Thesis.bib

@misc{Yoo17,
  author        = {Philsang Yoo},
  title         = {Course Notes: ``Geometric Langlands and Derived Algebraic Geometry''},
  year          = {Fall 2017},
  publisher={Yale University}
}

@misc{Yoo18,
  author        = {Philsang Yoo},
  title         = {Course Notes: ``Seminar on the Langlands Program''},
  year          = {Spring 2018},
  publisher={Yale University}
}


@article{langlands1967,
  title={Letter to Andr{\'e} Weil},
  author={Langlands, Robert P},
  journal={unpublished, January},
  year={1967}
}

@article{arthur1989,
  title={Harmonic Analysis of Tempered Distributions on Semisimple Lie Groups},
  author={Arthur, James G},
  journal={Representation theory and harmonic analysis on semisimple Lie groups},
  number={31},
  pages={13},
  year={1989},
  publisher={American Mathematical Soc.}
}

@book{meinrenken2013,
  title={Clifford algebras and Lie theory},
  author={Meinrenken, Eckhard},
  volume={58},
  year={2013},
  publisher={Springer}
}

@incollection{deligne1982,
  title={Tannakian categories},
  author={Deligne, Pierre and Milne, James S},
  booktitle={Hodge cycles, motives, and Shimura varieties},
  pages={101--228},
  year={1982},
  publisher={Springer}
}

@article{satake1963,
  title={Theory of spherical functions on reductive algebraic groups over p-adic fields},
  author={Satake, Ichir{\^o}},
  journal={Publications Math{\'e}matiques de l'Institut des Hautes {\'E}tudes Scientifiques},
  volume={18},
  number={1},
  pages={5--9},
  year={1963},
  publisher={Springer}
}

@book{hartshorne1977,
  title={Algebraic geometry},
  author={Hartshorne, Robin},
  volume={52},
  year={1977},
  publisher={Springer Science \& Business Media}
}

@misc{stackoverflow1,
    title = {Why does the group act on the right on the principal bundle?},
    author = {Qfwfq (https://mathoverflow.net/users/4721/qfwfq)},
    howpublished = {MathOverflow},
    note = {URL: https://mathoverflow.net/q/50587 (version: 2010-12-30)},
    eprint = {https://mathoverflow.net/q/50587},
    url = {https://mathoverflow.net/q/50587}
}

@misc{beilinson1991,
  title={Quantization of Hitchin’s integrable system and Hecke eigensheaves},
  author={Beilinson, Alexander and Drinfeld, Vladimir},
  year={1991}
}

@article{lafforgue2009,
  title={Quelques calculs reli{\'e}sa la correspondance de Langlands g{\'e}om{\'e}trique pour P1 (version provisoire)},
  author={Lafforgue, Vincent},
  journal={Available at author’s website: http://www. math. jussieu. fr/\~{} vlafforg},
  year={2009}
}

@article{arinkin2015,
  title={Singular support of coherent sheaves and the geometric Langlands conjecture},
  author={Arinkin, Dima and Gaitsgory, Dennis},
  journal={Selecta Mathematica},
  volume={21},
  number={1},
  pages={1--199},
  year={2015},
  publisher={Springer}
}

@article{carqueville2017,
  title={Introductory lectures on topological quantum field theory},
  author={Carqueville, Nils and Runkel, Ingo},
  journal={arXiv preprint arXiv:1705.05734},
  year={2017}
}

@incollection{kudla2004,
  title={From modular forms to automorphic representations},
  author={Kudla, Stephen S},
  booktitle={An Introduction to the Langlands Program},
  pages={133--151},
  year={2004},
  publisher={Springer}
}

@techreport{quevedo2010,
  title={Cambridge lectures on supersymmetry and extra dimensions},
  author={Quevedo, Fernando and Krippendorf, Sven and Schlotterer, Oliver},
  year={2010}
}

