Professor

Department of Mathematics

Northwestern University

2033 Sheridan Road

Evanston, IL 60208

email : `gaborsz at northwestern.edu`

I am
interested in geometric analysis and
complex differential geometry. Much of my work is motivated by trying
to find canonical metrics, such as extremal or Kähler-Einstein
metrics on projective manifolds.

Special Metrics in Complex Geometry, May 16--20, 2022

Notre Dame Geometry & Topology RTG

Northwestern, UIC Complex Geometry Seminar

Center for Mathematics Thematic Program on Kähler geometry, June 12 - 30, 2017

Notre Dame Geometric Analysis Seminar, Past years

MMP and Ricci flow learning seminar

Previous teaching

- (with N. Edelen)
A Liouville-type theorem for cylindrical cones

[abstract] [pdf] - (with J. D. Lotay, F. Schulze)
Neck pinches along the Lagrangian mean curvature flow of surfaces

[abstract] [pdf] - (with J. D. Lotay, F. Schulze)
Ancient solutions and translators of Lagrangian mean curvature flow

[abstract] [pdf] - (with S.-K. Chiu)
Higher regularity for singular Kähler-Einstein metrics

[abstract] [pdf] to appear in Duke Math. J. -
Minimal hypersurfaces with cylindrical tangent cones

[abstract] [pdf] -
Uniqueness of certain cylindrical tangent cones

[abstract] [pdf] - (with B. Weinkove)
Weak Harnack inequalities for eigenvalues and constant rank theorems

[abstract] [pdf] Comm. Partial Differential Equations 46 (2021), no. 8, 1585--1600 -
(with J. Ross)

Twisted Kähler-Einstein metrics

[abstract] [pdf] to appear in Pure Appl. Math. Q. -
Uniqueness of some Calabi-Yau metrics on C ^{n}

[abstract] [pdf] Geom. Funct. Anal. 30 (2020), no. 4, 1152--1182. -
(with G. Liu)

Gromov-Hausdorff limits of Kähler manifolds with Ricci curvature bounded below, II

[abstract] [pdf] to appear in Comm. Pure Appl. Math. -
(with G. Liu)

Gromov-Hausdorff limits of Kähler manifolds with Ricci curvature bounded below

[abstract] [pdf] to appear in Geom. Funct. Anal. -
(with M. Gursky)

A local existence result for Poincaré-Einstein metrics

[abstract] [pdf] Adv. Math. 361 (2020), 106912, 50 pp. -
Kähler-Einstein metrics

[abstract] [pdf] Proc. Sympos. Pure Math., 99., 331--361 -
Degenerations of C ^{n}and Calabi-Yau metrics

[abstract] [pdf] Duke Math. J. 168 (2019), no. 14, 2651--2700 -
(with R. Dervan)

The Kähler-Ricci flow and optimal degenerations

[abstract] [pdf] to appear in J. Differential Geom. -
(with R. Seyyedali)

Extremal metrics on blowups along submanifolds

[abstract] [pdf] J. Differential Geom. 114 (2020), no. 1, 171--192 -
(with T. Collins)

Sasaki-Einstein metrics and K-stability

[abstract] [pdf] Geom. Topol. 23 (2019), no. 3, 1339--1413. -
(with B. Weinkove)

On a constant rank theorem for nonlinear elliptic PDEs

[abstract] [pdf] Discrete Contin. Dyn. Syst. Ser. A, 36 (2016) no. 11, 6523--6532 -
(with V. Datar)

Kähler-Einstein metrics along the smooth continuity method

[abstract] [pdf] Geom. Funct. Anal. 26 (2016) no. 4, 975--1010 -
(with V. Tosatti, B. Weinkove)

Gauduchon metrics with prescribed volume form

[abstract] [pdf] Acta Math. 219 (2017), no. 1, 181--211 -
Fully non-linear elliptic equations on compact Hermitian manifolds

[abstract] [pdf] J. Differential Geom. 109 (2018), no. 2, 337--378 -
(with T. Collins)

Convergence of the J-flow on toric manifolds

[abstract] [pdf] J. Differential Geom. 107 (2017) no. 1, 47--81 -
Extremal Kähler metrics

[abstract] [pdf] Proceedings of the ICM, 2014 -
The partial C ^{0}-estimate along the continuity method

[abstract] [pdf] J. Amer. Math. Soc. 29 (2016), 537--560 -
(with M. Lejmi)

The J-flow and stability

[abstract] [pdf] Adv. Math. 274 (2015), 404--431 -
Blowing up extremal Kähler manifolds II

[abstract] [pdf] Invent. Math. 200 (2015), no. 3, 925--977 -
A remark on conical Kähler-Einstein metrics

[abstract] [pdf] Math. Res. Lett. 20 (2013) n. 3., 581--590 -
Remark on the Calabi flow with bounded curvature

[abstract] [pdf] Univ. Iagel. Acta Math. 50 (2013), 107--115 -
(with T. Collins)

The twisted Kähler-Ricci flow

[abstract] [pdf] J. Reine Angew. Math. 716 (2016), 179--205 -
(with T. Collins)

K-Semistability for irregular Sasakian manifolds

[abstract] [pdf] J. Differential Geom. 109 (2018), no. 1, 81--109 -
Filtrations and test-configurations

[abstract] [pdf] Math. Ann. 362 (2015), 451--484 -
(with J. Song and B. Weinkove)

The Kähler-Ricci flow on projective bundles

[abstract] [pdf] Int. Math. Res. Not. 2013, 243--257 -
(with D. McFeron)

On the positive mass theorem for manifolds with corners

[abstract] [pdf] Comm. Math. Phys. 313 (2012), 425--443 -
(with Renjie Feng)

Periodic solutions of Abreu's equation

[abstract] [pdf] Math. Res. Lett. 18 (2011) n. 6., 1271--1279 -
On blowing up extremal Kähler manifolds

[abstract] [pdf] Duke Math. J., 161 (2012) n. 8, 1411--1453 -
(with J. Stoppa)

Relative K-stability of extremal metrics

[abstract] [pdf] J. Eur. Math. Soc. 13 (2011) n. 4, 899--909 -
(with V. Tosatti)

Regularity of weak solutions of a complex Monge-Ampère equation

[abstract] [pdf] Analysis & PDE 4 (2011), n. 3, 369--378 -
(with O. Munteanu)

On convergence of the Kähler-Ricci flow

[abstract] [pdf] Comm. Anal. Geom. 19 (2011), n. 5, 887--904 -
Greatest lower bounds on the Ricci curvature of Fano manifolds

[abstract] [pdf] Compositio Math. 147 (2011), 319--331 -
The Kähler-Ricci flow and K-polystability

[abstract] [pdf] Amer. J. Math. 132 (2010), 1077--1090 -
The Calabi functional on a ruled surface

[abstract] [pdf] Ann. Sci. Éc. Norm. Supér. 42 (2009), 837--856 -
Optimal test-configurations for toric varieties

[abstract] [pdf] J. Differential Geom. 80 (2008), 501--523 -
Extremal metrics and K-stability

[abstract] [pdf] Bull. London Math. Soc. 39 (2007), 76--84 - (with M. Laczkovich)
Harmonic analysis on discrete Abelian groups

[abstract] [link] Proc. Amer. Math. Soc. 133 (2005), 1581--1586

- Great Lakes Geometry Conference 2014 - website
- Northwestern Math Department
- Notre Dame Math Department
- Geometry at Imperial
- Columbia Math Department
- László Székelyhidi Jr.
- Sonja Mapes Székelyhidi