## Dori Bejleri

### About me

I am a Benjamin Peirce and NSF postdoctoral fellow at Harvard University. I spent the 2018-2019 academic year as an NSF postdoctoral fellow at MIT. I received my PhD in 2018 from Brown University under the supervision of Dan Abramovich.

### Contact Info

Department of MathematicsScience Center 525

Harvard University

One Oxford Street

Cambridge MA 02138 USA

bejleri [at] math [dot] university [dot] edu

### Curriculum Vitae

### Research

I'm mainly interested in algebraic geometry -- specifically moduli spaces and birational geometry with connections to enumerative geometry, combinatorics and geometric representation theory.

One of my current focuses is on compactifying moduli spaces of surfaces using ideas from the minimal model program. More specifically, I'm studying surfaces that admit a fibration to a smooth curve. Using the theory of twisted stable maps to Deligne-Mumford stacks, one can construct natural degenerations of such fibered surfaces and apply them to compactify moduli spaces by KSBA stable pairs.

My other current focus is on the combinatorial and enumerative geometry of moduli spaces of sheaves, and particularly Hilbert schemes of points. I'm interested in the rich interplay between partition combinatorics and the geometry of Hilbert schemes of points on smooth surfaces and surface orbifolds. I'm also interested in the structure of Hilbert schemes of points on singular curves, espcially generalizing results about planar curves to larger embedding dimension and connections with curve counting on threefolds. I'd also like to understand tropicalizations of these moduli spaces.

### Papers and preprints

*Smoothability of relative stable maps to stacky curves.*(With Kenny Ascher). Submitted.*Wall crossing for moduli of stable log varieties.*(With Kenny Ascher, Giovanni Inchiostro, and Zsolt Patakfalvi). Submitted.*Moduli of double covers and degree one del Pezzo surfaces.*(With Kenny Ascher).Volume 7 (2021), no. 2.**Eur. J. Math.***Compact moduli of elliptic K3 surfaces.*(With Kenny Ascher).To appear.**Geom. Topol.***Stable pairs with a twist and gluing morphism for moduli of surfaces.*(With Giovanni Inchiostro).Volume 27 (2021) no. 3.**Selecta Math (N.S.)***Compact moduli of degree one del Pezzo surfaces.*(With Kenny Ascher).To appear.**Math. Annalen.***The Hilbert zeta function is constructible in families of curves.*Draft.*Motivic Hilbert zeta functions of curves are rational.*(With Dhruv Ranganathan & Ravi Vakil).Volume 19, Issue 3 (2020).**J. Inst. Math. Jussieu.***The SYZ conjecture via homological mirror symmetry.***Superschool on derived categories and D-branes**. Springer Proceedings in Mathematics & Statistics.*Moduli of weighted stable elliptic surfaces and invariance of log plurigenera.*(With Kenny Ascher).Volume 122 (2021), no. 5.**Proc. Lond. Math. Soc. (3)***Moduli of fibered surface pairs from twisted stable maps.*(With Kenny Ascher).. Volume 374 (2019).**Math. Annalen***Log canonical models of elliptic surfaces.*(With Kenny Ascher).. Volume 320 (2017), 210-243.**Advances in Mathematics***The tangent space of the punctual Hilbert scheme.*(With David Stapleton).Volume 66 (2017), no. 3, 595 - 610.**Mich. Math. J.***The topology of equivariant Hilbert schemes.*(With Gjergji Zaimi).To appear.**Res. Math. Sci.***Quantum field theory over F1.*(With Matilde Marcolli).Volume 69 (2013), 40 – 59.**Journal of Geometry and Physics.**

### Harvard-MIT Algebraic Geometry Seminar.

### Open Neighborhood Seminar.

### Albanian Journal of Mathematics.

### Teaching

Math 260X: Rationality questions in algebraic geometry. Spring 2022.Math 136: Differential geometry. Fall 2021.

Math 290: Birational geometry of algebraic varieties. Fall 2020.

Math 259X: Moduli spaces in algebraic geometry. Fall 2019.

### Notes

Notes on $A_{\mathrm{inf}}$ and perfectoid rings from a learning workshop on integral p-adic hodge theory.Notes from a talk given at Brown in February of 2016 on motivic Hilbert zeta functions.

These are notes on the geometry of the Hilbert scheme of points on $\mathbb{A}^2$ for the Brown Graduate Student Seminar. They are aimed at first year graduate students.

Here are some rough notes from my talk on cohomology of equivariant Hilbert schemes. There may be some "typos".

### Some Math Links

### Personal

A long time ago, I was studying math at Caltech and spending my time in Ricketts House.This is a picture of me and my beautiful wife and our dog Grizzly.

I also like playing music. Here are some very rough performances.