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22/06/2026, 10:00
The non-abelian Hodge correspondence over a compact Riemann surface X establishes a homeomorphism between the moduli space of G-Higgs bundles and the G-character variety of the fundamental group of X, for a connected semisimple complex Lie group G. Even though the group G is connected, in the study of the geometry of G-Higgs bundles, one has to deal with Higgs pairs of different sorts with...
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22/06/2026, 11:15
The nonabelian Hodge correspondence relates Higgs bundles on a compact Riemann surface to representations of the fundamental group of the underlying topological surface. In this talk, I will give a characterization
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and some properties of representations where the Higgs bundles under this correspondence vary holomorphically as the Riemann surface deforms. -
22/06/2026, 13:15
I will discuss joint work with Sebastian Heller and Claudio Meneses on a small-weight degeneration of the Hitchin hyperkähler metric for strongly parabolic $\mathfrak{sl}_2(\mathbb C)$-Higgs bundles on the $n$-punctured sphere. Scaling the parabolic weights to $t\alpha$ and letting $t \to 0$, we use the parabolic Deligne–Hitchin moduli space to relate twistor lines for the small-weight...
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22/06/2026, 14:15
Let $X$ be a compact Riemann surface. For a positive line bundle $L\to X$, a continuous Hermitian metric $e^{-\phi}h_\ast$ on $L$, and a nonpolar compact subset $K\subseteq X$, one can construct an equilibrium metric from the envelope of subharmonic weight functions bounded above by $\phi$ on $K$. The approximation of equilibrium metrics by sequences of singular metrics has been studied in a...
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22/06/2026, 15:30
We will discuss the geometry of strongly parabolic Hitchin systems for classical groups over smooth curves. We begin by relating the singularities of generic spectral curves to Kazhdan--Lusztig maps, and then explain how the generic Hitchin fibers can be identified with natural abelian varieties. If time permits, we will also discuss the structure of the Hitchin base for even special...
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23/06/2026, 10:00
For a possibly noncommutative finite-dimensional algebra $A$ with an anti-involution $\sigma$ many classical Lie groups can be realized as certain symplectic or orthogonal Lie groups over the pair $(A, \sigma)$. When the involutive algebra $(A, \sigma)$ is Hermitian, one can define and study the associated Riemannian symmetric space of such Lie groups. We will describe different geometric...
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23/06/2026, 11:00
The space of Virasoro conformal blocks on a Riemann surface is a central object in conformal field theory, studied from many different points of view. I will recall what this space is and what some of its expected structures are, and then describe a new method for constructing conformal blocks, when the Virasoro central charge is c=1. Potential applications include new formulas for...
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23/06/2026, 13:15
I will discuss symplectic leaves in moduli spaces of meromorphic $GL_r$-Higgs bundles on a smooth projective curve. These moduli spaces carry natural Poisson structures, studied independently by Bottacin and Markman, and their symplectic leaves are expected to be governed by the adjoint orbits of the residues at the marked points. However, it has not been clear whether the corresponding loci...
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23/06/2026, 14:15
The parabolic Higgs bundle moduli spaces on the n-punctured sphere are hyperkahler manifolds with integrable system structures. Star-shaped Nakajima quiver varieties are hyperkahler manifolds which were used by Kronheimer and Nakajima to model ALE spaces. In higher dimensional cases, they were recently shown by Dimakis and Rochon to be quasi-asymptotically conical (QAC).
We generalize a...
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23/06/2026, 15:30
In this talk, I would like to discuss the joint deformation problem of a Kahler manifold and a Higgs bundle.
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I will introduce the DGLA which governs this deformation problem.
Moreover, I will show that if the Higgs bundle is polystable with zero Chern classes, the Kuraishi space of pair (Higgs bundle, Kahler manifold) is isomorphic to the Kuranishi space of (Higgs bundle) x the Kuranishi... -
24/06/2026, 10:00
Higher Teichmüller theory is the study of connected components in the $G^R$-character variety consisting entirely of discrete and faithful surface group representations. Under the nonabelian Hodge correspondence, various problems in higher Teichmüller theory can be approached by using topological methods on the $G^R$-Higgs bundle moduli space.
Following recent developments of...
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24/06/2026, 11:15
Some quivers appearing in four-dimensional supersymmetric field theory have a surprisingly simple geometric origin. I will explain how they arise from vanishing cycles of Lefschetz fibrations, and how their tensor-product structure reflects a natural operation on the underlying geometry. The aim is to discuss the geometry, algebra, and physics underlying such tensor-product quivers. This talk...
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24/06/2026, 13:15
I will discuss a precise formulation of the Dolbeault geometric
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Langlands conjecture, introduced by Donagi–Pantev as the classical
limit of the de Rham geometric Langlands correspondence. On the
automorphic side, the formulation involves limit categories, which may
be viewed as classical limits of categories of D-modules on moduli
stacks of bundles over curves. It predicts an equivalence...
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