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This is a monthly community-building Seminar/Meeting, connecting PhD-students and early career researchers who think about Geometric Structures, Geometry of Moduli Spaces, Integrable Systems, Higgs bundles, Non-Abelian Hodge Theory, Higher Teichmüller Theory, Hyperkähler Manifolds, Topological Recursion and Enumerative Invariants, Geometric Langlands etc.
In order to sign up for the mailing-list please send me a quick email Menelaos.
Participants are given a podium to talk about their latest research endevours in the form of short talks ~20-30min. After each talk, the meeting continues with discussions on a series of subjects proposed by the participants, of either mathematical nature or other. The monthly meetings are taking place online, with the prospective of a yearly multi-day meeting in person at an undisclosed location on the planet.
Planned Future Talks :
Higher Complex Structures and SL(3,R) Hitchin Components - [Alex Nolte- Rice University] (23.09.22 - 16:00 UTC)
Abstract: A source of richness in Teichmüller theory is that Teichmüller spaces have descriptions both in terms of group representations and in terms of hyperbolic and complex structures. A program in higher-rank Teichmüller theory is to understand to what extent there are analogous geometric interpretations of Hitchin components. In this talk, I'll discuss higher degree complex structures, which were defined by Fock and Thomas and are conjectured to parameterize SL(n,R) Hitchin components. I'll then talk about recent results describing the SL(3,R) Hitchin component in terms of higher complex structures, and some intrinsic structural features of Fock-Thomas spaces.
Notes/Sildes . Video avalaible for those in the mailing-list.
Past Talks :
Defining Parahoric Higgs Sheaves- [Karim Rega- Edinburgh] (27.06.22- 16:00 UTC)
Abstract: Soon after the development of the theory of Higgs bundles and non-abelian Hodge theory on complex projective curves, Simpson looked at the formulation of these notions over punctured curves. Earlier work for regular bundles by Mehta and Seshadri already showed that the natural structure here is that of a parabolic bundle, leading to the notion of a parabolic Higgs bundle. Recently, it has become clear that a more uniform way to look at these subjects is through the study of parahoric torsors. In this talk I will attempt to motivate the need for the parahoric story, give some elements of the definition and formulate the notion of a parahoric Higgs bundle.
Fourier-Mukai Transforms for Compactified Prym Varieties [Robbie Hanson- IST Lisbon](27.05.22) 11:00 CET
Abstract: Moduli of Higgs bundles naturally fit into an SYZ mirror symmetry picture, which predicts dualities on the fibers of the Hitchin fibration. We shall explore these predictions for the structure groups G = GL_n and G = SL_n, connecting work of Dima Arinkin with a forthcoming paper of Emilio Franco, João Ruano and myself.
Subjects to Chat about over a Cuppa Tea:
Let's get our N.A.H.-stacks in order. Menelaos shall propose a series of definitions of things that should resemble the relative stacks appearing in the non-Abelian Hodge world. People will rebel. Menelaos can only be glad that the first meeting is online. A reform will arise. Most will be happy.
Link to our researchseminars.org site: https://researchseminars.org/seminar/GeometricStrNxtGn
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