King's College London

Strand Campus, Office S5.43

Strand, London, WC2R 2LS

rosa.winter (at) kcl.ac.uk

I am a research associate in the Number Theory Group of King's College London, working with Rachel Newton.

From 2020 until 2021 I was a postdoctoral researcher in the Nonlinear Algebra group of Bernd Sturmfels at MPI-MiS in Leipzig. Before this I was a PhD student under the supervision of Martin Bright and Ronald van Luijk at Universiteit Leiden.

My research interests are mainly in arithmetic geometry, more specifically, in the arithmetic of surfaces. I mostly focus on low-degree del Pezzo surfaces, and study their arithmetic, geometric, and combinatorial aspects. More broadly, I like to explore applications of algebraic geometry and number theory to other areas of mathematics.

From 2020 until 2021 I was a postdoctoral researcher in the Nonlinear Algebra group of Bernd Sturmfels at MPI-MiS in Leipzig. Before this I was a PhD student under the supervision of Martin Bright and Ronald van Luijk at Universiteit Leiden.

My research interests are mainly in arithmetic geometry, more specifically, in the arithmetic of surfaces. I mostly focus on low-degree del Pezzo surfaces, and study their arithmetic, geometric, and combinatorial aspects. More broadly, I like to explore applications of algebraic geometry and number theory to other areas of mathematics.

- [9]
**Weak weak approximation and the Hilbert property for degree-two del Pezzo surfaces**(with J. Demeio and S. Streeter).*Submitted*.

Link to arXiv (2023). - [8]
**Campana points on diagonal hypersurfaces**(with F. Balestrieri, J. Brandes, M. Kaesberg, M. Pieropan, and J. Ortmann).*Accepted for publication in Women in Numbers Europe 4 - Research Directions in Number Theory.*.

Link to arXiv (2023). - [7]
**Torsion points and concurrent exceptional curves on del Pezzo surfaces of degree one**(with J. Desjardins).*Submitted*.

Link to arXiv (2022), and magma code. - [6]
**Recovery from Power Sums**(with B. Sturmfels and H. Melánová). Experimental Mathematics (2022).

Link to the journal (open access). - [5]
**Density of rational points on a family of del Pezzo surfaces of degree one**(with J. Desjardins). Advances in Mathematics, Vol 405 (2022).

Link to the journal (open access), and magma code. - [4]
**Linear Spaces of Symmetric Matrices with Non-Maximal Maximum Likelihood Degree**(with Y. Jiang and K. Kohn). Le Matematiche, Vol 76 No 2 (2021), pp. 461-481.

Link to the journal (open access). - [3]
**Fields of definition of elliptic fibrations on covers of certain extremal rational ellipic surfaces**(with V. Cantoral-Farfán, A. Garbagnati, C. Salgado, and A. Trbović). Women in Numbers Europe III: Research Directions in Number Theory. Springer, Association for Women in Mathematics Series, Vol 24 (2021), pp. 171-205.

Link to the book, and to the accepted version on arXiv. - [2]
**Concurrent exceptional curves on del Pezzo surfaces of degree one**(with R. van Luijk). Mathematics of Computation, Vol 92 (2023), pp. 451-481.

Link to the journal, and to the accepted version on arXiv, with magma code 1 and magma code 2. - [1]
**The action of the Weyl group on the**(with R. van Luijk). Graphs and Combinatorics, Vol 37 No 6 (2021), pp. 1965-2064.*E*root system_{8}

Link to the journal (open access), and to the accepted version on arXiv, with magma code. - PhD thesis: Geometry and arithmetic of del Pezzo surfaces of degree 1 (2021).
- Master thesis: Concurrent exceptional curves on del Pezzo surfaces of degree one (2014).
- Bachelor thesis: Elliptic curves over
**Q**_{p}(2011).

- OSCAR code with with some basic commands for number theory in OSCAR.
- Magma code used in Chapter 2 of my PhD thesis.
- Magma code used in Chapter 5 of my PhD thesis.

