[{"author":[{"full_name":"Sisak, Maria A","first_name":"Maria A","last_name":"Sisak","id":"44A03D04-AEA4-11E9-B225-EA2DE6697425"}],"year":"2024","OA_place":"publisher","article_processing_charge":"No","title":"T-dual branes on hyperkähler manifolds","oa_version":"Published Version","publication_status":"published","publisher":"Institute of Science and Technology Austria","date_created":"2024-10-19T12:00:37Z","status":"public","project":[{"_id":"6286e8c4-2b32-11ec-9570-f5297902f67f","name":"Branes on hyperkähler manifolds","grant_number":"26069"}],"date_published":"2024-10-24T00:00:00Z","page":"178","ddc":["516"],"day":"24","type":"dissertation","license":"https://creativecommons.org/licenses/by/4.0/","language":[{"iso":"eng"}],"file_date_updated":"2024-10-24T08:09:13Z","citation":{"chicago":"Sisak, Maria A. “T-Dual Branes on Hyperkähler Manifolds.” Institute of Science and Technology Austria, 2024. <a href=\"https://doi.org/10.15479/at:ista:18443\">https://doi.org/10.15479/at:ista:18443</a>.","apa":"Sisak, M. A. (2024). <i>T-dual branes on hyperkähler manifolds</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:18443\">https://doi.org/10.15479/at:ista:18443</a>","mla":"Sisak, Maria A. <i>T-Dual Branes on Hyperkähler Manifolds</i>. Institute of Science and Technology Austria, 2024, doi:<a href=\"https://doi.org/10.15479/at:ista:18443\">10.15479/at:ista:18443</a>.","ista":"Sisak MA. 2024. T-dual branes on hyperkähler manifolds. Institute of Science and Technology Austria.","ieee":"M. A. Sisak, “T-dual branes on hyperkähler manifolds,” Institute of Science and Technology Austria, 2024.","short":"M.A. Sisak, T-Dual Branes on Hyperkähler Manifolds, Institute of Science and Technology Austria, 2024.","ama":"Sisak MA. T-dual branes on hyperkähler manifolds. 2024. doi:<a href=\"https://doi.org/10.15479/at:ista:18443\">10.15479/at:ista:18443</a>"},"degree_awarded":"PhD","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","OA_type":"free access","has_accepted_license":"1","doi":"10.15479/at:ista:18443","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"publication_identifier":{"issn":["2663-337X"]},"date_updated":"2026-04-07T12:42:44Z","alternative_title":["ISTA Thesis"],"oa":1,"corr_author":"1","file":[{"checksum":"8c4893e726aaa4b3efb82758da9b6851","creator":"msisak","content_type":"application/pdf","success":1,"date_created":"2024-10-23T14:42:45Z","file_size":1672547,"file_id":"18467","date_updated":"2024-10-23T14:42:45Z","access_level":"open_access","relation":"main_file","file_name":"MASisak_dissertation.pdf"},{"date_updated":"2024-10-24T08:09:13Z","access_level":"closed","relation":"source_file","file_name":"MASisak_source.zip","checksum":"1831b072e861a1e5481024ca9d02b036","creator":"msisak","file_size":617913,"date_created":"2024-10-23T14:43:56Z","content_type":"application/x-zip-compressed","file_id":"18468"}],"_id":"18443","abstract":[{"lang":"eng","text":"In [KW06] Kapustin and Witten conjectured that there is a mirror symmetry relation between\r\nthe hyperkähler structures on certain Higgs bundle moduli spaces. As a consequence, they\r\nconjecture an equivalence between categories of BBB and BAA-branes. At the classical\r\nlevel, this mirror symmetry is given by T-duality between semi-flat hyperkähler structures on\r\nalgebraic integrable systems.\r\nIn this thesis, we investigate the T-duality relation between hyperkähler structures and the\r\ncorresponding branes on affine torus bundles. We use the techniques of generalized geometry\r\nto show that semi-flat hyperkähler structures are T-dual on algebraic integrable systems.\r\nWe also describe T-duality for generalized branes. Motivated by Fourier-Mukai transform\r\nwe upgrade the T-duality between generalized branes to T-duality of submanifolds endowed\r\nwith U(1)-bundles and connections. This T-duality in the appropriate context specializes to\r\nT-duality between BBB and BAA-branes.