Tamás Darvas
Professor, University of Maryland

I am a geometric analyst with a concentration of research on complex differential geometry. All my papers can be found in preprint form on the arXiv. I am also present on Google Scholar.


SURVEY PAPERS:

Relative pluripotential theory on compact Kähler manifolds, with E. Di Nezza, C. H. Lu, Pure. Appl. Math. Q. 21 (2025), no. 3, pp. 1037-1118. arXiv:2303.11584

Geometric pluripotential theory on Kähler manifolds, Advances in complex geometry, 1-104, Contemp. Math. 735, Amer. Math. Soc., Providence, RI, 2019, arXiv:1902.01982


RESEARCH PAPERS:

A YTD correspondence for constant scalar curvature metrics, with K. Zhang, preprint, arXiv:2509.15173

Lines in the space of Kähler metrics, with N. McCleerey, preprint, arXiv:2507.17375

The trace operator of quasi-plurisubharmonic functions on compact Kähler manifolds, with M. Xia, preprint, arXiv:2403.08259

Transcendental Okounkov bodies, with R. Reboulet, M. Xia, D. Witt Nystrom, K. Zhang, preprint, to appear in J. Differ. Geom. arXiv:2309.07584

A transcendental approach to non-Archimedean metrics of pseudoeffective classes, with M. Xia, K. Zhang, preprint, to appear in Comment. Math. Helv. arXiv:2302.02541

Twisted Kähler-Einstein metrics in big classes, with K. Zhang, Comm. Pure Appl. Math. 77 (2024), no. 12, 4289--4327. arXiv:2208.08324

The volume of pseudoeffective line bundles and partial equilibrium, with M. Xia, Geom. and Topol. 28-4 (2024), 1957--1993 arXiv:2112.03827

The Mabuchi geometry of low energy classes, Math. Ann. 389 (2024), no. 1, 427--450. arXiv:2109.11581

The closures of test configurations and algebraic singularity types, with M. Xia, Adv. Math. 397 (2022), Paper No. 108198. arXiv:2003.04818

Griffiths extremality, interpolation of norms, and Kähler quantization, with K.-R. Wu, J. Geom. Anal. 32 (2022), no. 7, Paper No. 203. arXiv:1910.01782

The metric geometry of singularity types, with E. Di Nezza and C.H. Lu, J. Reine Angew. Math. 771 (2021), 137-170. arXiv:1909.00839

The isometries of the space of Kähler metrics, J. Eur. Math. Soc. 23 (2021), no. 12, 4091--4108. arXiv:1902.06124

Geodesic stability, the space of rays, and uniform convexity in Mabuchi geometry, with C.H. Lu, Geom. and Topol. 24 (2020), no. 4, 1907-1967 arXiv:1810.04661

Quantization in geometric pluripotential theory, with C.H. Lu and Y.A. Rubinstein, Comm. Pure Appl. Math. 73 (2020), no. 5, 1100-1138 arXiv:1809.03800

Log-concavity of volume and complex Monge-Ampere equations with prescribed singularity, with E. Di Nezza and C.H. Lu, Math. Ann. 379 (2021), no. 1-2, 95-132. arXiv:1807.00276

L^1 metric geometry of big cohomology classes, with E. Di Nezza and C.H. Lu, Ann. Inst. Fourier (Grenoble) 68 (2018), no. 7, 3053-3086. arXiv:1802.00087

Compactness of Kähler metrics with bounds on Ricci curvature and I functional, with X.X. Chen and W. He, Calc. Var. PDE 58 (2019), no. 4, Paper No. 139. arXiv:1712.05095

Convergence of the Kähler-Ricci iteration, with Y.A. Rubinstein, Analysis & PDE 12 (2019), no. 3. 721-735. arXiv:1705.06253

Monotonicity of non-pluripolar products and complex Monge-Ampere equations with prescribed singularity, with E. Di Nezza and C.H. Lu, Analysis & PDE 11 (2018), no. 8. arXiv:1705.05796

A minimum principle for Lagrangian graphs, with Y.A. Rubinstein, Comm. Anal. Geom. 27 (2019), no. 4, 857-876. arXiv:1606.08818

On the singularity type of full mass currents in big cohomology classes, with E. Di Nezza and C.H. Lu, Compos. Math. 154 (2018), no. 2, 380-409. arXiv:1606.01527

Metric geometry of normal Kähler spaces, energy properness, and existence of canonical metrics, IMRN (2017), no. 22, 6752-6777. arXiv:1604.07127

Regularity of weak minimizers of the K-energy and applications to properness and K-stability, with R. Berman and C.H. Lu, Ann. Sci. Ec. Norm. Super. 53 (2020), no. 4, 267-289, arXiv:1602.03114

Comparison of the Calabi and Mabuchi geometries and applications to geometric flows, Ann. Inst. H. Poincare Anal. Non Lineaire 34 (2017), no. 5, 1131-1140. arXiv:1602.04309

Convexity of the extended K-energy and the long time behavior of the Calabi flow, with R.J. Berman and C.H. Lu, Geom. and Topol. 21 (2017), no. 5, 2945-2988. arXiv:1510.01260

Tian's properness conjectures and Finsler geometry of the space of Kähler metrics, with Y.A. Rubinstein, J. Amer. Math. Soc. 30 (2017), no. 2, 347-387. arXiv:1506.07129

Geodesic rays and Kähler-Ricci trajectories on Fano manifolds, with W. He, Trans. Amer. Math. Soc. 369 (2017), no. 7, 5069-5085. arXiv:1411.0774

The Mabuchi geometry of finite energy classes, Adv. Math. 285 (2015), 182-219. arXiv:1409.2072

Kiselman's principle, the Dirichlet problem for the Monge-Ampere equation, and rooftop obstacle problems, with Y.A. Rubinstein, J. Math. Soc. Japan 68 (2016), no. 2, 773-796. arXiv:1405.6548

The Mabuchi completion of the space of Kähler potentials, Amer. J. Math. 139 (2017), no. 5, 1275-1313. arXiv:1401.7318

Weak geodesic rays in the space of Kähler potentials and the class E(X,ω), J. Inst. Math. Jussieu 16 (2017), no. 4, 837-858. arXiv:1307.6822

Morse theory and geodesics in the space of Kähler metrics, Proc. Amer. Math. Soc. 142 (2014), no. 8, 2775-2782. arXiv:1207.4465

Weak geodesics in the space of Kähler metrics, with L. Lempert, Math. Res. Lett. 19 (2012), no. 5, 1127-1135. arXiv:1205.0840


RESEARCH PAPERS WITH UNDERGRADUATES:

The Hausdorff distance and metrics on toric singularity types, with A. Aitokhuehi, B. Braiman, D. Cutler, R. Deaton, P. Gupta, J. Horsley, V. Pidaparthy, J. Tang, to appear in Bull. Sci. Math., arXiv:2411.11246

Extremizers of the J functional with respect to the d_1 metric, with S. Bachhuber, A. Benda, B. Christophel, Analysis Math. 48 (2022), no. 2, 307-330. arXiv:2304.06323

Optimal asymptotic of the J functional with respect to the d_1 metric, with E. George and K. Smith, Selecta Math. (N.S.) 28 (2022), no. 2, Paper No. 43. arXiv:2101.02589