@article {Seiberg:1994rs,
    AUTHOR = {Seiberg, N. and Witten, E.},
     TITLE = {Electric-magnetic duality, monopole condensation, and
              confinement in {$N=2$} supersymmetric {Y}ang--{M}ills theory},
   JOURNAL = {Nuclear Phys.~B},
  FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and
              Experimental High Energy Physics. Quantum Field Theory and
              Statistical Systems},
    VOLUME = {426},
      YEAR = {1994},
    NUMBER = {1},
     PAGES = {19--52},
       URL = {https://doi.org/10.1016/0550-3213(94)90124-4},
    EPRINT = {hep-th/9407087},
      NOTE = {{E}rratum, \href{https://doi.org/10.1016/0550-3213(94)00449-8}{\textit{Nuclear Phys.~B}} \textbf{430} (1994), 485--486},
}

@article {Strominger:1996sh,
    AUTHOR = {Strominger, Andrew and Vafa, Cumrun},
     TITLE = {Microscopic origin of the {B}ekenstein--{H}awking entropy},
   JOURNAL = {Phys. Lett.~B},
  FJOURNAL = {Physics Letters. B. Particle Physics, Nuclear Physics and
              Cosmology},
    VOLUME = {379},
      YEAR = {1996},
    NUMBER = {1-4},
     PAGES = {99--104},
       URL = {https://doi.org/10.1016/0370-2693(96)00345-0},
    EPRINT = {hep-th/9601029},
}

@article {Katz:1999xq,
    AUTHOR = {Katz, Sheldon and Klemm, Albrecht and Vafa, Cumrun},
     TITLE = {M-theory, topological strings and spinning black holes},
   JOURNAL = {Adv. Theor. Math. Phys.},
  FJOURNAL = {Advances in Theoretical and Mathematical Physics},
    VOLUME = {3},
      YEAR = {1999},
    NUMBER = {5},
     PAGES = {1445--1537},
       URL = {https://doi.org/10.4310/ATMP.1999.v3.n5.a6},
    EPRINT = {hep-th/9910181},
}

@incollection {Seiberg:1996nz,
    AUTHOR = {Seiberg, N. and Witten, E.},
     TITLE = {Gauge dynamics and compactification to three dimensions},
 BOOKTITLE = {The Mathematical Beauty of Physics ({S}aclay, 1996)},
    SERIES = {Adv. Ser. Math. Phys.},
    VOLUME = {24},
     PAGES = {333--366},
 PUBLISHER = {World Sci. Publ., River Edge, NJ},
      YEAR = {1997},
    EPRINT = {hep-th/9607163},
}

@article {Gaiotto:2008cd,
    AUTHOR = {Gaiotto, Davide and Moore, Gregory W. and Neitzke, Andrew},
     TITLE = {Four-dimensional wall-crossing via three-dimensional field
              theory},
   JOURNAL = {Comm. Math. Phys.},
  FJOURNAL = {Communications in Mathematical Physics},
    VOLUME = {299},
      YEAR = {2010},
    NUMBER = {1},
     PAGES = {163--224},
       URL = {https://doi.org/10.1007/s00220-010-1071-2},
    EPRINT = {0807.4723},
}

@mics {Kontsevich:2008fj,
    AUTHOR = {Kontsevich, Maxim and Soibelman, Yan},
     TITLE = {Stability structures, motivic {D}onaldson--{T}homas invariants and cluster transformations},
    EPRINT = {0811.2435},
}

@article {Gaiotto:2009hg,
    AUTHOR = {Gaiotto, Davide and Moore, Gregory W. and Neitzke, Andrew},
     TITLE = {Wall-crossing, {H}itchin systems, and the {WKB} approximation},
   JOURNAL = {Adv. Math.},
  FJOURNAL = {Advances in Mathematics},
    VOLUME = {234},
      YEAR = {2013},
     PAGES = {239--403},
       URL = {https://doi.org/10.1016/j.aim.2012.09.027},
    EPRINT = {0907.3987},
}

