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The Moduli Space of Stable Coherent Sheaves via Non-archimedean Geometry
We provide a construction of the moduli space of stable coherent sheaves in the world of non-archimedean geometry, where we use the notion of...
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Rouquier dimension is Krull dimension for normal toric varieties
We prove that for any normal toric variety, the Rouquier dimension of its bounded derived category of coherent sheaves is equal to its Krull...
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An inclusion–exclusion principle for tautological sheaves on Hilbert schemes of points
We show an equation of Euler characteristics of tautological sheaves on Hilbert schemes of points on the fibers of a double point degeneration. This...
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Generators for K-theoretic Hall algebras of quivers with potential
K-theoretic Hall algebras (KHAs) of quivers with potential ( Q , W ) are a generalization of preprojective KHAs of quivers, which are conjecturally...
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Quantum Curve and Bilinear Fermionic Form for the Orbifold Gromov–Witten Theory of ℙ[r]
We construct the quantum curve for the Baker–Akhiezer function of the orbifold Gromov–Witten theory of the weighted projective line ℙ[ r ]....
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Riemannian metrics on differentiable stacks
We study Riemannian metrics on Lie groupoids in the relative setting. We show that any split fibration between proper groupoids can be made...
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Equivariant cohomology of the moduli space of genus three curves with symplectic level two structure via point counts
We determine the cohomology groups of the quartic and hyperelliptic loci inside the moduli space of genus three curves with symplectic level two...
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Categorified Hall Products on DT Categories
In this chapter, we use categorified Hall products for DT categories to give an approach toward Conjectures 4.3.3...
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A Stacky Approach to Crystals
Inspired by a theorem of Bhatt–Morrow–Scholze, we develop a stacky approach to crystals and isocrystals on “Frobenius-smooth” schemes over...
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K-theoretic Hall algebras, quantum groups and super quantum groups
We prove that the K-theoretic Hall algebra of a preprojective algebra of affine type is isomorphic to the positive half of a quantum toroidal quantum...
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Descent of vector bundles under wildly ramified extensions
Given an irreducible normal Noetherian scheme and a finite Galois extension of the field of rational functions, we discuss the comparison of the...
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Symmetric Differentials and the Dimension of Hitchin Components for Orbi-Curves
This note is based on a talk given at the 2019 ISAAC Congress in Aveiro. We give an expository account of joint work with Daniele Alessandrini and...
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Generators for Hall algebras of surfaces
For a smooth surface S , Porta–Sala defined a categorical Hall algebra generalizing previous work in K-theory of Zhao and Kapranov–Vasserot. We...
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Torsors on semistable curves and degenerations
In this paper, we answer two long-standing questions on the classification of G -torsors on curves for an almost simple, simply connected algebraic...
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On the noncommutative Bondal–Orlov conjecture for some toric varieties
We show that all toric noncommutative crepant resolutions (NCCRs) of affine GIT quotients of “weakly symmetric” unimodular torus representations are...
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Compactifying Subvarieties of Tori
In this chapter, we will develop some techniques for compactifying varieties in general.
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Siegel Modular Forms of Degree Two and Three and Invariant Theory
This is a survey based on the construction of Siegel modular forms of degree 2 and 3 using invariant theory in joint work with Fabien Cléry and Carel...
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Generators for Hall algebras of surfaces
For a smooth surface S , Porta–Sala defined a categorical Hall algebra generalizing previous work in K-theory of Zhao and Kapranov–Vasserot. We...
