I am currently an associate professor and Chancellor's Fellow at UC Irvine.
My research is supported in part by NSF grants DMS-2140781 and DMS-2302550.
Here is my CV.

Algebraic & arithmetic geometry-- moduli spaces of higher dimensional varieties, birational geometry, logarithmic geometry, and hyperbolicity.

- The algebraic Green-Griffiths-Lang conjecture for complements of very general pairs of divisors. (with
*Amos Turchet*and*Wern Yeong*). - Boundedness results for families of non-canonically polarized projective varieties. (with
*Behrouz Taji*). - Moduli of boundary polarized Calabi-Yau pairs. (with
*Dori Bejleri, Harold Blum, Kristin DeVleming, Giovanni Inchiostro, Yuchen Liu,*and*Xiaowei Wang*). - Wall crossing for moduli of stable log pairs.
**Annals of Mathematics,**Vol. 198 No. 2 (2023), 825-866. (with*Dori Bejleri, Giovanni Inchiostro,*and*Zsolt Patakfalvi*). - K-stability and birational models of moduli of quartic K3 surfaces.
**Inventiones Mathematicae,**232 (2023), no. 2, 471–552. (with*Kristin DeVleming*and*Yuchen Liu*). - Smoothability of relative stable maps to stacky curve.
**Épijournal de Géométrie Algébrique**, 7 (2023), Art. 2. (with*Dori Bejleri*). - K-moduli of curves on a quadric surface and K3 surfaces.
**Journal of the Institute of Mathematics of Jussieu,**22 (2023), no.3, 1251–1291. (with*Kristin DeVleming*and*Yuchen Liu*). - Moduli of double covers and degree one del Pezzo surfaces.
**European Journal of Mathematics,**7, 557–569 (2021) (with*Dori Bejleri*). - Wall crossing for K-moduli spaces of plane curves. (with
*Kristin DeVleming*and*Yuchen Liu*).**Proceedings of the London Mathematical Society,**To appear. - Compact moduli of elliptic K3 surfaces.
**Geometry & Topology,**27–5 (2023) 1891-1946. (with*Dori Bejleri*). - The Erdős-Ulam problem, Lang's conjecture, and uniformity.
**Bulletin of the London Mathematical Society,**52 (2020), issue 6, 1053–1063 (with*Lucas Braune*and*Amos Turchet*). - Hyperbolicity and uniformity of varieties of log general type.
**International Math Research Notices,**Volume 2022, Issue 4, February 2022, Pages 2532–2581. (with*Kristin DeVleming*and*Amos Turchet*). - Compact moduli of degree one del Pezzo surfaces. (with
*Dori Bejleri*).**Mathematische Annalen,**384, 1–31 (2022). -
Enumerating Hassett's wall and chamber decomposition of the moduli space of weighted stable curves.
**Experimental Mathematics,**Vol 29:1, (2020) 36–53 (with*Connor Dubé*,*Daniel Gershenson*, and*Elaine Hou*)*. -
Moduli of weighted stable elliptic surfaces & invariance of log plurigenera.
**Proceedings of the London Mathematical Society,**122: 617–677 (2021) (with*Dori Bejleri*, appendix by*Giovanni Inchiostro*). -
Moduli of fibered surface pairs from twisted stable maps.
**Mathematische Annalen,***374 (2019) no. 1-2, 1007–1032.*(with*Dori Bejleri*). - Log canonical models of elliptic surfaces.
**Advances in Mathematics***, Vol 320 (2017), 210–243*(with*Dori Bejleri*). - Bounding heights uniformly in families of hyperbolic varieties.
**New York Journal of Math,***23 (2017) 1791–1808*(with*Ariyan Javanpeykar*). - A generic slice of the moduli space of line arrangements.
**Algebra & Number Theory***, 12-4 (2018), 751–778.*(with*Patricio Gallardo*). - A fibered power theorem for pairs of log general type.
**Algebra & Number Theory***, 10-7 (2016), 1581–1600*(with*Amos Turchet*). - Rational points on twisted K3 surfaces and derived equivalences.
**Brauer groups and obstruction problems: moduli spaces and arithmetic**(with*Krishna Dasaratha*,*Alex Perry*, and*Rong Zhou*). [Supplemental Magma Code] - Logarithmic stable toric varieties and their moduli.
**Algebraic Geometry**,*(3) 2016, 296–319*(with*Sam Molcho*).

- Hyperbolicity of varieties of log general type: geometry and arithmetic. (with
*Amos Turchet*). In December 2018, we gave a mini-course on various notions of hyperbolicity for varieties of log general type from the viewpoint of both arithmetic and birational geometry as part of the Geometry and arithmetic of orbifolds workshop at UQÁM. In Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces -- Hyperbolicity in Montréal.*CRM Short Courses.*

- I am actively involved with the high school iteration of Math CEO.

Perspectives on Moduli in Algebraic Geometry @ Brin Center at the University of Maryland, College Park (Jan 2025)

Explicit moduli problems in higher dimensions @ Banff (Feb 2023).

Arithmetic, Birational Geometry, and Moduli Spaces @ Brown University (June 2023).

Explicit moduli problems in higher dimensions @ Banff (Feb 2023).

Arithmetic, Birational Geometry, and Moduli Spaces @ Brown University (June 2023).

Last updated: Oct 2024