@article {Alim:2011kw,
    AUTHOR = {Alim, Murad and Cecotti, Sergio and C\'{o}rdova, Clay and
              Espahbodi, Sam and Rastogi, Ashwin and Vafa, Cumrun},
     TITLE = {{$\mathcal{N}=2$} quantum field theories and their {BPS} quivers},
   JOURNAL = {Adv. Theor. Math. Phys.},
  FJOURNAL = {Advances in Theoretical and Mathematical Physics},
    VOLUME = {18},
      YEAR = {2014},
    NUMBER = {1},
     PAGES = {27--127},
       URL = {https://doi.org/10.4310/ATMP.2014.v18.n1.a2},
    EPRINT = {1112.3984},
}

@article {Cecotti:2014zga,
    AUTHOR = {Cecotti, Sergio and Del Zotto, Michele},
     TITLE = {{$Y$}-systems, {$Q$}-systems, and 4{D} {$\mathcal{N}=2$}
              supersymmetric {QFT}},
   JOURNAL = {J.~Phys.~A: Math. Theor.},
  FJOURNAL = {Journal of Physics. A. Mathematical and Theoretical},
    VOLUME = {47},
      YEAR = {2014},
    NUMBER = {47},
     PAGES = {474001, 40~pages},
       URL = {https://doi.org/10.1088/1751-8113/47/47/474001},
    EPRINT = {1403.7613},
}

@article {ELZ02,
    AUTHOR = {Edelsbrunner, Herbert and Letscher, David and Zomorodian,
              Afra},
     TITLE = {Topological persistence and simplification},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {28},
      YEAR = {2002},
    NUMBER = {4},
     PAGES = {511--533},
       URL = {https://doi.org/10.1007/s00454-002-2885-2},
}

@article {ZC05,
    AUTHOR = {Zomorodian, Afra and Carlsson, Gunnar},
     TITLE = {Computing persistent homology},
   JOURNAL = {Discrete Comput. Geom.},
  FJOURNAL = {Discrete \& Computational Geometry. An International Journal
              of Mathematics and Computer Science},
    VOLUME = {33},
      YEAR = {2005},
    NUMBER = {2},
     PAGES = {249--274},
       URL = {https://doi.org/10.1007/s00454-004-1146-y},
}

@article {C09,
    AUTHOR = {Carlsson, Gunnar},
     TITLE = {Topology and data},
   JOURNAL = {Bull. Amer. Math. Soc. (N.S.)},
  FJOURNAL = {American Mathematical Society. Bulletin. New Series},
    VOLUME = {46},
      YEAR = {2009},
    NUMBER = {2},
     PAGES = {255--308},
       URL = {https://doi.org/10.1090/S0273-0979-09-01249-X},
}

@incollection {EH08,
    AUTHOR = {Edelsbrunner, Herbert and Harer, John},
     TITLE = {Persistent homology~-- a~survey},
 BOOKTITLE = {Surveys on Discrete and Computational Geometry},
    SERIES = {Contemp. Math.},
    VOLUME = {453},
     PAGES = {257--282},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2008},
       URL = {https://doi.org/10.1090/conm/453/08802},
}

@mics {G14,
    AUTHOR = {Ghrist, R.},
     TITLE = {Elementary applied topology},
      NOTE = {ed.~1.0, Createspace, 2014},
}

@article {CIdSZ08,
    AUTHOR = {Carlsson, Gunnar and Ishkhanov, Tigran and de Silva, Vin and
              Zomorodian, Afra},
     TITLE = {On the local behavior of spaces of natural images},
   JOURNAL = {Int.~J. Comput. Vis.},
  FJOURNAL = {International Journal of Computer Vision},
    VOLUME = {76},
      YEAR = {2008},
    NUMBER = {1},
     PAGES = {1--12},
       URL = {https://doi.org/10.1007/s11263-007-0056-x},
}

@article {CCR13,
    AUTHOR = {Chan, Joseph Minhow and Carlsson, Gunnar and Rabadan, Raul},
     TITLE = {Topology of viral evolution},
   JOURNAL = {Proc. Natl. Acad. Sci. USA},
  FJOURNAL = {Proceedings of the National Academy of Sciences of the United
              States of America},
    VOLUME = {110},
      YEAR = {2013},
    NUMBER = {46},
     PAGES = {18566--18571},
       URL = {https://doi.org/10.1073/pnas.1313480110},
}

