RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Uspekhi Mat. Nauk, 2004, Volume 59, Issue 5(359), Pages 101–134 (Mi umn772)  

This article is cited in 7 scientific papers (total in 7 papers)

Lectures on mirror symmetry, derived categories, and $D$-branes

A. N. Kapustina, D. O. Orlovb

a California Institute of Technology
b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: This paper, mainly intended for a mathematical audience, is an introduction to homological mirror symmetry, derived categories, and topological $D$-branes. Mirror symmetry from the point of view of physics is explained, along with the relationship between symmetry and derived categories, and the reason why the Fukaya category must be extended by using co-isotropic $A$-branes. There is also a discussion of how to extend the definition of the Floer homology to these objects and a description of mirror symmetry for flat tori. The paper consists of four lectures given at the Institute of Pure and Applied Mathematics (Los Angeles) in March 2003, as a part of the programme “Symplectic Geometry and Physics”.

DOI: https://doi.org/10.4213/rm772

Full text: PDF file (484 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2004, 59:5, 907–940

Bibliographic databases:

ArXiv: math/0308173
Document Type: Article
UDC: 512.7+514.7
MSC: Primary 14J32, 18E30; Secondary 14F05, 53D12, 57R58, 81T30, 32Q25, 81T45, 57R56
Received: 05.08.2004

Citation: A. N. Kapustin, D. O. Orlov, “Lectures on mirror symmetry, derived categories, and $D$-branes”, Uspekhi Mat. Nauk, 59:5(359) (2004), 101–134; Russian Math. Surveys, 59:5 (2004), 907–940

Citation in format AMSBIB
\Bibitem{KapOrl04}
\by A.~N.~Kapustin, D.~O.~Orlov
\paper Lectures on mirror symmetry, derived categories, and $D$-branes
\jour Uspekhi Mat. Nauk
\yr 2004
\vol 59
\issue 5(359)
\pages 101--134
\mathnet{http://mi.mathnet.ru/umn772}
\crossref{https://doi.org/10.4213/rm772}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2125928}
\zmath{https://zbmath.org/?q=an:1074.14036}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2004RuMaS..59..907K}
\elib{http://elibrary.ru/item.asp?id=13445867}
\transl
\jour Russian Math. Surveys
\yr 2004
\vol 59
\issue 5
\pages 907--940
\crossref{https://doi.org/10.1070/RM2004v059n05ABEH000772}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000227131700003}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-14544308714}


Linking options:
  • http://mi.mathnet.ru/eng/umn772
  • https://doi.org/10.4213/rm772
  • http://mi.mathnet.ru/eng/umn/v59/i5/p101

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R. Bocklandt, “Graded Calabi Yau algebras of dimension 3”, J. Pure Appl. Algebra, 212:1 (2008), 14–32  crossref  mathscinet  zmath  isi
    2. A. Kapustin, L. Katzarkov, D. Orlov, M. Yotov, “Homological mirror symmetry for manifolds of general type”, Centr. Eur. J. Math., 7:4 (2009), 571–605  crossref  mathscinet  zmath  isi  elib
    3. M. Aldi, “Twisted homogeneous coordinate rings of abelian surfaces via mirror symmetry”, Proc. Amer. Math. Soc., 137:8 (2009), 2741–2747  crossref  mathscinet  zmath  isi  elib
    4. B. Keller, W. Lowen, P. Nicolás, “On the (non)vanishing of some “derived” categories of curved dg algebras”, J. Pure Appl. Algebra, 214:7 (2010), 1271–1284  crossref  mathscinet  zmath  isi
    5. M. Herbst, “On higher rank coisotropic $A$-branes”, J. Geom. Phys., 62:2 (2012), 156–169  crossref  mathscinet  zmath  adsnasa  isi  elib
    6. Khoroshkov Yu.V., “Mirror Symmetry as a Basis For Constructing a Space-Time Continuum”, 60, no. 5, 2015, 468–477  crossref  isi
    7. Omer H., “Matrix factorizations and elliptic fibrations”, Nucl. Phys. B, 910 (2016), 431–457  crossref  mathscinet  zmath  isi  elib  scopus
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:1069
    Full text:538
    References:68
    First page:4

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019