@misc{osserman2008,
  title={The Weil conjectures},
  author={Osserman, Brian},
  journal={Princeton companion to mathematics},
  pages={729--732},
  year={2008},
  publisher={Princeton University Press}
}

@book{jacquet2006,
  title={Automorphic forms on GL (2)},
  author={Jacquet, Herv{\'e} and Langlands, Robert P},
  volume={114},
  year={2006},
  publisher={Springer}
}

@article{matthew2012,
  title={Notes on the Kodaira vanishing theorem},
  author={Mathew, Akhil},
  year={2012}
}

@article{miyake1971,
  title={On automorphic forms on GL2 and Hecke operators},
  author={Miyake, Toshitsune},
  journal={Annals of Mathematics},
  pages={174--189},
  year={1971},
  publisher={JSTOR}
}

@book{kobayashi1963,
  title={Foundations of differential geometry},
  author={Kobayashi, Shoshichi and Nomizu, Katsumi},
  volume={1},
  number={2},
  year={1963},
  publisher={Interscience publishers New York}
}

@book{bott1982,
  title={Differential forms in algebraic topology},
  author={Bott, Raoul and Tu, Loring W},
  volume={82},
  year={1982},
  publisher={Springer Science \& Business Media}
}

@article{breuil2001,
  title={On the modularity of elliptic curves over Q: wild 3-adic exercises},
  author={Breuil, Christophe and Conrad, Brian and Diamond, Fred and Taylor, Richard},
  journal={Journal of the American Mathematical Society},
  volume={14},
  number={4},
  pages={843--940},
  year={2001},
  publisher={Providence, RI, USA: The Society, c1988-}
}


@MISC {66515,
    TITLE = {Why is Class Field Theory the same as Langlands for GL1?},
    AUTHOR = {Keerthi Madapusi Pera (https://mathoverflow.net/users/7868/keerthi-madapusi-pera)},
    HOWPUBLISHED = {MathOverflow},
    NOTE = {URL: https://mathoverflow.net/q/66515 (version: 2011-05-31)},
    EPRINT = {https://mathoverflow.net/q/66515},
    URL = {https://mathoverflow.net/q/66515}
}

@article{hooft1978,
  title={On the phase transition towards permanent quark confinement},
  author={Hooft, Gerard’t},
  journal={Nuclear Physics: B},
  volume={138},
  number={1},
  pages={1--25},
  year={1978},
  publisher={Elsevier}
}

@article{montonen1977,
title = "Magnetic monopoles as gauge particles?",
journal = "Physics Letters B",
volume = "72",
number = "1",
pages = "117 - 120",
year = "1977",
issn = "0370-2693",
doi = "https://doi.org/10.1016/0370-2693(77)90076-4",
url = "http://www.sciencedirect.com/science/article/pii/0370269377900764",
author = "C. Montonen and D. Olive"
}

@article{goddard1977,
title = "Gauge theories and magnetic charge",
journal = "Nuclear Physics B",
volume = "125",
number = "1",
pages = "1 - 28",
year = "1977",
issn = "0550-3213",
doi = "https://doi.org/10.1016/0550-3213(77)90221-8",
url = "http://www.sciencedirect.com/science/article/pii/0550321377902218",
author = "P. Goddard and J. Nuyts and D. Olive"
}

@article{zhu2016,
  title={An introduction to affine Grassmannians and the geometric Satake equivalence},
  author={Zhu, Xinwen},
  journal={arXiv preprint arXiv:1603.05593},
  year={2016}
}

@article{laumon1996,
  title={Transformation de Fourier g{\'e}n{\'e}ralis{\'e}e},
  author={Laumon, Gerard},
  journal={arXiv preprint alg-geom/9603004},
  year={1996}
}

@book{bachman1964,
  title={Introduction to p-adic numbers and valuation theory},
  author={Bachman, George},
  year={1964},
  publisher={Academic Press. Inc}
}

@book{milnor1974,
  title={Characteristic Classes.(AM-76)},
  author={Milnor, John and Stasheff, James D},
  volume={76},
  year={1974},
  publisher={Princeton university press}
}