@inproceedings {jholes,
    AUTHOR = {Binchi, Jacopo and Merelli, Emanuela and Rucco, Matteo and
              Petri, Giovanni and Vaccarino, Francesco},
     TITLE = {j{H}oles: a tool for understanding biological complex networks
              via clique weight rank persistent homology},
 BOOKTITLE = {Proceedings of the 5th {I}nternational {W}orkshop on
              {I}nteractions between {C}omputer {S}cience and {B}iology
              ({CS}2{B}io'14)},
    SERIES = {Electron. Notes Theor. Comput. Sci.},
    VOLUME = {306},
     PAGES = {5--18},
 PUBLISHER = {Elsevier Sci.~B.V., Amsterdam},
      YEAR = {2014},
       URL = {https://doi.org/10.1016/j.entcs.2014.06.011},
}

@article {NLC11,
    AUTHOR = {Nicolau, Monica and Levine, Arnold J. and Carlsson, Gunnar},
     TITLE = {Topology based data analysis identifies a subgroup of breast cancers with a unique
 mutational profile and excellent survival},
   JOURNAL = {Proc. Natl. Acad. Sci. USA},
  FJOURNAL = {Proceedings of the National Academy of Sciences of the United
              States of America},
    VOLUME = {108},
      YEAR = {2011},
    NUMBER = {17},
     PAGES = {7265--7270},
       URL = {https://doi.org/10.1073/pnas.1102826108},
}

@article {MA15,
    AUTHOR = {Port, Alexander and Gheorghita, Iulia and Guth, Daniel and
              Clark, John M. and Liang, Crystal and Dasu, Shival and
              Marcolli, Matilde},
     TITLE = {Persistent topology of syntax},
   JOURNAL = {Math. Comput. Sci.},
  FJOURNAL = {Mathematics in Computer Science},
    VOLUME = {12},
      YEAR = {2018},
    NUMBER = {1},
     PAGES = {33--50},
       URL = {https://doi.org/10.1007/s11786-017-0329-x},
    EPRINT = {1507.05134},
}

@article {TDAvacua,
    AUTHOR = {Cirafici, Michele},
     TITLE = {Persistent homology and string vacua},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics},
    VOLUME = {2016},
      YEAR = {2016},
    NUMBER = {3},
     PAGES = {no.~3, 045, 34~pages},
       URL = {https://doi.org/10.1007/JHEP03(2016)045},
    EPRINT = {1512.01170},
}

@mics {programs,
    AUTHOR = {Cirafici, Michele},
     TITLE = {\textsc{matlab} programs and the accompanying datasets},
      NOTE = {available at \url{https://cirafici.dmg.units.it/BPSbarcodesFiles/}},
}

@incollection {javaplex,
    AUTHOR = {Tausz, A. and Vejdemo-Johansson, M. and Adams, H.},
     TITLE = {{JavaPlex}: a research software package for persistent (co)homology},
 BOOKTITLE = {Mathematical Software~-- ICMS~2014},
    EDITOR = {Hong, Han and Yap, Chee},
    SERIES = {Lecture Notes in Computer Sci.},
    VOLUME = {8592},
     PAGES = {129--136},
 PUBLISHER = {Springer, Berlin~-- Heidelberg},
      YEAR = {2008},
       URL = {https://doi.org/10.1007/978-3-662-44199-2_23},
      NOTE = {software available at \url{http://appliedtopology.github.io/javaplex/}},
}

@article {Joyce:2008pc,
    AUTHOR = {Joyce, Dominic and Song, Yinan},
     TITLE = {A theory of generalized {D}onaldson--{T}homas invariants},
   JOURNAL = {Mem. Amer. Math. Soc.},
  FJOURNAL = {Memoirs of the American Mathematical Society},
    VOLUME = {217},
      YEAR = {2012},
    NUMBER = {1020},
     PAGES = {iv+199~pages},
       URL = {https://doi.org/10.1090/S0065-9266-2011-00630-1},
    EPRINT = {0810.5645},
}

@article {Manschot:2010qz,
    AUTHOR = {Manschot, Jan and Pioline, Boris and Sen, Ashoke},
     TITLE = {Wall crossing from {B}oltzmann black hole halos},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics},
    VOLUME = {2011},
      YEAR = {2011},
    NUMBER = {7},
     PAGES = {no.~7, 059, 73~pages},
       URL = {https://doi.org/10.1007/JHEP07(2011)059},
    EPRINT = {1011.1258},
}

