Indo-European Symposium on Differential and Complex Geometry

IISER Pune (India), 16 January 2026

Coordinators

Dates and venue

This symposium is part of the 1st Indo-European Conference on Mathematics, jointly organised by the European Mathematical Society and the (Indian) Mathematics Consortium, to be held January 12-16, 2026 at IISER Pune (India).

Speakers

  1. Omprokash Das (TIFR Mumbai, India).
  2. Thibaut Delcroix (Université de Montpellier, France).
  3. Tommaso Scognamiglio (Università di Bologna and Indam, Italy).
  4. (CANCELLED) Harish Seshadri (IISc Bengaluru, India)
    (replaced by) Mainak Poddar (IISER Pune, India).
  5. Anoop Singh (IIT(BHU) Varanasi, India).
  6. Marco Zambon (KU Leuven, Belgium).

Titles and abstract

All talks in this symposium (S19) will take place on Friday January 16th, 2026.

Omprokash Das, Minimal Model Program for Kähler 4-folds.

The Minimal Model Program (MMP) or Mori Program is one of the fundamental tools of birational classification of algebraic varieties. Since Mori proved the existence of flips in dimension 3 in the 1980s, there has been astonishing progress in higher-dimensional MMP, for example, the 2006 Hacon-McKernan extension theorem and subsequent proof of the existence of flips in all dimensions. However, there has been very little progress on the same program in non-algebraic settings. In 2015, Campana, Höring, and Peternell showed in a series of three papers that the main results of MMP work for compact Kähler manifolds of dimension 3. Since then, there have been a lot of developments in the Kähler MMP. In my talk, I will show that most of the main results of Kähler MMP hold in dimension 4.

Thibaut Delcroix, Canonical metrics in weighted Kähler geometry.

In weighted Kähler geometry, we consider Kähler manifolds equipped with a torus action, and a fixed positive function on the moment polytope. I will introduce this setting, as well as the notions of canonical metrics in weighted Kähler geometry: weighted solitons and weighted cscK metrics. I will then review some results on existence of such metrics, and applications to the more classical Kähler-Einstein metrics, Kähler-Ricci solitons and Calabi’s extremal Kähler metrics.

Tommaso Scognamiglio, Higgs bundles on a Riemann surface and antiholomorphic involutions.

The study of Higgs bundles on a Riemann surface \(X\) is a central topic, at the bridge of complex and differential geometry. Their moduli spaces are algebraic varieties with a rich and interesting topology. In this talk, we will look at these objects under an additional reality condition, i.e. an antiholomorphic involution on \(X\). I will recall the definition of these objects and of real and quaternionic Higgs bundles and talk about some recent results concerning the topology of their moduli spaces (which are real algebraic varieties), which are part of a joint work with Florent Schaffahauser.

(CANCELLED) Harish Seshadri, Uniformization of noncompact positively curved Kahler manifolds.

I will outline recent work with V. Datar and V. Pingali proving a special case of a conjecture of Yau: Any complete noncompact Kähler surface with positive and bounded positive sectional curvature is biholomorphic to \(\mathbb{C}^2\).

(Replacement for the above) Mainak Poddar, Strong generalized holomorphic vector bundles.

I will describe the notion of a strong generalized holomorphic vector bundle over a generalized complex manifold, first introduced by Lang, Jia and Liu. This is a special case of the notion of a generalized holomorphic vector bundle over a generalized complex manifold, due to Gualtieri, but a generalization of the notion of a holomorphic vector bundle over a complex manifold. In a joint work with Debjit Pal, we recently showed that many constructions and results of complex geometry such as Dolbeault cohomology, Chern-Weil theory, Hodge theory and vanishing theorems extend to strong generalized holomorphic vector bundles under reasonably mild assumptions.

Anoop Singh, Lie algebroid connections and their moduli over a compact Riemann surface.

We describe the notion of Lie algebroid connections on vector bundles over a compact Riemann surface. We consider the moduli space of Lie algebroid connections. We give a compactification of the moduli space and a criterion for the numerical effectiveness of the boundary divisor. We compute its Picard group and analyse Lie algebroid Atiyah bundles associated with an ample line bundle over the moduli space of stable vector bundles. We also discuss the rationality of the moduli space. This is a joint work with Indranil Biswas.

Marco Zambon, Moduli spaces of spacefilling branes in symplectic 4-manifolds.

On a symplectic manifold \((M,ω)\), a space-filling brane structure is a closed 2-form \(F\) which determines a complex structure, with respect to which \(F + i ω\) is holomorphic symplectic. For holomorphic symplectic compact Kähler 4-manifolds, we show that the moduli space of spacefilling branes is smooth, and determine its dimension. The proof relies on the local Torelli theorem for K3 surfaces and tori. This talk is based on joint work with Charlotte Kirchhoff-Lukat.