Conjecture that simple geodesics on finite modular covers have transcendental or algebraic endpoints, proved for minimal laminations.
The symplectic nature of fundamental groups of surfaces
5 Pith papers cite this work. Polarity classification is still indexing.
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Equivariant K-theory of Gieseker spaces is identified with the Jucys-Murphy center of the cyclotomic Hecke algebra.
For the standard representation of Sp_{2n}(C), the Gaiotto locus is the Bialynicki-Birula closure associated to U(Sp_{2n-2}(C)) inside the nilpotent cone, and its intersection with the stable cotangent chart is the closure of the conormal bundle to the one-spinor stratum of the generalized theta-div
Ergodic mapping class group invariant measures on Deroin-Tholozan character varieties are either counting measures on finite orbits or the Liouville measure from the Goldman symplectic form.
A comprehensive introduction to spectral networks that develops higher-rank Teichmüller theory in parallel with class S gauge theory and BPS spectra.
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Transcendence of simple geodesics on finite modular covers
Conjecture that simple geodesics on finite modular covers have transcendental or algebraic endpoints, proved for minimal laminations.
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K-theory of Gieseker variety and type A cyclotomic Hecke algebra
Equivariant K-theory of Gieseker spaces is identified with the Jucys-Murphy center of the cyclotomic Hecke algebra.
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Gaiotto Loci and the Nilpotent Cone for $\mathrm{Sp}_{2n}(\mathbb C)$
For the standard representation of Sp_{2n}(C), the Gaiotto locus is the Bialynicki-Birula closure associated to U(Sp_{2n-2}(C)) inside the nilpotent cone, and its intersection with the stable cotangent chart is the closure of the conormal bundle to the one-spinor stratum of the generalized theta-div
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Invariant measures for Deroin-Tholozan representations
Ergodic mapping class group invariant measures on Deroin-Tholozan character varieties are either counting measures on finite orbits or the Liouville measure from the Goldman symplectic form.
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Spectral Networks: Bridging higher-rank Teichm\"uller theory and BPS states
A comprehensive introduction to spectral networks that develops higher-rank Teichmüller theory in parallel with class S gauge theory and BPS spectra.