@mics {MooreFelix,
    AUTHOR = {Moore, Gregory W.},
     TITLE = {Lecture notes for Felix Klein lectures},
      NOTE = {available at \url{http://www.physics.rutgers.edu/~gmoore/FelixKleinLectureNotes.pdf}},
}

@incollection {Kontsevich:2013rda,
    AUTHOR = {Kontsevich, Maxim and Soibelman, Yan},
     TITLE = {Wall-crossing structures in {D}onaldson--{T}homas invariants,
              integrable systems and mirror symmetry},
 BOOKTITLE = {Homological Mirror Symmetry and Tropical Geometry},
    SERIES = {Lect. Notes Unione Mat. Ital.},
    VOLUME = {15},
     PAGES = {197--308},
 PUBLISHER = {Springer, Cham},
      YEAR = {2014},
       URL = {https://doi.org/10.1007/978-3-319-06514-4_6},
    EPRINT = {1303.3253},
}

@article {Galakhov:2013oja,
    AUTHOR = {Galakhov, Dmitry and Longhi, Pietro and Mainiero, Tom and Moore, Gregory W. and Neitzke, Andrew},
     TITLE = {Wild wall crossing and {BPS} giants},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics},
    VOLUME = {2013},
      YEAR = {2013},
    NUMBER = {11},
     PAGES = {no.~11, 046, 101~pages},
       URL = {https://doi.org/10.1007/JHEP11(2013)046},
    EPRINT = {1305.5454},
}

@mics {Jafferis:2008uf,
    AUTHOR = {Jafferis, Daniel L. and Moore, Gregory W.},
     TITLE = {Wall crossing in local {C}alabi {Y}au manifolds},
    EPRINT = {0810.4909},
}

@article {Andriyash:2010yf,
    AUTHOR = {Andriyash, Evgeny and Denef, Frederik and Jafferis, Daniel L. and Moore Gregory W.},
     TITLE = {Bound state transformation walls},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics},
    VOLUME = {2012},
      YEAR = {2012},
    NUMBER = {3},
     PAGES = {no.~3, 007, 65~pages},
       URL = {https://doi.org/10.1007/JHEP03(2012)007},
    EPRINT = {1008.3555},
}

@article {szendroi,
    AUTHOR = {Szendr\H{o}i, Bal\'{a}zs},
     TITLE = {Non-commutative {D}onaldson--{T}homas invariants and the
              conifold},
   JOURNAL = {Geom. Topol.},
  FJOURNAL = {Geometry \& Topology},
    VOLUME = {12},
      YEAR = {2008},
    NUMBER = {2},
     PAGES = {1171--1202},
       URL = {https://doi.org/10.2140/gt.2008.12.1171},
    EPRINT = {0705.3419},
}

@article {nakanagao,
    AUTHOR = {Nagao, Kentaro and Nakajima, Hiraku},
     TITLE = {Counting invariant of perverse coherent sheaves and its
              wall-crossing},
   JOURNAL = {Int. Math. Res. Not.},
  FJOURNAL = {International Mathematics Research Notices. IMRN},
    VOLUME = {2011},
      YEAR = {2011},
    NUMBER = {17},
     PAGES = {3885--3938},
       URL = {https://doi.org/10.1093/imrn/rnq195},
    EPRINT = {0809.2992},
}

@article {Denef:2007vg,
    AUTHOR = {Denef, Frederik and Moore, Gregory W.},
     TITLE = {Split states, entropy enigmas, holes and halos},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics},
    VOLUME = {2011},
      YEAR = {2011},
    NUMBER = {11},
     PAGES = {no.~11, 129, 153~pages},
       URL = {https://doi.org/10.1007/JHEP11(2011)129},
    EPRINT = {hep-th/0702146},
}

@article {Iqbal:2003ds,
    AUTHOR = {Iqbal, Amer and Vafa, Cumrun and Nekrasov, Nikita and
              Okounkov, Andrei},
     TITLE = {Quantum foam and topological strings},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics. A SISSA Journal},
    VOLUME = {2008},
      YEAR = {2008},
    NUMBER = {4},
     PAGES = {no.~4, 011, 47~pages},
       URL = {https://doi.org/10.1088/1126-6708/2008/04/011},
    EPRINT = {hep-th/0312022},
}