\r\n"}],"month":"10","keyword":["hyperkaehler geometry","branes","mirror symmetry","T-duality"],"department":[{"_id":"GradSch"},{"_id":"TaHa"}],"supervisor":[{"last_name":"Hausel","id":"4A0666D8-F248-11E8-B48F-1D18A9856A87","first_name":"Tamás","full_name":"Hausel, Tamás","orcid":"0000-0002-9582-2634"}]},{"arxiv":1,"oa_version":"Preprint","ec_funded":1,"title":"Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems","article_processing_charge":"No","year":"2021","author":[{"last_name":"Chen","full_name":"Chen, Joe P.","first_name":"Joe P."},{"full_name":"Sau, Federico","first_name":"Federico","id":"E1836206-9F16-11E9-8814-AEFDE5697425","last_name":"Sau"}],"date_created":"2022-01-10T14:02:31Z","status":"public","acknowledgement":"F.S. would like to thank Mario Ayala and Frank Redig for useful discussions. J.P.C. acknowledges partial financial support from the US National Science Foundation (DMS-1855604). F.S. was financially supported by the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411.\r\n","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"publication_status":"published","publisher":"Polymat Publishing","issue":"3","date_published":"2021-03-16T00:00:00Z","language":[{"iso":"eng"}],"type":"journal_article","day":"16","page":"339-380","quality_controlled":"1","citation":{"ieee":"J. P. Chen and F. Sau, “Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems,” <i>Markov Processes And Related Fields</i>, vol. 27, no. 3. Polymat Publishing, pp. 339–380, 2021.","chicago":"Chen, Joe P., and Federico Sau. “Higher-Order Hydrodynamics and Equilibrium Fluctuations of Interacting Particle Systems.” <i>Markov Processes And Related Fields</i>. Polymat Publishing, 2021.","mla":"Chen, Joe P., and Federico Sau. “Higher-Order Hydrodynamics and Equilibrium Fluctuations of Interacting Particle Systems.” <i>Markov Processes And Related Fields</i>, vol. 27, no. 3, Polymat Publishing, 2021, pp. 339–80.","ista":"Chen JP, Sau F. 2021. Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems. Markov Processes And Related Fields. 27(3), 339–380.","apa":"Chen, J. P., &#38; Sau, F. (2021). Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems. <i>Markov Processes And Related Fields</i>. Polymat Publishing.","ama":"Chen JP, Sau F. Higher-order hydrodynamics and equilibrium fluctuations of interacting particle systems. <i>Markov Processes And Related Fields</i>. 2021;27(3):339-380.","short":"J.P. Chen, F. Sau, Markov Processes And Related Fields 27 (2021) 339–380."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2008.13403"}],"publication_identifier":{"issn":["1024-2953"]},"oa":1,"corr_author":"1","external_id":{"arxiv":["2008.13403"]},"related_material":{"link":[{"url":"http://math-mprf.org/journal/articles/id1614/","relation":"other","description":"Link to Abstract on publisher's website"},{"description":"Referred to in Abstract","relation":"used_for_analysis_in","url":"https://arxiv.org/abs/2004.08412"}]},"date_updated":"2025-06-26T11:57:53Z","keyword":["interacting particle systems","higher-order fields","hydrodynamic limit","equilibrium fluctuations","duality"],"volume":27,"department":[{"_id":"JaMa"}],"publication":"Markov Processes And Related Fields","_id":"10613","intvolume":"        27","abstract":[{"text":"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.","lang":"eng"}],"article_type":"original","month":"03"},{"external_id":{"isi":["000697748500005"],"arxiv":["1911.12564"]},"date_updated":"2025-04-14T07:43:46Z","oa":1,"_id":"10024","abstract":[{"lang":"eng","text":"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)."