Kenneth Ascher

About me:

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.

Research Interests

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

Publications & Preprints

1. The algebraic Green-Griffiths-Lang conjecture for complements of very general pairs of divisors. (with Amos Turchet and Wern Yeong).
2. Boundedness results for families of non-canonically polarized projective varieties. (with Behrouz Taji).
3. Moduli of boundary polarized Calabi-Yau pairs. (with Dori Bejleri, Harold Blum, Kristin DeVleming, Giovanni Inchiostro, Yuchen Liu, and Xiaowei Wang).
4. 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).
5. 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).
6. Smoothability of relative stable maps to stacky curve. Épijournal de Géométrie Algébrique, 7 (2023), Art. 2. (with Dori Bejleri).
7. 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).
8. Moduli of double covers and degree one del Pezzo surfaces. European Journal of Mathematics, 7, 557–569 (2021) (with Dori Bejleri).
9. Wall crossing for K-moduli spaces of plane curves. (with Kristin DeVleming and Yuchen Liu). Proceedings of the London Mathematical Society, To appear.
10. Compact moduli of elliptic K3 surfaces. Geometry & Topology, 27–5 (2023) 1891-1946. (with Dori Bejleri).
11. 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).
12. 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).
13. Compact moduli of degree one del Pezzo surfaces. (with Dori Bejleri). Mathematische Annalen, 384, 1–31 (2022).
14. 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)*.
15. 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).
16. Moduli of fibered surface pairs from twisted stable maps. Mathematische Annalen, 374 (2019) no. 1-2, 1007–1032. (with Dori Bejleri).
17. Log canonical models of elliptic surfaces. Advances in Mathematics, Vol 320 (2017), 210–243 (with Dori Bejleri).
18. Bounding heights uniformly in families of hyperbolic varieties. New York Journal of Math, 23 (2017) 1791–1808 (with Ariyan Javanpeykar).
19. A generic slice of the moduli space of line arrangements. Algebra & Number Theory, 12-4 (2018), 751–778. (with Patricio Gallardo).
20. A fibered power theorem for pairs of log general type. Algebra & Number Theory, 10-7 (2016), 1581–1600 (with Amos Turchet).
21. 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]
22. Logarithmic stable toric varieties and their moduli. Algebraic Geometry, (3) 2016, 296–319 (with Sam Molcho).

Outreach

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

Recent Conference Organization

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).