@article {Cirafici:2008sn,
    AUTHOR = {Cirafici, Michele and Sinkovics, Annamaria and Szabo, Richard
              J.},
     TITLE = {Cohomological gauge theory, quiver matrix models and
              {D}onaldson--{T}homas theory},
   JOURNAL = {Nuclear Phys.~B},
  FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and
              Experimental High Energy Physics. Quantum Field Theory and
              Statistical Systems},
    VOLUME = {809},
      YEAR = {2009},
    NUMBER = {3},
     PAGES = {452--518},
       URL = {https://doi.org/10.1016/j.nuclphysb.2008.09.024},
    EPRINT = {0803.4188},
}

@article {Cirafici:2010bd,
    AUTHOR = {Cirafici, Michele and Sinkovics, Annamaria and Szabo, Richard
              J.},
     TITLE = {Instantons, quivers and noncommutative {D}onaldson--{T}homas
              theory},
   JOURNAL = {Nuclear Phys.~B},
  FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and
              Experimental High Energy Physics. Quantum Field Theory and
              Statistical Systems},
    VOLUME = {853},
      YEAR = {2011},
    NUMBER = {2},
     PAGES = {508--605},
       URL = {https://doi.org/10.1016/j.nuclphysb.2011.08.002},
    EPRINT = {1012.2725},
}

@article {Cirafici:2012qc,
    AUTHOR = {Cirafici, Michele and Szabo, Richard J.},
     TITLE = {Curve counting, instantons and {M}c{K}ay correspondences},
   JOURNAL = {J.~Geom. Phys.},
  FJOURNAL = {Journal of Geometry and Physics},
    VOLUME = {72},
      YEAR = {2013},
     PAGES = {54--109},
       URL = {https://doi.org/10.1016/j.geomphys.2013.03.020},
    EPRINT = {1209.1486},
}

@article {framedquivers,
    AUTHOR = {Cirafici, Michele},
     TITLE = {On framed quivers, {BPS} invariants and defects},
   JOURNAL = {Confluentes Math.},
  FJOURNAL = {Confluentes Mathematici},
    VOLUME = {9},
      YEAR = {2017},
    NUMBER = {2},
     PAGES = {71--99},
       URL = {https://doi.org/10.5802/cml.42},
    EPRINT = {1801.03778},
}

@mics {Gopakumar:1998ii,
    AUTHOR = {Gopakumar, Rajesh and Vafa, Cumrun},
     TITLE = {M-theory and topological strings.~{I}},
    EPRINT = {hep-th/9809187},
}

@mics {Gopakumar:1998jq,
    AUTHOR = {Gopakumar, Rajesh and Vafa, Cumrun},
     TITLE = {M-theory and topological strings.~{II}},
    EPRINT = {hep-th/9812127},
}

@incollection {Huang:2006hq,
    AUTHOR = {Huang, M.-X. and Klemm, A. and Quackenbush, S.},
     TITLE = {Topological string theory on compact {C}alabi--{Y}au:
              modularity and boundary conditions},
 BOOKTITLE = {Homological Mirror Symmetry},
    SERIES = {Lecture Notes in Phys.},
    VOLUME = {757},
     PAGES = {45--102},
 PUBLISHER = {Springer, Berlin},
      YEAR = {2009},
       URL = {https://doi.org/10.1007/978-3-540-68030-7_3},
    EPRINT = {hep-th/0612125},
}

@article {Huang:2007sb,
    AUTHOR = {Huang, Min-Xin and Klemm, Albrecht and Mari\~{n}o, Marcos and
              Tavanfar, Alireza},
     TITLE = {Black holes and large order quantum geometry},
   JOURNAL = {Phys. Rev.~D},
  FJOURNAL = {Physical Review D. Particles, Fields, Gravitation, and
              Cosmology},
    VOLUME = {79},
      YEAR = {2009},
    NUMBER = {6},
     PAGES = {066001, 22~pages},
       URL = {https://doi.org/10.1103/PhysRevD.79.066001},
    EPRINT = {0704.2440},
}