@book{baez1994gauge,
  title={Gauge fields, knots and gravity},
  author={Baez, John and Muniain, Javier P},
  volume={4},
  year={1994},
  publisher={World Scientific Publishing Company}
}

@misc{nlab:function_field_analogy,
  author = {{nLab authors}},
  title = {function field analogy},
  howpublished = {\url{http://ncatlab.org/nlab/show/function%20field%20analogy}},
  note = {\href{http://ncatlab.org/nlab/revision/function%20field%20analogy/23}{Revision 23}},
  month = apr,
  year = 2018
}

@book{hatcher,
  title={Algebraic topology},
  author={Hatcher, Allen},
  year={2002},
  publisher={清华大学出版社有限公司}
}

@incollection{langlands1970,
  title={Problems in the theory of automorphic forms to Salomon Bochner in gratitude},
  author={Langlands, Robert P},
  booktitle={Lectures in modern analysis and applications III},
  pages={18--61},
  year={1970},
  publisher={Springer}
}

@article{kapustin2006,
  title={Electric-magnetic duality and the geometric Langlands program},
  author={Kapustin, Anton and Witten, Edward},
  journal={arXiv preprint hep-th/0604151},
  year={2006}
}

@article{witten2010,
  title={Geometric Langlands duality and the equations of Nahm and Bogomolny},
  author={Witten, Edward},
  journal={Proceedings of the Royal Society of Edinburgh Section A: Mathematics},
  volume={140},
  number={4},
  pages={857--895},
  year={2010},
  publisher={Royal Society of Edinburgh Scotland Foundation}
}

@article{donaldson1984,
  title={Instantons and geometric invariant theory},
  author={Donaldson, Simon K},
  journal={Communications in Mathematical Physics},
  volume={93},
  number={4},
  pages={453--460},
  year={1984},
  publisher={Springer}
}


@article{hitchin1987,
	author = "Hitchin, Nigel",
	doi = "10.1215/S0012-7094-87-05408-1",
	fjournal = "Duke Mathematical Journal",
	journal = "Duke Math. J.",
	number = "1",
	pages = "91--114",
	publisher = "Duke University Press",
	title = "Stable bundles and integrable systems",
	url = "https://doi.org/10.1215/S0012-7094-87-05408-1",
	volume = "54",
	year = "1987"
}

@article{ward1985,
  title={Integrable and solvable systems, and relations among them},
  author={Ward, RS},
  journal={Phil. Trans. R. Soc. Lond. A},
  volume={315},
  number={1533},
  pages={451--457},
  year={1985},
  publisher={The Royal Society}
}


@book{atiyahhitchin1988,
 URL = {http://www.jstor.org/stable/j.ctt7zv206},
 abstract = {<p>Systems governed by non-linear differential equations are of fundamental importance in all branches of science, but our understanding of them is still extremely limited. In this book a particular system, describing the interaction of magnetic monopoles, is investigated in detail. The use of new geometrical methods produces a reasonably clear picture of the dynamics for slowly moving monopoles. This picture clarifies the important notion of solitons, which has attracted much attention in recent years. The soliton idea bridges the gap between the concepts of "fields" and "particles," and is here explored in a fully three-dimensional context. While the background and motivation for the work comes from physics, the presentation is mathematical.</p><p>This book is interdisciplinary and addresses concerns of theoretical physicists interested in elementary particles or general relativity and mathematicians working in analysis or geometry. The interaction between geometry and physics through non-linear partial differential equations is now at a very exciting stage, and the book is a contribution to this activity.</p><p>Originally published in 1988.</p><p>ThePrinceton Legacy Libraryuses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.</p>},
 author = {Michael Francis Atiyah and Nigel Hitchin},
 publisher = {Princeton University Press},
 title = {The Geometry and Dynamics of Magnetic Monopoles},
 year = {1988}
}

