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Arvind Borde

Graduate Co-Director, Mathematics DepartmentSenior Professor of Mathematics and Physics

B.S., Bombay UniversityM.A., Ph.D., Stony Brook University


Relativity & Cosmology, Topology, Computers, Cookery, Design and Cricket.

Selected Work: Relativity, Cosmology and Particle Physics

  • Inflationary spacetimes are incomplete in past directions
    (with A.H. Guth and A. Vilenkin), Phys. Rev. Lett., Vol. 90, 151301 (2003).
  • Constraints on spatial distributions of negative energy
    (with L.H. Ford and T.A. Roman), Phys. Rev. D Vol. 65, 084002 (2002)
  • Causal continuity in degenerate spacetimes
    (with F. Dowker, R. Garcia, R. Sorkin and S. Surya), Class. and Quant. Grav., Vol. 16, 3457 (1999).
  • Creation and structure of baby universes in monopole collisions
    (with Mark Trodden and Tanmay Vachaspati), Phys. Rev. D, Vol. 59, 043513 (1999).
  • How impossible is topology change?
    Bull. Astr. Soc. India, Vol. 25, 571 (1997).
  • Violations of the weak energy condition in inflating spacetimes
    (with Alexander Vilenkin), Phys. Rev. D, Vol. 56, 717 (1997).
  • Regular black holes and topology change
    Phys. Rev. D, Vol. 55, 7615 (1997).
  • Open and Closed Universes, Initial Singularities and Inflation
    Phys. Rev. D, Vol. 50, 3692 (1994).
  • Eternal Inflation and the Initial Singularity
    (with Alexander Vilenkin), Phys. Rev. Lett., Vol. 72, 3305 (1994).
  • Geodesic Focusing, Energy Conditions and Singularities
    Class. and Quant. Grav., Vol. 4, 343 (1987).
  • Hamiltonian Formalism for the Spin-5/2 Gauge Field
    Phys. Rev. D, Vol. 26, 407 (1982).

Selected Work: Computers

  • TeXHelp
    (a hypertext encyclopedia, for DOS computers, on the computer typesetting system TeX; with Tomas Rokicki), Academic Press (1993).
  • Mathematical TeX by Example
    (a book on the computer typesetting system TeX, with emphasis on the American Mathematical Society's version of that language), Academic Press (1992).
  • TeX by Example
    (an introductory book on the computer typesetting system TeX), Academic Press (1991).
  • Arithmetica!
    (an interactive program on arithmetic, encompassing topics from simple fractions to elementary number theory), distributed by Wisc-Ware, a now-defunct software division of the University of Wisconsin, and by other software groups (1990).

Selected Work: Design

  • Eva Zeisel: Her Work and Life
    (with Francesca Di Stefano Borde), 2005.


  • Trustees Award for Scholarly achievement 1995/96 (single work) and 2005 (lifetime achievement).
  • KITP Scholar, Kavli Institute of Theoretical Physics, UC Santa Barbara, 2007—09.

Research Summary

Arvind Borde’s work in mathematical physics addresses some of the largest scientific questions there are (Did the Universe have a beginning? What is the shape of the Universe?) and are generally regarded as having made significant contributions to our understanding. (Talks on three separate days at Stephen Hawking's 60th birthday symposium prominently featured his work.) He’s also published two books on computers and produced several large pieces of software, and is considered an expert on the computer typesetting language known as TeX.

Several broad, sometimes overlapping, themes run through his work:

  • The birth of the Universe
  • The shape of the Universe
  • The nature and effects of energy
  • Digital document design
  • Software design
  • General design

The first three themes are from subareas of the theory of relativity. Although he has also worked on other branches of mathematical physics, the theory of relativity has been his major research interest. He has

concentrated here on using and extending an abstract mathematical approach introduced in the mid-1960s, by Roger Penrose, Stephen Hawking and Robert Geroch. The approach is very powerful and it enables us to prove broad and general statements about the behavior of the Universe. His papers in this area include the one in 2003 with Alan Guth and Alex Vilenkin, possibly the most significant of his career. This paper, simply put, offers the most general proof we have that the Universe had a beginning. It has been widely cited and was the subject of a review in the famous scientific journal Nature.  

Borde’s interests in recent years have expanded to include design (where he has co-authored with his daughter a biography of the noted ceramics designer Eva Zeisel) and the history of food and cooking.


Borde has held visiting positions at MIT (2001--2002), at the Institute for Cosmology at Tufts University  (1993—2003), and at Brookhaven National Lab (1987—2000), and was appointed KITP Scholar at the Kavli Institute of Theoretical Physics at the University of California at Santa Barbara, where he spent six months in early 2007. He has given lectures at institutions worldwide. Here is a selected list:

  • USA: The Universities of Chicago, Oregon, Maryland; Kent State, Central Connecticut State, Tufts Universities; M.I.T.; Caltech (at the invitation of the 2017 Physics Nobel Prize co-winner, Kip Thorne); Harvard.
  • India: Bombay University, Pune University, Tata Institute of Fundamental Research, Raman Research Institute in Bangalore, Inter-University Center for Astronomy and Astrophysics.
  • UK: Oxford University, Cambridge University, University of Southampton, Newcastle University, University of Wales at Cardiff.
  • China: The University of the Chinese Academy of Sciences.

Selected press

  • All about Eva. A long piece on the great ceramist Eva Zeisel, based partly on interviews with Borde, and illustrated by pictures of his collection of her work, Boston Globe, June 6, 2005.
  • Chips Off the Old Block. A short piece on his history of computing project, Newsday, August 4, 2002. The computer museum he established may be viewed at the office of the Department of Physics and Mathematics at LIU Post.
  • Computers for 'Star Wars' or Just the Stars., an article on Southampton College (at the time a campus of LIU) Technology Center, an advanced computing facility that Borde founded and directed, The New York Times, June 6, 1999.
  • A Mathematician Who Asks Questions Without Answers.
    A long profile of Borde and his research in The New York Times, April 20, 1997.