@article {LopesCardoso:1998wt,
    AUTHOR = {Lopes Cardoso, Gabriel and de Wit, Bernard and Mohaupt,
              Thomas},
     TITLE = {Corrections to macroscopic supersymmetric black-hole entropy},
   JOURNAL = {Phys. Lett.~B},
  FJOURNAL = {Physics Letters. B. Particle Physics, Nuclear Physics and
              Cosmology},
    VOLUME = {451},
      YEAR = {1999},
    NUMBER = {3-4},
     PAGES = {309--316},
       URL = {https://doi.org/10.1016/S0370-2693(99)00227-0},
    EPRINT = {hep-th/9812082},
}

@article {Ooguri:2004zv,
    AUTHOR = {Ooguri, Hirosi and Strominger, Andrew and Vafa, Cumrun},
     TITLE = {Black hole attractors and the topological string},
   JOURNAL = {Phys. Rev.~D},
  FJOURNAL = {Physical Review. D. Third Series},
    VOLUME = {70},
      YEAR = {2004},
    NUMBER = {10},
     PAGES = {106007, 13~pages},
       URL = {https://doi.org/10.1103/PhysRevD.70.106007},
    EPRINT = {hep-th/0405146},
}

@article {LopesCardoso:2006bg,
    AUTHOR = {Lopes Cardoso, Gabriel and de Wit, Bernard and K\"{a}ppeli, J\"{u}rg
              and Mohaupt, Thomas},
     TITLE = {Black hole partition functions and duality},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics. A SISSA Journal},
    VOLUME = {2006},
      YEAR = {2006},
    NUMBER = {3},
     PAGES = {no.~3, 074, 37~pages},
       URL = {https://doi.org/10.1088/1126-6708/2006/03/074},
    EPRINT = {hep-th/0601108},
}

@article {Cardoso:2014kwa,
    AUTHOR = {Lopes Cardoso, Gabriel and de Wit, B. and Mahapatra, S.},
     TITLE = {Deformations of special geometry: in search of the topological
              string},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics},
    VOLUME = {2014},
      YEAR = {2014},
    NUMBER = {9},
     PAGES = {096, 46~pages},
       URL = {https://doi.org/10.1007/JHEP09(2014)096},
    EPRINT = {1406.5478},
}

@article {Dijkgraaf:1996it,
    AUTHOR = {Dijkgraaf, Robbert and Verlinde, Erik and Verlinde, Herman},
     TITLE = {Counting dyons in {$N=4$} string theory},
   JOURNAL = {Nuclear Phys.~B},
  FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and
              Experimental High Energy Physics. Quantum Field Theory and
              Statistical Systems},
    VOLUME = {484},
      YEAR = {1997},
    NUMBER = {3},
     PAGES = {543--561},
       URL = {https://doi.org/10.1016/S0550-3213(96)00640-2},
    EPRINT = {hep-th/9607026},
}

@article {LopesCardoso:2004xf,
    AUTHOR = {Lopes Cardoso, Gabriel and de Wit, Bernard and K\"{a}ppeli, J\"{u}rg
              and Mohaupt, Thomas},
     TITLE = {Asymptotic degeneracy of dyonic {$N=4$} string states and
              black hole entropy},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics. A SISSA Journal},
    VOLUME = {2004},
      YEAR = {2004},
    NUMBER = {12},
     PAGES = {no.~12, 075, 16~pages},
       URL = {https://doi.org/10.1088/1126-6708/2004/12/075},
    EPRINT = {hep-th/0412287},
}

@article {Shih:2005he,
    AUTHOR = {Shih, David and Yin, Xi},
     TITLE = {Exact black hole degeneracies and the topological string},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics. A SISSA Journal},
    VOLUME = {2006},
      YEAR = {2006},
    NUMBER = {4},
     PAGES = {no.~4, 034, 19~pages},
       URL = {https://doi.org/10.1088/1126-6708/2006/04/034},
    EPRINT = {hep-th/0508174},
}

@article {Dabholkar:2005dt,
    AUTHOR = {Dabholkar, Atish and Denef, Frederik and Moore, Gregory W. and
              Pioline, Boris},
     TITLE = {Precision counting of small black holes},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics. A SISSA Journal},
    VOLUME = {2005},
      YEAR = {2005},
    NUMBER = {10},
     PAGES = {no.~10, 096, 90~pages},
       URL = {https://doi.org/10.1088/1126-6708/2005/10/096},
    EPRINT = {hep-th/0507014},
}

