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Jill Pipher
Professor of Mathematics
- CONTACT INFO
Office: Kassar 214
Phone: (401) 863-3323
Dept. Phone: (401) 863-2708
Fax: (401) 863-9013
Email: jpipher<at>math<dot>brown<dot>edu
Mailing Address:
Mathematics Department
Box 1917
Brown University
Providence, RI 02912
- RESEARCH INTERESTS
Harmonic Analysis
Elliptic PDE
Cryptography
See also http://www.ntru.com/cryptolab/.
Current CV CV.pdf
- BACKGROUND
Education: Ph.D. UCLA, 1985.
- RECENT PUBLICATIONS
Practical Lattice-based Cryptography: NTRUEncrypt and NTRUSign with J. Hoffstein, N. Howgrave-Graham, W. Whyte, in The LLL Algorithm: Survey and Applications, Springer, 2010.
Multiparameter div-curl lemmas with M. Lacey, S. Petermichl, B. Wick, mpdivcurl.pdf
Directional discrepancy in two dimensions with D. Bilyk, X. Ma, and C. Spencer, bmpsLMS.pdf
Geometric-arithmetic averaging of dyadic weights with L. Ward and X. Xiao, PWX2009.pdf
Weak-star convergence in multiparameter Hardy spaces, with S. Treil, available on Arxiv here
BMO solvability and the A^infinity condition for elliptic operators, with M. Dindos, C. Kenig bmoJul29.pdf, To appear J. Geometric Analysis
Iterated Riesz Commutators: a simple proof of boundedness, with M. Lacey, S. Petermichl, B. Wick, RieszUpperBound.pdf Proceedings of Analysis at El Escorial, 2008.
Book: An Introduction to Mathematical Cryptography with J. Hoffstein, J. Silverman, Series: Undergraduate Textbooks in Mathematics, Springer, July 2008.
Multiparameter Riesz Commutators, with M. Lacey, S. Petermichl, and B. Wick, multiParameterRieszComm.pdf,, Amer. J. Math, Vol. 131, No.3, (2009) p. 731-771.
The L^p Dirichlet problem for second order elliptic operators and a p-adapted square function , with M. Dindos and S. Petermichl psqFinal.pdf , J. Funct. Anal. Vol. 249 issue 2, 2007, p. 372-392
BMO from dyadic BMO on the bidisc, with Lesley Ward BMOdyadicBMObidisc.pdf J. London Math. Soc. Vol. 77, Number 2 (2008), p. 524-544.
On Estimating the Lattice Security of NTRU, with N. Howgrave-Graham, J. Hoffstein, W. Whyte, NTRULattice-2005-1.pdf
Variations on the theme of Journe's lemma, with C. Cabrillo, M. Lacey, U. Molter, JourneLemma.pdf Houston J. Math., Vol 32, No. 3 (2006), p. 833.
Multiparameter paraproducts, with C. Muscalu, T. Tao, C. Thiele, preprint, polydisc.pdf Revista M. Ibero. Vol. 22, Number 3, 2006, p. 963-976.
Biparameter paraproducts, with C. Muscalu, T. Tao, C. Thiele, biparam.pdf , Acta Mathematica, 193, (2004), p. 269-296
A short proof of the Coifman-Meyer paraproduct theorem, , with C. Muscalu, T. Tao, C. Thiele, C-M.pdf
A covering lemma for rectangles in $\R^n$, with R. Fefferman, 133 No. 11 (2005), p.3235-3241. Proc. AMS., coveringlemma.pdf
NTRUSign: Digital signatures using the NTRU lattice, with J. Hoffstein, N. Howgrave-Graham, J.Silverman, W.Whyte, Proceedings of CT-RSA 2003, NTRUSign.pdf
NTRUSign: Digital signatures using the NTRU lattice, extended version, with J. Hoffstein, N. Howgrave-Graham, J.Silverman, W.Whyte,2002 , NTRUSignextended.pdf
Lectures at the L'Institut Fourier 2002 Summer School in Cryptology on NTRU encryption and digital signatures, grenoble.pdf
NSS: An NTRU lattice-based signature scheme, with J. Hoffstein and J. Silverman, Proceedings of Eurocrypt 2001.
The Dirichlet problem for elliptic equations with drift terms, with C. Kenig, Publicaciones Matematiques 45 (2001), 199-217 Dir.dvi
A new approach to absolute continuity of elliptic measure, with applications to non-symmetric equations. Adv. Math. 153 (2000), no. 2, 231--298. w/Kenig, C.; Koch, H.; Toro, T. AbsoluteContinuity.pdf
NTRU: a ring-based public key cryptosystem. Algorithmic number theory (Portland, OR, 1998), 267--288, Lecture Notes in Comput. Sci., 1423, Springer, Berlin, 1998. w/Hoffstein, Jeffrey; Silverman, Joseph H.
