Carl Tipler

Research interests

• Differential geometry: canonical Kähler metrics, perturbative techniques, moment maps.
• Complex algebraic geometry: K-stability, slope stability, GIT, deformation theory, toric varieties.
• Mathematical physics: Yang-Mills connections, Calabi-Yau varieties, Hull-Strominger system.

Publications

Complete list, see also CV.

Selected publications

1. "Blowing-up Hermitian Yang--Mills connections", with Andrew Clarke, to appear in Annali della Scuola Normale Superiore di Pisa (2025). Journal . ArXiv 2301.00525
2. "Hermitian Yang-Mills connections on pullback bundles", with Lars Martin Sektnan, Calc. Var. Partial Differ. Equ. 63, Paper No. 13, 63p. (2024). Journal . ArXiv 2006.06453
3. "The Zariski-Lipman conjecture for toric varieties", J. Algebra, 609 (2022), pp. 547-551. Journal . ArXiv 2202.02109
4. "Gauge theory for string algebroids", with Mario Garcia-Fernandez and Roberto Rubio, J. Differential Geom. 128(1): 77-152 (2024). Journal . ArXiv 2004.11399
5. "Canonical metrics on holomorphic Courant algebroids", with M. Garcia-Fernandez, R. Rubio and C. Shahbazi, Proc. London Math. Soc., 125: 700-758 (2022). Journal . ArXiv 1803.01873
6. "Extremal metrics and lower bound of the modified K-energy" with Yuji Sano, J. Eur. Math. Soc. (JEMS) 17 (2015), no. 9, 2289-2310. Journal . ArXiv 1211.5585
7. "Lower bounds on the modified K-energy and complex deformations" with Andrew Clarke, Adv. Math. 252 (2014), 449-470. Journal . ArXiv 1302.0556

Preprints

1. "Subspace concentration condition and Bogomolov-Gieseker inequality", preprint 2026, pdf
2. "Stable toric sheaves. I : Chern classes", ArXiv 2510.14651
3. "Polynomial stability conditions for vector bundles: Positivity, equivariance and blow-ups", with Rémi Delloque, Achim Napame and Carlo Scarpa, ArXiv 2506.23842

Other texts

• “Métriques extrémales et système de Strominger”, Habilitation. pdf (in French)
• “Constructions de Métriques extrémales, résolutions de singularités et déformations complexes”, Thesis supervised by Yann Rollin at Laboratoire de mathématiques Jean Leray de Nantes. pdf (in French)

PhD students

• Jean-Baptiste Cadart (2026-...), co-supervision L. M. Sektnan: “Boundary points in the cscK moduli of ruled surfaces”.
• Remi Delloque (2023-2026): “Perturbative techniques for geometric PDEs with moment map pictures”.
• Achim Napame (2020-2023): “Equivariant stable sheaves on toric varieties”.