@phdthesis{18443,
  abstract     = {In [KW06] Kapustin and Witten conjectured that there is a mirror symmetry relation between
the hyperkähler structures on certain Higgs bundle moduli spaces. As a consequence, they
conjecture an equivalence between categories of BBB and BAA-branes. At the classical
level, this mirror symmetry is given by T-duality between semi-flat hyperkähler structures on
algebraic integrable systems.
In this thesis, we investigate the T-duality relation between hyperkähler structures and the
corresponding branes on affine torus bundles. We use the techniques of generalized geometry
to show that semi-flat hyperkähler structures are T-dual on algebraic integrable systems.
We also describe T-duality for generalized branes. Motivated by Fourier-Mukai transform
we upgrade the T-duality between generalized branes to T-duality of submanifolds endowed
with U(1)-bundles and connections. This T-duality in the appropriate context specializes to
T-duality between BBB and BAA-branes.
},
  author       = {Sisak, Maria A},
  issn         = {2663-337X},
  keywords     = {hyperkaehler geometry, branes, mirror symmetry, T-duality},
  pages        = {178},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{T-dual branes on hyperkähler manifolds}},
  doi          = {10.15479/at:ista:18443},
  year         = {2024},
}

@article{10613,
  abstract     = {Motivated by the recent preprint [\emph{arXiv:2004.08412}] by Ayala, Carinci, and Redig, we first provide a general framework for the study of scaling limits of higher-order fields. Then, by considering the same class of infinite interacting particle systems as in [\emph{arXiv:2004.08412}], namely symmetric simple exclusion and inclusion processes in the d-dimensional Euclidean lattice, we prove the hydrodynamic limit, and convergence for the equilibrium fluctuations, of higher-order fields. In particular, the limit fields exhibit a tensor structure. Our fluctuation result differs from that in [\emph{arXiv:2004.08412}], since we considered-dimensional Euclidean lattice, we prove the hydrodynamic limit, and convergence for the equilibrium fluctuations, of higher-order fields. In particular, the limit fields exhibit a tensor structure. Our fluctuation result differs from that in [\emph{arXiv:2004.08412}], since we consider a different notion of higher-order fluctuation fields.},
  author       = {Chen, Joe P. and Sau, Federico},
  issn         = {1024-2953},
  journal      = {Markov Processes And Related Fields},
  keywords     = {interacting particle systems, higher-order fields, hydrodynamic limit, equilibrium fluctuations, duality},
  number       = {3},
  pages        = {339--380},
  publisher    = {Polymat Publishing},
  title        = {{Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems}},
  volume       = {27},
  year         = {2021},
}

@article{10024,
  abstract     = {In this paper, we introduce a random environment for the exclusion process in  obtained by assigning a maximal occupancy to each site. This maximal occupancy is allowed to randomly vary among sites, and partial exclusion occurs. Under the assumption of ergodicity under translation and uniform ellipticity of the environment, we derive a quenched hydrodynamic limit in path space by strengthening the mild solution approach initiated in Nagy (2002) and Faggionato (2007). To this purpose, we prove, employing the technology developed for the random conductance model, a homogenization result in the form of an arbitrary starting point quenched invariance principle for a single particle in the same environment, which is a result of independent interest. The self-duality property of the partial exclusion process allows us to transfer this homogenization result to the particle system and, then, apply the tightness criterion in Redig et al. (2020).},
  author       = {Floreani, Simone and Redig, Frank and Sau, Federico},
  issn         = {0304-4149},
  journal      = {Stochastic Processes and their Applications},
  keywords     = {hydrodynamic limit, random environment, random conductance model, arbitrary starting point quenched invariance principle, duality, mild solution},
  pages        = {124--158},
  publisher    = {Elsevier},
  title        = {{Hydrodynamics for the partial exclusion process in random environment}},
  doi          = {10.1016/j.spa.2021.08.006},
  volume       = {142},
  year         = {2021},
}

@article{10033,
  abstract     = {The ⊗*-monoidal structure on the category of sheaves on the Ran space is not pro-nilpotent in the sense of [3]. However, under some connectivity assumptions, we prove that Koszul duality induces an equivalence of categories and that this equivalence behaves nicely with respect to Verdier duality on the Ran space and integrating along the Ran space, i.e. taking factorization homology. Based on ideas sketched in [4], we show that these results also offer a simpler alternative to one of the two main steps in the proof of the Atiyah-Bott formula given in [7] and [5].},
  author       = {Ho, Quoc P},
  issn         = {1090-2082},
  journal      = {Advances in Mathematics},
  keywords     = {Chiral algebras, Chiral homology, Factorization algebras, Koszul duality, Ran space},
  publisher    = {Elsevier},
  title        = {{The Atiyah-Bott formula and connectivity in chiral Koszul duality}},
  doi          = {10.1016/j.aim.2021.107992},
  volume       = {392},
  year         = {2021},
}

@article{9359,
  abstract     = {We prove that the factorization homologies of a scheme with coefficients in truncated polynomial algebras compute the cohomologies of its generalized configuration spaces. Using Koszul duality between commutative algebras and Lie algebras, we obtain new expressions for the cohomologies of the latter. As a consequence, we obtain a uniform and conceptual approach for treating homological stability, homological densities, and arithmetic densities of generalized configuration spaces. Our results categorify, generalize, and in fact provide a conceptual understanding of the coincidences appearing in the work of Farb--Wolfson--Wood. Our computation of the stable homological densities also yields rational homotopy types, answering a question posed by Vakil--Wood. Our approach hinges on the study of homological stability of cohomological Chevalley complexes, which is of independent interest.
},
  author       = {Ho, Quoc P},
  issn         = {1364-0380},
  journal      = {Geometry & Topology},
  keywords     = {Generalized configuration spaces, homological stability, homological densities, chiral algebras, chiral homology, factorization algebras, Koszul duality, Ran space},
  number       = {2},
  pages        = {813--912},
  publisher    = {Mathematical Sciences Publishers},
  title        = {{Homological stability and densities of generalized configuration spaces}},
  doi          = {10.2140/gt.2021.25.813},
  volume       = {25},
  year         = {2021},
}