and Topology Seminar (extended notes)

13. Hyperpolar homogeneous foliations on symmetric spaces of noncompact type, 27 November 2020 at ZoomerFEST seminar (following arXiv:0807.3517v3 [math.DG] ; extended notes)

14. Homogeneous and symmetric spaces, 16 October 2020 at Imperial Junior Geometry Seminar (notes)

15. Intrinsically harmonic forms, 8 October 2020 at KCL/UCL Junior Geometry Seminar (notes)

16. Uniformization and Steinness, 24 January 2019 at Geometric Structures on Manifolds Seminar (HSE, Moscow) and 15 February 2019 at Functional Analysis and Noncommutative Geometry Seminar (HSE, Moscow) (following arXiv:1705.05113 [math.CV])

17. Uniqueness theorems for free boundary minimal disks in space forms, 3 and 17 November 2018 at Spectral Geometry Seminar (IUM, Moscow) (following arXiv:1409.1632 [math.DG])

18. Calibrated geometry, 24 October 2018 at a student seminar (HSE, Moscow)

19. Geometry of the total space of the tangent bundle to a Riemannian manifold, 22 and 29 September 2018 at Spectral Geometry Seminar (IUM, Moscow) and 4 October 2018 at Geometric Structures on Manifolds Seminar (HSE, Moscow)

20. Serre-Swan theorem, 6 September 2018 at Geometric Structures on Manifolds Seminar (HSE, Moscow)

21. Cosmic censorship of smooth structures, 19 April 2018 at Geometric Structures on Manifolds Seminar (HSE, Moscow) (following arXiv:1201.6070 [math.GT])

22. Ergodicity of the geodesic flow, 14 December 2017 at Geometric Structures on Manifolds Seminar (HSE, Moscow) (following an appendix by Misha Brin in W. Ballmann's book 'Lectures on Spaces of Nonpositive Curvature' and my third year undergraduate project)

23. Invariant differential operators, 25 November 2017 at a student seminar (HSE, Moscow) (following my second year undergraduate project)

Teaching

I've been a teaching assistant for a number of undergraduate and master level courses:

1. 017810000 Lie group actions, Summer semester 2023-24, Department of mathematics of the University of Stuttgart

2. 016230000 Riemannian geometry, Summer semester 2023-24, Department of mathematics of the University of Stuttgart

3. 015300000 Differential geometry, Winter semester 2023-24, Department of mathematics of the University of Stuttgart

4. MA103 Introduction to Abstract Mathematics, 2022-23, Department of mathematics of London School of Economics

5. MA102 Mathematical Proof and Analysis, 1st term 2022-23, Department of mathematics of London School of Economics

6. 6CCM351A Representation Theory of Finite Groups, 2nd term 2021-22, Department of mathematics of King's College London

7. MA203 Real Analysis, 1st term 2021-22, Department of mathematics of London School of Economics

8. 5CCM223A/6CCM223B Geometry of Surfaces, 2nd term 2020-21, Department of mathematics of King's College London

9. 7CCMMS01 Lie Groups and Lie Algebras, 1st term 2020-21, Department of mathematics of King's College London

10. 5CCM224A/6CCM224B Introduction of number theory, 1st term 2020-21, Department of mathematics of King's College London

11. Differential geometry, 2nd semester 2018-19, Independent University of Moscow

12. Foundations of algebra and geometry, 1st semester 2018-19, Faculty of mathematics, Higher School of Economy (Moscow)

13. Functional analysis, 2st semester 2017-18, Faculty of mathematics, Higher School of Economy (Moscow)

14. Topology, 2st semester 2017-18, Faculty of mathematics, Higher School of Economy (Moscow)

15. Galois theory, 1st semester 2017-18, Faculty of mathematics, Higher School of Economy (Moscow)

16. Topology, 2st semester 2016-17, Faculty of mathematics, Higher School of Economy (Moscow)