@article{cherkis2007,
      author         = "Cherkis, Sergey A.",
      title          = "{A Journey Between Two Curves}",
      booktitle      = "{Proceedings, Workshop on the Geometric Aspects of
                        Integrable Systems: Coimbra, Portugal, July 17-19, 2006}",
      journal        = "SIGMA",
      volume         = "3",
      year           = "2007",
      pages          = "043",
      doi            = "10.3842/SIGMA.2007.043",
      eprint         = "hep-th/0703108",
      archivePrefix  = "arXiv",
      primaryClass   = "HEP-TH",
      SLACcitation   = "%%CITATION = HEP-TH/0703108;%%"
}

@INPROCEEDINGS{nakajima1993,
    author = {Hiraku Nakajima},
    title = {Monopoles And {N}ahm's Equations},
    booktitle = {Einstein Metrics And Yang-Mills Connections: Proceedings of the 27th Taniguchi International Symposium, T. Mabuchi and},
    year = {1993}
}

@article{donaldson1984nahm,
  title={Nahm's equations and the classification of monopoles},
  author={Donaldson, Simon K},
  journal={Communications in Mathematical Physics},
  volume={96},
  number={3},
  pages={387--407},
  year={1984},
  publisher={Springer}
}

@article{tong2005tasi,
  title={TASI lectures on solitons},
  author={Tong, David},
  journal={arXiv preprint hep-th/0509216},
  year={2005}
}

@article{hitchin1982,
author = "Hitchin, Nigel",
fjournal = "Communications in Mathematical Physics",
journal = "Comm. Math. Phys.",
number = "4",
pages = "579--602",
publisher = "Springer",
title = "Monopoles and geodesics",
url = "https://projecteuclid.org:443/euclid.cmp/1103920970",
volume = "83",
year = "1982"
}

@article{hitchin1983,
author = "Hitchin, N. J.",
fjournal = "Communications in Mathematical Physics",
journal = "Comm. Math. Phys.",
number = "2",
pages = "145--190",
publisher = "Springer",
title = "On the construction of monopoles",
url = "https://projecteuclid.org:443/euclid.cmp/1103922679",
volume = "89",
year = "1983"
}

@article{atiyah1977,
  title={Instantons and algebraic geometry},
  author={Atiyah, Michael F and Ward, Richard S},
  journal={Communications in Mathematical Physics},
  volume={55},
  number={2},
  pages={117--124},
  year={1977},
  publisher={Springer}
}

@article{bogomolny1976,
  title={The stability of classical solutions},
  author={Bogomolny, EB},
  journal={Yad. Fiz.},
  volume={24},
  pages={861--870},
  year={1976}
}

@article{prasad1975,
  title={Exact classical solution for the't Hooft monopole and the Julia-Zee dyon},
  author={Prasad, MK and Sommerfield, Charles M},
  journal={Physical Review Letters},
  volume={35},
  number={12},
  pages={760},
  year={1975},
  publisher={APS}
}

@article{hurtubise1989,
author = "Hurtubise, Jacques and Murray, Michael K.",
fjournal = "Communications in Mathematical Physics",
journal = "Comm. Math. Phys.",
number = "1",
pages = "35--89",
publisher = "Springer",
title = "On the construction of monopoles for the classical groups",
url = "https://projecteuclid.org:443/euclid.cmp/1104178316",
volume = "122",
year = "1989"
}

@techreport{nahm1982,
  title={The construction of all self-dual multimonopoles by the ADHM method},
  author={Nahm, Werner},
  year={1982},
  institution={International Centre for Theoretical Physics}
}


@article{nirenberg1957,
 ISSN = {0003486X},
 URL = {http://www.jstor.org/stable/1970051},
 author = {A. Newlander and L. Nirenberg},
 journal = {Annals of Mathematics},
 number = {3},
 pages = {391-404},
 publisher = {Annals of Mathematics},
 title = {Complex Analytic Coordinates in Almost Complex Manifolds},
 volume = {65},
 year = {1957}
}

