Kenny Ascher

Email: kascher@uci.edu

Office: 540B

About me:

I am currently an assistant professor at UC Irvine. Previously, I was an instructor and NSF postdoc at Princeton and MIT. Before that, I was a PhD student at Brown University under Dan Abramovich.

My research is supported in part by NSF grant DMS-2140781.

Here is my CV.

Research Interests

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

Publications & Preprints

  1. Wall crossing for moduli of stable log pairs. Annals of Mathematics, To appear. (with Dori Bejleri, Giovanni Inchiostro, and Zsolt Patakfalvi).
  2. K-stability and birational models of moduli of quartic K3 surfaces. Inventiones Mathematicae, To appear. (with Kristin DeVleming and Yuchen Liu).
  3. Smoothability of relative stable maps to stacky curve. Épijournal de Géométrie Algébrique, To appear. (with Dori Bejleri).
  4. K-moduli of curves on a quadric surface and K3 surfaces. Journal of the Institute of Mathematics of Jussieu, To appear. (with Kristin DeVleming and Yuchen Liu).
  5. Moduli of double covers and degree one del Pezzo surfaces. European Journal of Mathematics, 7, 557–569 (2021) (with Dori Bejleri).
  6. Wall crossing for K-moduli spaces of plane curves. (with Kristin DeVleming and Yuchen Liu).
  7. Compact moduli of elliptic K3 surfaces. Geometry & Topology, To appear. (with Dori Bejleri).
  8. 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).
  9. 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).
  10. Compact moduli of degree one del Pezzo surfaces. (with Dori Bejleri). Mathematische Annalen, 384, 1-31 (2022).
  11. 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)*.
  12. 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).
  13. Moduli of fibered surface pairs from twisted stable maps. Mathematische Annalen, 374 (2019) no. 1-2, 1007-1032. (with Dori Bejleri).
  14. Log canonical models of elliptic surfaces. Advances in Mathematics, Vol 320 (2007), 210–243 (with Dori Bejleri).
  15. Bounding heights uniformly in families of hyperbolic varieties. New York Journal of Math, 23 (2017) 1791-1808 (with Ariyan Javanpeykar).
  16. A generic slice of the moduli space of line arrangements. Algebra & Number Theory, 12-4 (2018), 751--778. (with Patricio Gallardo).
  17. A fibered power theorem for pairs of log general type. Algebra & Number Theory, 10-7 (2016), 1581--1600 (with Amos Turchet).
  18. 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]
  19. Logarithmic stable toric varieties and their moduli. Algebraic Geometry, (3) 2016, 296-319 (with Sam Molcho).

Expository Writing

  • 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. To appear in Arithmetic Geometry of Logarithmic Pairs and Hyperbolicity of Moduli Spaces Hyperbolicity in Montréal. CRM Short Courses.

Teaching

I am currently teaching Math 140A (Elementary Analysis) -- see canvas for details.

Outreach

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

- In Summer 2018 and 2019 I gave lectures to high school students as part of the SIMUW program at the University of Washington.

- In Summer 2017 I worked at Yale University as a project mentor for SUMRY, where I mentored 3 undergraduates in a research project (see paper * above).

- While at Brown, I was an active member of the Math CoOp organized by Kavita Ramanan. We discuss, create, and deliver (applicable) mathematics presentations to K - 12 students in the New England area.

Conference Organization

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

Arithmetic, Birational Geometry, and Moduli Spaces @ Brown University (June 2023).
Last updated: 20 January 2023