The inhomogeneous Dirichlet problem for $\Delta\sp 2$ in Lipschitz domains. J. Funct. Anal. 159 (1998), no. 1, 137--190. w/Adolfsson, Vilhelm
The absolute continuity of elliptic measure revisited. J. Fourier Anal. Appl. 4 (1998), no. 4-5, 463--468. w/Kenig, Carlos E.
Vector potential theory on nonsmooth domains in ${R}\sp 3$ and applications to electromagnetic scattering. J. Fourier Anal. Appl. 3 (1997), no. 2, 131--192. w/Mitrea, Dorina; Mitrea, Marius;
Area integral estimates for higher order elliptic equations and systems. Ann. Inst. Fourier (Grenoble) 47 (1997), no. 5, 1425--1461. w/Dahlberg, B. E. J.; Kenig, C. E.; Verchota, G. C.
Littlewood-Paley estimates: some applications to elliptic boundary value problems. Partial differential equations and their applications (Toronto, ON, 1995), 221--238, CRM Proc. Lecture Notes, 12, Amer. Math. Soc., Providence, RI, 1997. fieldsinst.dvi
Multiparameter operators and sharp weighted inequalities. Amer. J. Math. 119 (1997), no. 2, 337--369. w/Fefferman, R.
Review of: Harmonic Analysis Techniques in Second Order Elliptic PDE, by Carlos Kenig, Bulletin of the AMS 33 (2) (1996), p. 229-236, review.pdf
The Neumann problem for elliptic equations with nonsmooth coefficients. II. A celebration of John F. Nash, Jr. Duke Math. J. 81 (1995), no. 1, 227--250 (1996). w/Kenig, Carlos E.
Boundary value problems for higher order operators in Lipschitz and $C\sp 1$ domains. Fourier analysis and partial differential equations (Miraflores de la Sierra, 1992), 297--309, Stud. Adv. Math., CRC, Boca Raton, FL, 1995.
Maximum principles for the polyharmonic equation on Lipschitz domains. Potential Anal. 4 (1995), no. 6, 615--636. w/Verchota, G. C.
Dilation invariant estimates and the boundary Gårding inequality for higher order elliptic operators. Ann. of Math. (2) 142 (1995), no. 1, 1--38. w/Verchota, Gregory C.
The Neumann problem for elliptic equations with nonsmooth coefficients. Invent. Math. 113 (1993), no. 3, 447--509. w/Kenig, Carlos E.
A maximum principle for biharmonic functions in Lipschitz and $C\sp 1$ domains. Comment. Math. Helv. 68 (1993), no. 3, 385--414. w/Verchota, G.
The Dirichlet problem in $L\sp p$ for the biharmonic equation on Lipschitz domains. Amer. J. Math. 114 (1992), no. 5, 923--972. w/Verchota, Gregory
A martingale inequality related to exponential square integrability. Proc. Amer. Math. Soc. 118 (1993), no. 2, 541--546.
The theory of weights and the Dirichlet problem for elliptic equations. Ann. of Math. (2) 134 (1991), no. 1, 65--124. w/Fefferman, R. A.; Kenig, C. E.
Partial differential equations with minimal smoothness and applications. Proceedings of the IMA Participating Institutions Conference held at the University of Chicago, Chicago, Illinois, March 21--25, 1990. Edited by B. Dahlberg, E. Fabes, R. Fefferman, D. Jerison, C. Kenig and J. Pipher. The IMA Volumes in Mathematics and its Applications, 42. Springer-Verlag, New York, 1992. xii+220 pp. ISBN: 0-387-97774-0
Area integral estimates for the biharmonic operator in Lipschitz domains. Trans. Amer. Math. Soc. 327 (1991), no. 2, 903--917. w/Verchota, Gregory
The $h$-path distribution of the lifetime of conditioned Brownian motion for nonsmooth domains. Probab. Theory Related Fields 82 (1989), no. 4, 615--623. w/Kenig, Carlos E.
Hardy spaces and the Dirichlet problem on Lipschitz domains. Rev. Mat. Iberoamericana 3 (1987), no. 2, 191--247. w/Kenig, Carlos E.
Oblique derivative problems for the Laplacian in Lipschitz domains. Rev. Mat. Iberoamericana 3 (1987), no. 3-4, 455--472.
The oblique derivative problem on Lipschitz domains with $L\sp p$ data. Amer. J. Math. 110 (1988), no. 4, 715--737. w/Kenig, Carlos E.
Bounded double square functions. Ann. Inst. Fourier (Grenoble) 36 (1986), no. 2, 69--82.
Journé's covering lemma and its extension to higher dimensions. Duke Math. J. 53 (1986), no. 3, 683--690.