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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
Directional discrepancy in two dimensions with D. Bilyk, X. Ma, and C. Spencer, bmpsLMS.pdf
Weak-star convergence in multiparameter Hardy spaces, with S. Treil, available on Arxiv here
The L^2 regularity problem for elliptic equations satisfying a Carleson measure condition, with M. Dindos and D. Rule, DPR.pdf
BMO solvability and the A^infinity condition for elliptic operators, with M. Dindos, C. Kenig bmoJul29.pdf
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 to appear, Houston J. Math.
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.