About me

My name is Morena Porzio (they/them) and I am a fifth-year PhD Math Student at Columbia University, New York. My advisor is Professor Aise Johan de Jong. Previously, I did my Master and Bachelor in Mathematics at University of Pisa and Scuola Normale Superiore, both in Pisa.

My research field is Algebraic Geometry. Currently my research focuses on the arithmetic of surfaces, the geometry of Hilbert schemes of points and cycles on Jacobians of curves (in particular the Ceresa cycle).

I am interested in the existence and density of degree d points on surfaces, full Del Pezzo surfaces, vanishing of cycles and obstruction techniques to the existence of rational points on varieties (with the Cassels Swinnerton-Dyer Conjecture for cubic surfaces as a main motivation). Moreover, I like algebraic-topology questions that can be tackled with algebraic-geometry tools (e.g. moduli spaces of vector bundles on complex curves).

Here is my CV (updated on 11/15/2024).

Contact

Department of Mathematics
Columbia University
Room 407, 2990 Broadway
New York, NY 10027

Email: mp3947 at columbia dot edu

Research

Preprints

• On the Homotopy type of the Beilinson--Drinfeld Grassmannian, joint work with G. Nocera. preprint.
• On the Stable Birationality of Hilbert schemes of points on surfaces, preprint.
• Higher Beauville Components of Ceresa Cycles and Modified Diagonals, joint work with L. Lagarde, M. Moakher, J. Rawson, and F. Trejos. In preparation.
• Density of degree d points on product of curves, joint work with J. Berg, Y. Fu, E. Gazaki, J. Rawson, I. Vogt. In preparation.
• Classification of full DP2's over characteristic 2, joint work with J. Desjardins, A. Knecht, J. Schneider, M. Trip. In preparation.

Publications

• An Estimation of Hailstone Radii using the Collatz Conjecture (with Rhea Gupta), Journal of Student Research (2022), 11(2).
• The torsion-free rank of Ext1(A,Z) and Whitehead’s problem, Graduate J. Math. 7 (2022), 10-16.

Thesis

• Picard groups of stacks of elliptic and hyperelliptic curves, Master thesis, University of Pisa (2020), Advisor: Professor Angelo Vistoli.
• The ranks of Ext1(A, Z) and Whitehead’s Problem, Bachelor thesis, University of Pisa (2018), Advisor: Professor Matteo Viale.

Teaching, TAing and Mentoring

Columbia University

• Fall 2024: Teaching assistant for Commutative Algebra GR6261
• Spring 2024: Teaching assistant for Arithmetic and Algebraic Geometry GR6262 and Ordinary Differential Equations UN2030
• Fall 2023: Teaching assistant for Teaching assistant for Commutative Algebra GR6261 (external link)
• Summer 2023: Instrictor of Ordinary Differential Equations UN2030. Notes are here: Lecture 1 Lecture 2 Lecture 3 Lecture 4 Lecture 5 Lecture 6 Lecture 7 Lecture 8 Lecture 9 Lecture 10
• Spring 2023: Teaching assistant for Algebraic Number Theory GU4043 (external link)
• Summer 2022/23: Mentor of Rhea Gupta via Lumiere education, Premium Research & Publication Program.
• Spring 2022: Teaching assistant for Ordinary Differential Equations UN2030
• Fall 2022: Teaching assistant for Ordinary Differential Equations UN2030
• Spring 2021: Teaching assistant for Ordinary Differential Equations UN2030
• Fall 2021: Teaching assistant for Ordinary Differential Equations UN2030

University of Pisa

• Fall 2018: Teaching assistant for Algebra

Seminars at Columbia

• Spring 2024: Organizer of a Learning Seminar on Elliptic Curves and Abelian Varieties in preparation for the Arizona Winter School 2024.
• Spring 2022: Organizer of a Learning Seminar on Motives, Standard Conjectures and Weil Cohomology Theories.

Miscellaneous

• This academic year (2023/2024) I am one of the two Grad Representants at the Math department. If you have any questions, please feel free to reach out to me.
• I strongly share and support Professor Ardila’s axioms.
• I am part of WIAG, Women and gender expansive Individuals in Algebraic Geometry.
• I am also part of Spectra, the Association of LGBTQ+ mathematicians.
• Summer 2023: Organizer of Study Groups at Math Department (Columbia University).