@article{nye2003,
  title={The geometry of calorons},
  author={Nye, Tom MW},
  journal={arXiv preprint hep-th/0311215},
  year={2003}
}

@misc{nlab:extended_topological_quantum_field_theory,
  author = {{nLab authors}},
  title = {extended topological quantum field theory},
  howpublished = {\url{http://ncatlab.org/nlab/show/extended%20topological%20quantum%20field%20theory}},
  note = {\href{http://ncatlab.org/nlab/revision/extended%20topological%20quantum%20field%20theory/36}{Revision 36}},
  month = may,
  year = 2018
}

@incollection{lee2003,
  title={Smooth manifolds},
  author={Lee, John M},
  booktitle={Introduction to Smooth Manifolds},
  pages={1--29},
  year={2003},
  publisher={Springer}
}

@article{lindenhovius2011,
  title={“Instantons and the ADHM Construction},
  author={Lindenhovius, AJ},
  journal={URL: http://dare. uva. nl/cgi/arno/show. cgi},
  year={2011}
}

@book{humphreys2012,
  title={Introduction to Lie algebras and representation theory},
  author={Humphreys, James E},
  volume={9},
  year={2012},
  publisher={Springer Science \& Business Media}
}

@article{atiyah65,
  title={Construction of instantons 1978 Phys},
  author={Atiyah, MF and Hitchin, NJ and Drinfeld, VG and Manin, Yu I},
  journal={Lett. A},
  volume={65},
  pages={185}
}

@article{witten2017,
  title={More on gauge theory and geometric Langlands},
  author={Witten, Edward},
  journal={Advances in Mathematics},
  year={2017},
  publisher={Elsevier}
}

@article{strominger1996,
  title={Mirror symmetry is T-duality},
  author={Strominger, Andrew and Yau, Shing-Tung and Zaslow, Eric},
  journal={Nuclear Physics B},
  volume={479},
  number={1-2},
  pages={243--259},
  year={1996},
  publisher={Elsevier}
}

@inproceedings{donaldson1988,
  title={Geometry of Four-manifolds: Icm 86; International Congress of Mathematicians, Berkeley, California, USA, August 1986},
  author={Donaldson, Simon K},
  year={1988},
  organization={American Math. Soc.}
}

@book{schwartz2014,
  title={Quantum field theory and the standard model},
  author={Schwartz, Matthew D},
  year={2014},
  publisher={Cambridge University Press}
}

@article{elliott2017,
  title={A Physical Origin for Singular Support Conditions in Geometric Langlands},
  author={Elliott, Chris and Yoo, Philsang},
  journal={arXiv preprint arXiv:1707.01292},
  year={2017}
}

@article{simmons2016,
  title={TASI lectures on the conformal bootstrap},
  author={Simmons-Duffin, David},
  journal={arXiv preprint arXiv:1602.07982},
  year={2016}
}

@misc{kapustin2008,
  title={Lectures on Electric-Magnetic Duality and the Geometric Langlands Program},
  author={Kapustin, Anton},
  year={2008}
}

@incollection{frenkel2007,
  title={Lectures on the Langlands program and conformal field theory},
  author={Frenkel, Edward},
  booktitle={Frontiers in number theory, physics, and geometry II},
  pages={387--533},
  year={2007},
  publisher={Springer}
}

@article{shin2005,
  title={Grothendieck Function-Sheaf Correspondence},
  author={Shin, Sug Woo},
  year={2005},
  publisher={Citeseer}
}

@incollection{van2005aspects,
  title={Aspects of BRST quantization},
  author={Van Holten, JW},
  booktitle={Topology and geometry in physics},
  pages={99--166},
  year={2005},
  publisher={Springer}
}



@book{weinberg1995quantum,
  title={The quantum theory of fields},
  author={Weinberg, Steven},
  volume={2},
  year={1995},
  publisher={Cambridge university press}
}

@book{kardar2007,
  title={Statistical physics of fields},
  author={Kardar, Mehran},
  year={2007},
  publisher={Cambridge University Press}
}