}],"intvolume":"       142","file":[{"file_name":"2021_StochasticProcessesAppl_Floreani.pdf","relation":"main_file","date_updated":"2022-05-13T07:55:50Z","access_level":"open_access","file_id":"11370","content_type":"application/pdf","success":1,"date_created":"2022-05-13T07:55:50Z","file_size":2115791,"creator":"dernst","checksum":"56768c553d7218ee5714902ffec90ec4"}],"article_type":"original","month":"08","keyword":["hydrodynamic limit","random environment","random conductance model","arbitrary starting point quenched invariance principle","duality","mild solution"],"volume":142,"department":[{"_id":"JaMa"}],"publication":"Stochastic Processes and their Applications","file_date_updated":"2022-05-13T07:55:50Z","citation":{"short":"S. Floreani, F. Redig, F. Sau, Stochastic Processes and Their Applications 142 (2021) 124–158.","ama":"Floreani S, Redig F, Sau F. Hydrodynamics for the partial exclusion process in random environment. <i>Stochastic Processes and their Applications</i>. 2021;142:124-158. doi:<a href=\"https://doi.org/10.1016/j.spa.2021.08.006\">10.1016/j.spa.2021.08.006</a>","ista":"Floreani S, Redig F, Sau F. 2021. Hydrodynamics for the partial exclusion process in random environment. Stochastic Processes and their Applications. 142, 124–158.","mla":"Floreani, Simone, et al. “Hydrodynamics for the Partial Exclusion Process in Random Environment.” <i>Stochastic Processes and Their Applications</i>, vol. 142, Elsevier, 2021, pp. 124–58, doi:<a href=\"https://doi.org/10.1016/j.spa.2021.08.006\">10.1016/j.spa.2021.08.006</a>.","apa":"Floreani, S., Redig, F., &#38; Sau, F. (2021). Hydrodynamics for the partial exclusion process in random environment. <i>Stochastic Processes and Their Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.spa.2021.08.006\">https://doi.org/10.1016/j.spa.2021.08.006</a>","chicago":"Floreani, Simone, Frank Redig, and Federico Sau. “Hydrodynamics for the Partial Exclusion Process in Random Environment.” <i>Stochastic Processes and Their Applications</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.spa.2021.08.006\">https://doi.org/10.1016/j.spa.2021.08.006</a>.","ieee":"S. Floreani, F. Redig, and F. Sau, “Hydrodynamics for the partial exclusion process in random environment,” <i>Stochastic Processes and their Applications</i>, vol. 142. Elsevier, pp. 124–158, 2021."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","quality_controlled":"1","doi":"10.1016/j.spa.2021.08.006","has_accepted_license":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"publication_identifier":{"issn":["0304-4149"]},"date_published":"2021-08-27T00:00:00Z","type":"journal_article","day":"27","page":"124-158","ddc":["519"],"language":[{"iso":"eng"}],"isi":1,"scopus_import":"1","year":"2021","author":[{"first_name":"Simone","full_name":"Floreani, Simone","last_name":"Floreani"},{"full_name":"Redig, Frank","first_name":"Frank","last_name":"Redig"},{"last_name":"Sau","id":"E1836206-9F16-11E9-8814-AEFDE5697425","full_name":"Sau, Federico","first_name":"Federico"}],"arxiv":1,"ec_funded":1,"oa_version":"Published Version","article_processing_charge":"Yes","title":"Hydrodynamics for the partial exclusion process in random environment","publication_status":"published","publisher":"Elsevier","status":"public","date_created":"2021-09-19T22:01:25Z","acknowledgement":"The authors would like to thank Marek Biskup and Alberto Chiarini for useful suggestions and  Cristian  Giardina,  Frank  den  Hollander  and  Shubhamoy  Nandan  for  inspiring  discussions.  S.F.  acknowledges  Simona  Villa  for  her  help  in  creating  the  picture.  Furthermore, the  authors  thank  two  anonymous  referees  for  the  careful  reading  of  the  manuscript.  S.F. acknowledges  financial  support  from  NWO,  The  Netherlands  via  the  grant  TOP1.17.019. F.S.  acknowledges  financial  support  from  NWO  via  the  TOP1  grant  613.001.552  as  well  as funding from the European Union’s Horizon 2020 research and innovation programme under the Marie-Skłodowska-Curie grant agreement No. 754411.","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}]},{"publication_identifier":{"eissn":["1090-2082"],"issn":["0001-8708"]},"has_accepted_license":"1","doi":"10.1016/j.aim.2021.107992","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"quality_controlled":"1","article_number":"107992","citation":{"ieee":"Q. P. Ho, “The Atiyah-Bott formula and connectivity in chiral Koszul duality,” <i>Advances