Beijing Algebraic Geometry Day    

August 12th, 2026  MCM110  

Invited Speakers

Organizers

Prof. Yunfeng Jiang (University of Kansas) 

On Bubbling method for the compactification of KSBA moduli spaces

In this talk we outline two methods for the construction of virtual fundamental class for the KSBA moduli space of surfaces of general type. One is the moduli stack of lci covers, where lci covering Deligne-Mumford stacks replace the slc surfaces. The other is the bubble tree compactification of KSBA moduli spaces, which is motivated by the bubble limit structure of collapsing of K\”ahler-Eistein metrics on general type surfaces. Both methods will produce a virtual fundamental class, which confirms a conjecture of Donaldson.

Dr. Promit Kundu (ShanghaiTech University)

Fixed-Point Loci of Moduli Spaces of Sheaves on Toric Orbifolds

I will present a combinatorial description of torus-equivariant sheaves on smooth projective toric orbifolds and apply it to fixed loci in moduli spaces of stable torsion-free sheaves. The main new ingredient is a gluing formula for stacky (S)-families on general toric quotient charts, which simultaneously keeps track of torus weights and the fine gradings determined by local stabilizers.

For characteristic functions supported in one box on every maximal chart, the stacky data reduce to compatible multifiltrations. Together with a balanced generating sheaf, this permits an extension of Kool's GIT method to modified Gieseker stability and gives a scheme-theoretic description of the corresponding fixed-locus components.

The talk will focus on the rank-one case, where the construction becomes explicit and leads to combinatorial generating functions. This example illustrates phenomena absent for ordinary toric varieties, particularly the contribution of stacky weights and fine gradings.

Dr. Siqing Zhang (Yale University)

Galois conjugate character varieties and cohomology rings

How subtle can the difference between two Galois conjugate complex varieties be? Can they have isomorphic homotopy groups and rational cohomology rings, but nonisomorphic integral cohomology rings? In joint work with Junliang Shen, we show that the answer is yes and the example is given by certain character varieties for curves, answering a 2005 question of Hausel. The proof uses non abelian Hodge theory and develops a systematic method for finding the lowest-degree relation among tautological classes in the cohomology of Higgs moduli spaces, a problem that had previously remained mysterious beyond rank two. If time permits, I will also describe related joint work with Runjie Hu, where we show that the etale cohomology ring of a positive characteristic variety is an effective obstruction to liftability.