Ron Donagi
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Cornering relative symmetry theories Open
The symmetry data of a d-dimensional quantum field theory (QFT) can often be captured in terms of a higher-dimensional symmetry topological field theory. In top-down (i.e., stringy) realizations of this structure, the QFT in question is lo…
The meromorphic Hitchin fibration over stable pointed curves: moduli spaces Open
We construct a universal partial compactification of the relative moduli space of semistable meromorphic Higgs bundles over the stack of stable pointed curves. It parametrizes meromorphic Gieseker Higgs bundles, and is equipped with a flat…
A measure on the moduli space of super Riemann surfaces with Ramond punctures Open
We construct a measure on the moduli space of super Riemann surfaces with Ramond punctures using the super Mumford isomorphism and a super period map.
View article: On Generalized Pfaffians
On Generalized Pfaffians Open
The determinant of an anti-symmetric matrix $g$ is the square of its Pfaffian, which like the determinant is a polynomial in the entries of $g$. Studies of certain super conformal field theories (of class S) suggested a conjectural general…
Cornering Relative Symmetry Theories Open
The symmetry data of a $d$-dimensional quantum field theory (QFT) can often be captured in terms of a higher-dimensional symmetry topological field theory (SymTFT). In top down (i.e., stringy) realizations of this structure, the QFT in que…
Twistor Hecke eigensheaves in genus 2 Open
Following the strategy outlined in [DP09] arXiv:math/0604617 and [DP22] arXiv:math/0604617 for bundles of rank 2 on a smooth projective curve of genus $2$, we construct flat connections over the moduli of stable bundles, with singularities…
The M-Theory Three-Form and Singular Geometries Open
While M- and F-theory compactifications describe a much larger class of vacua than perturbative string compactifications, they typically need singularities to generate non-abelian gauge fields and charged matter. The physical explanation i…
View article: The Hitchin Image in Type-D
The Hitchin Image in Type-D Open
Motivated by their appearance as Coulomb branch geometries of Class S theories, we study the image of the local Hitchin map in tame Hitchin systems of type-D with residue in a special nilpotent orbit $\mathcal{O}_H$. We describe two import…
Supermoduli Space with Ramond punctures is not projected Open
The supermoduli space $\frak{M}_{g,0,2r}$ is not projected for all $g \ge 5r +1 \ge 6$.
Improved statistics for F-theory standard models Open
Much of the analysis of F-theory-based Standard Models boils down to computing cohomologies of line bundles on matter curves. By varying parameters one can degenerate such matter curves to singular ones, typically with many nodes, where th…
The bad locus in the moduli of super Riemann surfaces with Ramond punctures Open
The bad locus in the moduli of super Riemann surfaces with Ramond punctures parametrizes those super Riemann surfaces that have more than the expected number of independent closed holomorphic 1-forms. There is a super period map that depen…
On the global moduli of Calabi–Yau threefolds Open
In this note we initiate a program to obtain global descriptions of\nCalabi-Yau moduli spaces, to calculate their Picard group, and to identify\nwithin that group the Hodge line bundle, and the closely-related Bagger-Witten\nline bundle. W…
View article: Families of Hitchin systems and $N=2$ theories
Families of Hitchin systems and $N=2$ theories Open
Motivated by the connection to 4d $\\mathcal{N}=2$ theories, we study the\nglobal behavior of families of tamely-ramified $SL_N$ Hitchin integrable\nsystems as the underlying curve varies over the Deligne-Mumford moduli space of\nstable po…
Root bundles and towards exact matter spectra of F-theory MSSMs Open
A bstract Motivated by the appearance of fractional powers of line bundles in studies of vector-like spectra in 4d F-theory compactifications, we analyze the structure and origin of these bundles. Fractional powers of line bundles are also…
Hodge classes on the moduli space of W(E_6)-covers and the geometry of\n A_6 Open
In previous work we showed that the Hurwitz space of W(E_6)-covers of the\nprojective line branched over 24 points dominates via the Prym-Tyurin map the\nmoduli space A_6 of principally polarized abelian 6-folds. Here we determine\nthe 25 …
Hodge classes on the moduli space of W(E_6)-covers and the geometry of A_6 Open
In previous work we showed that the Hurwitz space of W(E_6)-covers of the projective line branched over 24 points dominates via the Prym-Tyurin map the moduli space A_6 of principally polarized abelian 6-folds. Here we determine the 25 Hod…
Folding of Hitchin Systems and Crepant Resolutions Open
Folding of ADE-Dynkin diagrams according to graph automorphisms yields irreducible Dynkin diagrams of $\textrm{ABCDEFG}$-types. This folding procedure allows to trace back the properties of the corresponding simple Lie algebras or groups t…
View article: Families of Hitchin systems and N=2 theories
Families of Hitchin systems and N=2 theories Open
Motivated by the connection to 4d $\mathcal{N}=2$ theories, we study the global behavior of families of tamely-ramified $SL_N$ Hitchin integrable systems as the underlying curve varies over the Deligne-Mumford moduli space of stable pointe…
Parabolic Hecke eigensheaves Open
We study the Geometric Langlands Conjecture (GLC) for rank two flat bundles on the projective line $C$ with tame ramification at five points $\{p_{1}, p_{2}, p_{3}, p_{4}, p_{5} \}$. In particular we construct the automorphic $D$-modules p…
The uniformization of the moduli space of principally polarized abelian 6-folds Open
Starting from a beautiful idea of Kanev, we construct a uniformization of the moduli space 𝒜 6 \mathcal{A}_{6} of principally polarized abelian 6-folds in terms of curves and monodromy data. We show that the general principally polarized a…
Twisted spectral correspondence and torus knots Open
Cohomological invariants of twisted wild character varieties as constructed by Boalch and Yamakawa are derived from enumerative Calabi-Yau geometry and refined Chern-Simons invariants of torus knots. Generalizing the untwisted case, the pr…
On the global moduli of Calabi-Yau threefolds Open
In this note we initiate a program to obtain global descriptions of Calabi-Yau moduli spaces, to calculate their Picard group, and to identify within that group the Hodge line bundle, and the closely-related Bagger-Witten line bundle. We d…
Direct Images in Non Abelian Hodge Theory Open
In this paper we explain how non-abelian Hodge theory allows one to compute the $L^2$ cohomology or middle perversity higher direct images of harmonic bundles and twistor D-modules in a purely algebraic manner. Our main result is a new alg…