Arvind Borde

Arvind Borde
Senior Professor
Department of Mathematics, LIU-Post
720 Northern Blvd., Brookville, N.Y. 11548

Office: LS 239 / Tel: (516) 299 2447

B.S., Bombay University, 1976
M.A., Ph.D., State University of New York at Stony Brook, 1982

Email: arvind dot borde at liu dot edu


Current classes:


Administrative positions

Director, Technology Center, Southampton College, 1999--2005
Director, Natural Science Division, Southampton College, 2001--2003
Webmaster, Southampton College, 1995--2000

Other positions

KITP Scholar and General Member
Kavli Institute of Theoretical Physics, University of California at Santa Barbara, 2007--2009.
Visiting Scientist
Institute of Cosmology, Tufts University, 1993--2006.
Visiting Scientist
Center for Theoretical Physics, MIT, 2001--2002.
Guest Scientist
High Energy Theory Group, Brookhaven National Laboratory, 1987--2000.
Research Associate
Relativity Group, Syracuse University, 1985--1987.
Post-doctoral Fellow
with W.G. Unruh, University of British Columbia, 1982--1985.

Interests

Mathematical aspects of the general theory of relativity, the design of computer programs, digital typography and digital document design, Web programming and design, modern design, cricket, cooking.

Current work:
The existence and nature of initial singularities in inflationary cosmology; topology change, especially in spacetimes with degenerate metrics; averaged energy conditions; nonsingular black holes.


Awards


Selected press


Selected work, Design

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

Selected work, Relativity

  • 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).
  • Singularities in inflationary cosmology
    (with Alexander Vilenkin), Proceedings of the Sixth Quantum Gravity Seminar, Moscow, Int. J. Mod. Phys. D, Vol. 5, 813 (1996).
  • The impossibility of steady-state inflation
    (with Alexander Vilenkin), in Relativisitic Astrophysics: the Proceedings of the Eighth Yukawa Symposium, ed. by M. Sasaki, Universal Academic Press, Japan (1995).
  • 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).

Courses taught in the past

LIU-Post:
  • AST 10 (Introductory Astronomy II), 2015--2017.
  • AST 9 (Introductory Astronomy I), 2014--2016.
  • CSC 254 (Artificial intelligence), 2007.
  • MTH 521 (Linear programming), 2006.
  • MTH 511 (Set theory), 2008.
  • MTH 90 (Senior seminar), 2007, 2009--2015.
  • MTH 15 (Mathematics for elementary education), 2006--2008, 2009.
  • MTH 7 (Calculus and Analytical Geometry I), 2013--2016.
  • MTH 6 (Calculus for business and social science), 2006.
  • MTH 5 (Linear mathematics for business and social science), 2006.
  • MTH 4 (Introductory mathematics for business and social science), 2007.
  • MTH 3 (College algebra and trigonometry), 2006.
  • MTH 1 (Mathematics survey for non-science students), 2005--2008, 2009--2015.
  • PHY 12 (College Physics II), 2015--2017.
  • PHY 11 (College Physics I), 2015--2016.
Southampton College:
  • ART 400 (independent study on Web design), 1997.
  • CORE 172 / PHIL 176 (Philosophy of Logic), 2005.
  • CS 211 (introduction to scientific computing), 2000, 2002.
  • CS 111 (introduction to computer programming), 1990--1991, 1995, 1997.
  • DP 300 (special topics: java programming)), 1999.
  • MAT 400 (independent study on such topics as game theory, the uses of differential equations in biology and Web programming), 1989, 1997-1999.
  • MAT 399 (special topics, such as group theory and topology), 1989.
  • MAT 204 (differential equations), 1988, 1998.
  • MAT 202 (calculus II), 1988--1992, 1995--1999, 2001-2004.
  • MAT 201 (calculus I), 1987--1999, 2001--2005.
  • MAT 113 (statistics), 2003.
  • MAT 106 (pre-calculus), 1987--2005.
  • MAT 102 (introduction to college mathematics II), 1988--1991.

Elsewhere:

  • A Short Tour of the Universe (through scientific literature), Harvard Summer School, ASTR S-30, 2014, 2015
  • Independent study in general relativity (two graduate students), Syracuse University, 1987.
  • AST 201 and 202, Descriptive Astronomy (about 270 liberal arts students), Syracuse University, 1985--1986.
  • Graduate course in general relativity (12 graduate students), University of British Columbia, 1984.
  • Independent study in general relativity (three graduate students), University of British Columbia:1984.