in Mathematics</i>, vol. 392. Elsevier, 2021.","chicago":"Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul Duality.” <i>Advances in Mathematics</i>. Elsevier, 2021. <a href=\"https://doi.org/10.1016/j.aim.2021.107992\">https://doi.org/10.1016/j.aim.2021.107992</a>.","apa":"Ho, Q. P. (2021). The Atiyah-Bott formula and connectivity in chiral Koszul duality. <i>Advances in Mathematics</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.aim.2021.107992\">https://doi.org/10.1016/j.aim.2021.107992</a>","mla":"Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul Duality.” <i>Advances in Mathematics</i>, vol. 392, 107992, Elsevier, 2021, doi:<a href=\"https://doi.org/10.1016/j.aim.2021.107992\">10.1016/j.aim.2021.107992</a>.","ista":"Ho QP. 2021. The Atiyah-Bott formula and connectivity in chiral Koszul duality. Advances in Mathematics. 392, 107992.","ama":"Ho QP. The Atiyah-Bott formula and connectivity in chiral Koszul duality. <i>Advances in Mathematics</i>. 2021;392. doi:<a href=\"https://doi.org/10.1016/j.aim.2021.107992\">10.1016/j.aim.2021.107992</a>","short":"Q.P. Ho, Advances in Mathematics 392 (2021)."},"file_date_updated":"2021-09-21T15:58:52Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","keyword":["Chiral algebras","Chiral homology","Factorization algebras","Koszul duality","Ran space"],"volume":392,"publication":"Advances in Mathematics","department":[{"_id":"TaHa"}],"file":[{"checksum":"f3c0086d41af11db31c00014efb38072","creator":"qho","content_type":"application/pdf","date_created":"2021-09-21T15:58:52Z","file_size":840635,"file_id":"10034","date_updated":"2021-09-21T15:58:52Z","access_level":"open_access","relation":"main_file","file_name":"1-s2.0-S000187082100431X-main.pdf"}],"intvolume":"       392","_id":"10033","abstract":[{"lang":"eng","text":"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]."}],"article_type":"original","month":"09","oa":1,"corr_author":"1","date_updated":"2025-04-14T09:09:35Z","external_id":{"arxiv":["1610.00212"],"isi":["000707040300031"]},"acknowledgement":"The author would like to express his gratitude to D. Gaitsgory, without whose tireless guidance and encouragement in pursuing this problem, this work would not have been possible. The author is grateful to his advisor B.C. Ngô for many years of patient guidance and support. This paper is revised while the author is a postdoc in Hausel group at IST Austria. We thank him and the group for providing a wonderful research environment. The author also gratefully acknowledges the support of the Lise Meitner fellowship “Algebro-Geometric Applications of Factorization Homology,” Austrian Science Fund (FWF): M 2751.","status":"public","date_created":"2021-09-21T15:58:59Z","project":[{"name":"Algebro-Geometric Applications of Factorization Homology","grant_number":"M02751","call_identifier":"FWF","_id":"26B96266-B435-11E9-9278-68D0E5697425"}],"publication_status":"published","publisher":"Elsevier","arxiv":1,"article_processing_charge":"Yes (via OA deal)","title":"The Atiyah-Bott formula and connectivity in chiral Koszul duality","oa_version":"Published Version","author":[{"full_name":"Ho, Quoc P","first_name":"Quoc P","last_name":"Ho","id":"3DD82E3C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6889-1418"}],"year":"2021","isi":1,"language":[{"iso":"eng"}],"scopus_import":"1","day":"21","ddc":["514"],"type":"journal_article","date_published":"2021-09-21T00:00:00Z"},{"external_id":{"arxiv":["1802.07948"],"isi":["000682738600005"]},"date_updated":"2025-04-14T09:09:36Z","corr_author":"1","oa":1,"article_type":"original","month":"04","intvolume":"        25","_id":"9359","abstract":[{"lang":"eng","text":"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.