@mics {Dabholkar:2012nd,
    AUTHOR = {Dabholkar, Atish and Murthy, Sameer and Zagier, Don},
     TITLE = {Quantum black holes, wall crossing, and mock modular forms},
    EPRINT = {1208.4074},
}

@article {Cardoso:2014hma,
    AUTHOR = {Lopes Cardoso, Gabriel and Cirafici, Michele and Nampuri,
              Suresh},
     TITLE = {Indefinite theta functions for counting attractor backgrounds},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics},
    VOLUME = {2014},
      YEAR = {2014},
    NUMBER = {10},
     PAGES = {no.~10, 017, 25~pages},
       URL = {https://doi.org/10.1007/JHEP10(2014)017},
    EPRINT = {1407.0197},
}

@article {Cardoso:2013ysa,
    AUTHOR = {Lopes Cardoso, Gabriel and Cirafici, Michele and Jorge,
              Rog\'{e}rio and Nampuri, Suresh},
     TITLE = {Indefinite theta functions and black hole partition functions},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics},
    VOLUME = {2014},
      YEAR = {2014},
    NUMBER = {2},
     PAGES = {no.~2, 019, 36~pages},
       URL = {https://doi.org/10.1007/JHEP02(2014)019},
    EPRINT = {1309.4428},
}

@article {Denef:2004ze,
    AUTHOR = {Denef, Frederik and Douglas, Michael R.},
     TITLE = {Distributions of flux vacua},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics. A SISSA Journal},
    VOLUME = {2004},
      YEAR = {2004},
    NUMBER = {5},
     PAGES = {no.~5, 072, 46~pages},
       URL = {https://doi.org/10.1088/1126-6708/2004/05/072},
    EPRINT = {hep-th/0404116},
}

@article {Eguchi:2010ej,
    AUTHOR = {Eguchi, Tohru and Ooguri, Hirosi and Tachikawa, Yuji},
     TITLE = {Notes on the {$K3$} surface and the {M}athieu group
              {$M_{24}$}},
   JOURNAL = {Exp. Math.},
  FJOURNAL = {Experimental Mathematics},
    VOLUME = {20},
      YEAR = {2011},
    NUMBER = {1},
     PAGES = {91--96},
       URL = {https://doi.org/10.1080/10586458.2011.544585},
    EPRINT = {1004.0956},
}

@article {Duncan:2014vfa,
    AUTHOR = {Duncan, John F. R. and Griffin, Michael J. and Ono, Ken},
     TITLE = {Moonshine},
   JOURNAL = {Res. Math. Sci.},
  FJOURNAL = {Research in the Mathematical Sciences},
    VOLUME = {2},
      YEAR = {2015},
     PAGES = {Art.~11, 57~pages},
       URL = {https://doi.org/10.1186/s40687-015-0029-6},
    EPRINT = {1411.6571},
}

@incollection {Cheng:2012uy,
    AUTHOR = {Cheng, Miranda C. N. and Duncan, John F. R.},
     TITLE = {The largest {M}athieu group and (mock) automorphic forms},
 BOOKTITLE = {String-{M}ath 2011},
    SERIES = {Proc. Sympos. Pure Math.},
    VOLUME = {85},
     PAGES = {53--82},
 PUBLISHER = {Amer. Math. Soc., Providence, RI},
      YEAR = {2012},
       URL = {https://doi.org/10.1090/pspum/085/1374},
    EPRINT = {1201.4140},
}

@incollection {Gaberdiel:2012um,
    AUTHOR = {Gaberdiel, Matthias R. and Volpato, Roberto},
     TITLE = {Mathieu moonshine and orbifold {K}3s},
 BOOKTITLE = {Conformal Field Theory, Automorphic Forms and Related Topics},
    SERIES = {Contrib. Math. Comput. Sci.},
    VOLUME = {8},
     PAGES = {109--141},
 PUBLISHER = {Springer, Heidelberg},
      YEAR = {2014},
       URL = {https://doi.org/10.1007/978-3-662-43831-2_5},
    EPRINT = {1206.5143},
}

