Fatemeh Rezaee
I am a UKRI Fellow at the Department of Pure Mathematics and Mathematical Statistics (DPMMS) at the University of Cambridge, and a College Research Associate at Clare College. Part of the post also includes visiting ETH Zürich.
Before this, I was a postdoctoral fellow at MSRI, visiting scholar at the University of California, Berkeley, a Maxwell Institute Research Fellow at the University of Edinburgh, and a research associate at Loughborough University. I completed my Ph.D. at the University of Edinburgh under the supervision of Professor Arend Bayer.
Semester-long programs at MSRI (Berkeley) in which I have participated:
Analytic and Geometric Aspects of Gauge Theory, Fall 2022
Derived Algebraic Geometry, Spring 2019
email: fr414 at cam dot ac dot uk
Summer Research Program 2024
For students: Please note that the deadline has now passed and the decision has been made.
Research
I am primarily interested in numbers and the geometry of numbers in a broad sense: using pattern recognition, computational geometry, computer algebra, commutative algebra, lattice theory, convex geometry, and combinatorial methods in problems arising in enumerative geometry, moduli theory, and number theory.
I am also interested in applying tools from derived categories, Bridgeland stability conditions, derived algebraic geometry, differential geometry, and geometric analysis to understand geometric and enumerative aspects of moduli spaces.
Publication/Preprint
Conjectural criteria for the most singular points of the Hilbert schemes of points , submitted.
Constructing smoothings of stable maps, with M. Swaminathan. Submitted.
An interesting wall-crossing: Failure of the wall-crossing/MMP correspondence, arXiv. Submitted.
Geometry of canonical genus four curves, arXiv. Proceedings of the London Mathematical Society, Volume 128, Issue 1, 2024.
The desingularization of the theta divisor of a cubic threefold as a moduli space , with A. Bayer, S. Beentjes, S. Feyzbakhsh, G. Hein, D. Martinelli, B. Schmidt. Geometry & Topology, Volume 28, Issue 1, 2024.
Wall-crossing and birational geometry, a survey to appear in the Proceedings of Nottingham Algebraic Geometry Seminar, 2022.
Wall-crossing pathologies in three dimensions, a survey to appear in ZAG’s Handbook of Modern Algebraic Geometry, 2022.
Teaching/Supervision
Summer Research Program supervision, 2024, University of Cambridge.
Part III Essay supervision, 2023-2024, University of Cambridge.
Part II Riemann Surfaces: Supervisor, Fall (Michaelmas term) 2023, Clare College, University of Cambridge.
Engineering Mathematics/Mathematics for Natural Sciences: (co-)Lecturer, Spring 2022, University of Edinburgh.
Accelerated Algebra and Calculus for Direct Entry: (co-)Lecturer, Fall 2021, University of Edinburgh.
Fundamentals of Pure Mathematics: Tutor, Spring 2020, University of Edinburgh.
Honours Algebra (Skills): Tutor, Spring 2020, University of Edinburgh.
Commutative Algebra: Tutor, Fall 2019, University of Edinburgh.
Combinatorics and Graph Theory: Tutor, Fall 2019, University of Edinburgh.
Facets of mathematics : Tutor, Fall 2018, University of Edinburgh,
Proofs and problem solving: Tutor, Spring 2018, University of Edinburgh,
Honours algebra: Tutor, Spring 2018, University of Edinburgh,
Introduction to linear Algebra: Tutor, Fall 2018, University of Edinburgh,
Other activities
Organiser of seminars on derived categories, stability and applications, Spring/Summer 2021, Loughborough University,
Co-organiser of the Graduate Student Seminar, Spring 2019, MSRI, Berkeley,
Organiser of the arXiv review seminar in algebraic geometry, Fall 2017, University of Edinburgh,
