Samuël Borza

About me

Hello 👋 I’m Samuël Borza. I am a Postdoctoral Researcher in Mathematics at the University of Vienna in Austria. I work within the FWF-funded Emerging Fields Project - A new Geometry for Einstein’s Theory of Relativity & Beyond. The project is led by five Principal Investigators: Michael Kunzinger, Raquel Perales, Chiara Rigoni, Clemens Sämann, and Roland Steinbauer.

From 2021 to 2024, I was a Postdoctoral Researcher in Mathematics at the Scuola Internazionale Superiore di Studi Avanzati (SISSA) in Trieste, Italy. There, my research was supported by the ERC Starting Grant (grant agreement No. 945655) Project GEOSUB - Geometric analysis of sub-Riemannian spaces through interpolation inequalities. I was part of the research team led by Luca Rizzi.

I graduated from Durham University in the UK, where I obtained my PhD in 2021 under the guidance of Wilhelm Klingenberg.

Contact

Research

List of Publications

1. Samuël Borza and Kenshiro Tashiro, Curvature-dimension condition of sub-Riemannian \(\alpha\)-Grushin half-spaces, 2024. [arXiv]
2. Samuël Borza, Mattia Magnabosco, Tommaso Rossi and Kenshiro Tashiro, The curvature exponent of sub-Finsler Heisenberg groups, 2024. [arXiv, CVGMT]
3. Samuël Borza, Mattia Magnabosco, Tommaso Rossi and Kenshiro Tashiro, Measure contraction property and curvature-dimension condition on sub-Finsler Heisenberg groups, 2024. [arXiv, CVGMT]
4. Samuël Borza and Kenshiro Tashiro, Measure contraction property, curvature exponent and geodesic dimension of sub-Finsler Heisenberg groups, 2023. [arXiv, CVGMT]
5. Samuël Borza, Normal forms for the sub-Riemannian exponential map of \(\mathbb{G}_\alpha\), \(\mathrm{SU}(2)\), and \(\mathrm{SL}(2)\), 2023, to appear in Contemporary Mathematics. [arXiv, CVGMT]
6. Samuël Borza and Wilhelm Klingenberg, Local non-injectivity of the exponential map at critical points in sub-Riemannian geometry, Nonlinear Analysis (2024), Volume 239, pp. 113421. [DOI, arXiv, CVGMT]
7. Samuël Borza and Wilhelm Klingenberg, Regularity and Continuity Properties of the Sub-Riemannian Exponential Map, J. Dynam. Control Systems (2023), Volume 29, pp. 1385–1407. [DOI, arXiv, CVGMT]
8. Samuël Borza, Distortion coefficients of the \(\alpha\)-Grushin plane, J. Geom. Anal. 32 (2022), no. 3, Paper No. 78, 28. [DOI, arXiv, CVGMT]

PhD Thesis

Samuël Borza, Distortion coefficients and exponential map in sub-Riemannian geometry, Ph.D. thesis, Durham University, 2021. [Durham e-Theses]

Geometric Structures Research Seminar

Until 2024, I helped organize the Geometric Structures Research Seminar at SISSA with the research groups of Andrei Agrachev, Antonio Lerario, and Luca Rizzi.

Teaching

Academic year 2022-2023

Mathematical Analysis II

I was a teaching assistant of the course Mathematical Analysis II for second-year engineering students at the University of Trieste. One distinctive feature of the course is that, among other things, it focuses on introducing students to the Henstock-Kurzweil integral, a broader theory of integration that is easier to understand compared to what is typically taught at the undergraduate level. Its construction is simple and geometrically comprehensible, akin to Riemann sums, yet more general than Lebesgue's theory of integration. The course investigator is Alessandro Fonda.

Academic years 2017-2021

From 2017 to 2021, I was an academic tutor and/or a marker for several courses in the Department of Mathematical Sciences at Durham University, including Algebra II, Complex Analysis II, Partial Differential Equations III & IV, and Riemannian Geometry IV.

Academic year 2016-2017

Elementary Mathematics

I was one of the teaching assistants helping in the delivery of the course Elementary Mathematics (Fiche ECTS) to first-year students majoring in Mathematics, Physics, and Computer Science at the Faculty of Sciences of the University of Mons. The course, offered by the Department of Mathematics, aims to facilitate the transition from high school to university. Further information on the teaching methodology can be found here (in French).

Mathematics - Supplementary Course & Introduction to Differential Manifolds

I was a teaching assistant for the courses Mathematics - Supplementary Course and Introduction to Differential Manifolds during the preparation for the summer exam session at the Department of Mathematics of the University of Mons. I helped third-year students in Mathematics and Physics in passing their exams by thoroughly reviewing the course material and conducting practice sessions using past papers. The curriculum of the first course included topics on convergence of functions, Fourier transform, Hilbert space theory, and an introduction to the theory of distributions. The second course focused on the differential geometry of curves and surfaces: regular curves and surfaces in Euclidean spaces, Gauss map, First and Second fundamental forms, Gauss's Theorema Egregium.