@article {Cheng:2010pq,
    AUTHOR = {Cheng, Miranda C. N.},
     TITLE = {{$K3$} surfaces, {${\mathcal N}=4$} dyons and the {M}athieu group
              {$M_{24}$}},
   JOURNAL = {Commun. Number Theory Phys.},
  FJOURNAL = {Communications in Number Theory and Physics},
    VOLUME = {4},
      YEAR = {2010},
    NUMBER = {4},
     PAGES = {623--657},
       URL = {https://doi.org/10.4310/CNTP.2010.v4.n4.a2},
    EPRINT = {1005.5415},
}

@article {Gaberdiel:2010ch,
    AUTHOR = {Gaberdiel, Matthias R. and Hohenegger, Stefan and Volpato,
              Roberto},
     TITLE = {Mathieu twining characters for {$K3$}},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics},
    VOLUME = {2010},
      YEAR = {2010},
    NUMBER = {9},
     PAGES = {no.~9, 058, 20~pages},
       URL = {https://doi.org/10.1007/JHEP09(2010)058},
    EPRINT = {1006.0221},
}

@article {Gaberdiel:2010ca,
    AUTHOR = {Gaberdiel, Matthias R. and Hohenegger, Stefan and Volpato,
              Roberto},
     TITLE = {Mathieu {M}oonshine in the elliptic genus of {$K3$}},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics},
    VOLUME = {2010},
      YEAR = {2010},
    NUMBER = {10},
     PAGES = {no.~10, 062, 24~pages},
       URL = {https://doi.org/10.1007/JHEP10(2010)062},
    EPRINT = {1008.3778},
}

@article {Eguchi:2010fg,
    AUTHOR = {Eguchi, Tohru and Hikami, Kazuhiro},
     TITLE = {Note on twisted elliptic genus of {$K3$} surface},
   JOURNAL = {Phys. Lett.~B},
  FJOURNAL = {Physics Letters. B. Particle Physics, Nuclear Physics and
              Cosmology},
    VOLUME = {694},
      YEAR = {2011},
    NUMBER = {4-5},
     PAGES = {446--455},
       URL = {https://doi.org/10.1016/j.physletb.2010.10.017},
    EPRINT = {1008.4924},
}

@mics {Moore:1998pn,
    AUTHOR = {Moore, Gregory W.},
     TITLE = {Arithmetic and attractors},
    EPRINT = {hep-th/9807087},
}

@article {Cirafici:2013tna,
    AUTHOR = {Cirafici, Michele},
     TITLE = {Defects in cohomological gauge theory and {D}onaldson--{T}homas
              invariants},
   JOURNAL = {Adv. Theor. Math. Phys.},
  FJOURNAL = {Advances in Theoretical and Mathematical Physics},
    VOLUME = {20},
      YEAR = {2016},
    NUMBER = {5},
     PAGES = {945--1006},
       URL = {https://doi.org/10.4310/ATMP.2016.v20.n5.a1},
    EPRINT = {1302.7297},
}

@article {Cirafici:2013bha,
    AUTHOR = {Cirafici, Michele},
     TITLE = {Quivers, line defects and framed {BPS} invariants},
   JOURNAL = {Ann. Henri Poincar\'{e}},
  FJOURNAL = {Annales Henri Poincar\'{e}. A Journal of Theoretical and
              Mathematical Physics},
    VOLUME = {19},
      YEAR = {2018},
    NUMBER = {1},
     PAGES = {1--70},
       URL = {https://doi.org/10.1007/s00023-017-0611-0},
    EPRINT = {1307.7134},
}

@article {Gaiotto:2010be,
    AUTHOR = {Gaiotto, Davide and Moore, Gregory W. and Neitzke, Andrew},
     TITLE = {Framed {BPS} states},
   JOURNAL = {Adv. Theor. Math. Phys.},
  FJOURNAL = {Advances in Theoretical and Mathematical Physics},
    VOLUME = {17},
      YEAR = {2013},
    NUMBER = {2},
     PAGES = {241--397},
       URL = {https://doi.org/10.4310/ATMP.2013.v17.n2.a1},
    EPRINT = {1006.0146},
}

@article {Witten:1982im,
    AUTHOR = {Witten, Edward},
     TITLE = {Supersymmetry and {M}orse theory},
   JOURNAL = {J.~Differential Geom.},
  FJOURNAL = {Journal of Differential Geometry},
    VOLUME = {17},
      YEAR = {1982},
    NUMBER = {4},
     PAGES = {661--692},
       URL = {https://doi.org/10.4310/jdg/1214437492},
}