\r\n"}],"file":[{"file_name":"densities.pdf","access_level":"open_access","date_updated":"2021-05-03T06:54:06Z","relation":"main_file","file_size":479268,"date_created":"2021-05-03T06:54:06Z","success":1,"content_type":"application/pdf","file_id":"9366","checksum":"643a8d2d6f06f0888dcd7503f55d0920","creator":"qho"}],"department":[{"_id":"TaHa"}],"publication":"Geometry & Topology","keyword":["Generalized configuration spaces","homological stability","homological densities","chiral algebras","chiral homology","factorization algebras","Koszul duality","Ran space"],"volume":25,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"short":"Q.P. Ho, Geometry &#38; Topology 25 (2021) 813–912.","ama":"Ho QP. Homological stability and densities of generalized configuration spaces. <i>Geometry &#38; Topology</i>. 2021;25(2):813-912. doi:<a href=\"https://doi.org/10.2140/gt.2021.25.813\">10.2140/gt.2021.25.813</a>","chicago":"Ho, Quoc P. “Homological Stability and Densities of Generalized Configuration Spaces.” <i>Geometry &#38; Topology</i>. Mathematical Sciences Publishers, 2021. <a href=\"https://doi.org/10.2140/gt.2021.25.813\">https://doi.org/10.2140/gt.2021.25.813</a>.","mla":"Ho, Quoc P. “Homological Stability and Densities of Generalized Configuration Spaces.” <i>Geometry &#38; Topology</i>, vol. 25, no. 2, Mathematical Sciences Publishers, 2021, pp. 813–912, doi:<a href=\"https://doi.org/10.2140/gt.2021.25.813\">10.2140/gt.2021.25.813</a>.","ista":"Ho QP. 2021. Homological stability and densities of generalized configuration spaces. Geometry &#38; Topology. 25(2), 813–912.","apa":"Ho, Q. P. (2021). Homological stability and densities of generalized configuration spaces. <i>Geometry &#38; Topology</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/gt.2021.25.813\">https://doi.org/10.2140/gt.2021.25.813</a>","ieee":"Q. P. Ho, “Homological stability and densities of generalized configuration spaces,” <i>Geometry &#38; Topology</i>, vol. 25, no. 2. Mathematical Sciences Publishers, pp. 813–912, 2021."},"file_date_updated":"2021-05-03T06:54:06Z","quality_controlled":"1","doi":"10.2140/gt.2021.25.813","has_accepted_license":"1","publication_identifier":{"issn":["1364-0380"]},"date_published":"2021-04-27T00:00:00Z","issue":"2","type":"journal_article","page":"813-912","ddc":["514","516","512"],"day":"27","scopus_import":"1","language":[{"iso":"eng"}],"isi":1,"year":"2021","author":[{"full_name":"Ho, Quoc P","first_name":"Quoc P","last_name":"Ho","id":"3DD82E3C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-6889-1418"}],"oa_version":"Submitted Version","ec_funded":1,"article_processing_charge":"No","title":"Homological stability and densities of generalized configuration spaces","arxiv":1,"publisher":"Mathematical Sciences Publishers","publication_status":"published","project":[{"call_identifier":"FP7","_id":"25E549F4-B435-11E9-9278-68D0E5697425","grant_number":"320593","name":"Arithmetic and physics of Higgs moduli spaces"},{"grant_number":"M02751","name":"Algebro-Geometric Applications of Factorization Homology","_id":"26B96266-B435-11E9-9278-68D0E5697425","call_identifier":"FWF"}],"date_created":"2021-05-02T06:59:33Z","status":"public","acknowledgement":"This paper owes an obvious intellectual debt to the illuminating treatments of factorization homology by J.\r\nFrancis, D. Gaitsgory, and J. Lurie in [GL,G1, FG]. The author would like to thank B. Farb and J. Wolfson for\r\nbringing the question of explaining coincidences in homological densities to his attention. Moreover, the author\r\nthanks J. Wolfson for many helpful conversations on the subject, O. Randal-Williams for many comments which\r\ngreatly help improve the exposition, and G. C. Drummond-Cole for many useful conversations on L∞-algebras.\r\nFinally, the author is grateful to the anonymous referee for carefully reading the manuscript and for providing\r\nnumerous comments which greatly helped improve the clarity and precision of the exposition.\r\nThis work is supported by the Advanced Grant “Arithmetic and Physics of Higgs moduli spaces” No. 320593 of\r\nthe European Research Council and the Lise Meitner fellowship “Algebro-Geometric Applications of Factorization\r\nHomology,” Austrian Science Fund (FWF): M 2751."}]