Ronan Conlon

Assistant Professor
Department of Mathematical Sciences
The University of Texas at Dallas
Richardson, TX 75080

Office: SCI 1.164

Email: ronan.conlon at utdallas dot edu

Research Interests: Einstein manifolds, special holonomy, PDEs on Riemannian manifolds, geometric analysis

I co-organised the conference Special Metrics in Complex Geometry that took place at UT Dallas from May 16-20, 2022.

Preprints:

• (with P.-Y. Chan and Y. Lai) A family of Kähler flying wing steady Ricci solitons
  [arXiv] preprint 2024


• (with F. Rochon) Warped quasi-asymptotically conical Calabi-Yau metrics
  [arXiv] preprint 2023


• On the smoothability of certain Kähler cones
  [arXiv] preprint 2014

Publications:

• (with C. Cifarelli and A. Deruelle) An Aubin continuity path for shrinking gradient Kähler-Ricci solitons
  [arXiv] to appear in J. Reine Angew. Math. (Crelle)


• (with C. Cifarelli and A. Deruelle) On finite time Type I singularities of the Kähler-Ricci flow on compact Kähler surfaces
  [arXiv] to appear in J. Eur. Math. Soc. (JEMS)


• (with A. Deruelle) Steady gradient Kähler-Ricci solitons on crepant resolutions of Calabi-Yau cones
  [arXiv] to appear in Mem. Amer. Math. Soc.; see also Oberwolfach report 32-2021


• (with H.-J. Hein) Classification of asymptotically conical Calabi-Yau manifolds
  [arXiv] Duke Math. J. 173 (2024), 947-1015; supersedes arXiv:1405.7140


• (with A. Deruelle and S. Sun) Classification results for expanding and shrinking gradient Kähler-Ricci solitons
  [arXiv] Geom. Topol. 28 (2024), 267-351


• (with R. Bamler, C. Cifarelli, and A. Deruelle) A new complete two-dimensional shrinking gradient Kähler-Ricci soliton
  [arXiv] Geom. Funct. Anal. 34 (2024), 377-392; see also Oberwolfach report 29-2023


• (with F. Rochon) New examples of complete Calabi-Yau metrics on ℂⁿ for n≥3
  [arXiv] Ann. Sci. Éc. Norm. Supér. 54 (2021), 259-303


• (with A. Deruelle) Expanding Kähler-Ricci solitons coming out of Kähler cones
  [arXiv] J. Differential Geom. 115 (2020), 303-365; see also Oberwolfach report 31-2017


• (with A. Degeratu and F. Rochon) Quasi-asymptotically conical Calabi-Yau manifolds
  [arXiv] Geom. Topol. 23 (2019), 29-100


• (with R. Mazzeo and F. Rochon) The moduli space of asymptotically cylindrical Calabi-Yau manifolds
  [arXiv] Comm. Math. Phys. 338 (2015), 953-1009


• (with H.-J. Hein) Asymptotically conical Calabi-Yau metrics on quasi-projective varieties
  [arXiv] Geom. Funct. Anal. 25 (2015), 517-552


• (with H.-J. Hein) Asymptotically conical Calabi-Yau manifolds, I
  [arXiv] Duke Math. J. 162 (2013), 2855-2902