- 21/09/2023 An Afternoon of Diophantine Geometry, University of Manchester.
- 23/07/2023 Rational Points 2023, Franken-Akademie Schloss, Schney.
- 19/06/2023 Number Theory Seminar, Georg-August-Universität Göttingen.
- 12/06/2023 Foundations of Computational Mathematics 2023, Computational Number Theory workshop, Paris.
- 12/05/2023 Seminar Variétés Rationnelles, Sorbonne Université, Paris.
- 15/02/2023 Heilbronn Seminar, University of Bristol.
- 09/01/2023 Great Western Number Theory seminar, University of Oxford.
- 12/12/2022 The Advent of Rational Points, King's College London.
- 22/11/2022 Cambridge Number Theory Seminar, University of Cambridge.
- 14/11/2022 Number Theory Seminar, University of Warwick.
- 7/10/2022 Workshop on Solving Polynomial Equations and Applications, CWI, Amsterdam.
- 21/09/2022 Seminar in coding theory and cryptography, Université de Neuchâtel.
- 27/05/2022 Symbolic Computation Istanbul Meetings, Istanbul.
- 26/04/2022 Rational Points on Higher-Dimensional Varieties, ICMS, Edinburgh.
- 16/03/2022 Number/Representation Theory seminar (online), University of Toronto.
- 03/03/2022 Number Theory Seminar, University of Oxford.
- 02/03/2022 AGNT Seminar (online), Rice University, Houston.
- 04/02/2022 Algebra & Number Theory Seminar, Queen Mary University of London.
- 17/11/2021 London Number Theory Seminar, Imperial College London.
- 11/11/2021 Zoom Algebraic Geometry Seminar (ZAG).
- 07/07/2021 Browning group working seminar (online), IST Austria, Vienna.
- 22/06/2021 Nonlinear Algebra Seminar, MPI-MiS, Leipzig.
- 25/02/2021 Number Theory Seminar (online), University of California Irvine.
- 19/02/2021 Zoom On Rational Points (ZORP).
- 02/02/2021 Nonlinear Algebra Seminar Online, MPI-MiS Leipzig.
- 17/12/2020 Séminaire Arithmétique et Théorie de l’Information (online), Aix-Maseille Université.
- 11/11/2020 Algebra Seminar (online), Rijksuniversiteit Groningen.
- 29/10/2020 Quarantined Number Theory and Algebraic Geometry Seminar (online), Simon Fraser University.
- 22/09/2020 Arithmetic Geometry Seminar (online), Ohio State University.
- 03/06/2020 PhD colloquium (online), Universiteit Leiden.
- 14/04/2020 Nonlinear Algebra Seminar Online, MPI-MiS Leipzig.
- 26/02/2020 Heilbronn Number Theory Seminar, University of Bristol.
- 07/02/2020 Intercity Number Theory Seminar, Universiteit Leiden.
- 18/12/2019 Seminario di Natale, Università degli Studi di Milano.
- 11/12/2019 Number Theory Seminar, Københavns Universitet.
- 06/03/2019 Number/Representation Theory seminar, University of Toronto.
- 26/06/2018 Konstanz Women in Mathematics lecture series, Universität Konstanz.
- 31/05/2018 Bernoullis Tafelrunde Graduate Student Seminar, Universität Basel.
- 18/06/2018 Poster at GAeL XXVI, Université de Strasbourg.
- 21/03/2018
*Counting Curves*, Tropical Geometry Seminar, Universiteit Leiden. - 11/09/2017 Poster at Diophantine problems (DIOP), University of Manchester.
- 07/07/2017 Research talk at XXX-èmes Journées Arithmétiques, Université de Caen Normandie.
- 15/02/2017
*Introduction to local-global principles: the Hasse principle and weak approximation*, Seminar 'Obstructions to local-global principles', Universiteit Leiden. - 02/11/2016
*Isogenies*, Seminar 'Good reduction of Abelian Varieties', University of Amsterdam.

- London Number Theory Study Group on Manin's Conjecture and Szemerédi Regularity (spring 2023), co-organized with Ming Ng.
- Algebraic Statistics Seminar (fall 2018), co-organized with Rianne de Heide and Garnet Akeyr.
- Tropical Geometry Seminar (spring 2018), co-organized with Garnet Akeyr.
- Obstructions to local-global principles (spring 2017), co-organized with Julian Lyczak and Erik Visse.

- Summer 2022: Supervision of two master's students, King's College London
- Fall 2016 - Fall 2019: Calculus (Teacher), Leiden University College, The Hague
- Spring 2018: Elliptic curves (Teaching assistant), Dutch Mastermath course
- Fall 2013: Rational Points on Varieties (Teaching assistant), Dutch Mastermath course
- From 2014 until 2016 I was a mathematics teacher at Calandlyceum Amsterdam, as part of the traineeship Eerstde Klas.