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On Thursday, November 16, 2017 the Department of Mathematics will welcome Dr. Jill Pipher, the Elisha Andrews Professor of Mathematics from Brown University, as our 2017-18 Clanton Visiting Mathematician.

On that day there will be a reception at 3:00 p.m. followed by afternoon colloquium talk at 4:00 and an evening presentation at 7:30 p.m. designed for a more general audience. 

                                        Afternoon Reception

Drop-in to enjoy some refreshments and have an opportunity to meet and talk with Professor Pipher at 3:00 p.m. in the Mathematics Department office suite, Riley Hall 205. 

                                    Afternoon Colloquium Talk
4:00 p.m. in McEachern Lecture Hall, Furman Hall 214

                                  Geometric Discrepancy Theory

Discrepancy theory originated with some apparently simple questions about sequences of numbers.  The discrepancy of an infinite sequence in an interval is a quantitative measure of how uniformly it is distributed.  In the 1950's, Roth showed that the discrepancy problem for infinite sequences in [0,1] had an equivalent geometric formulation in terms of the discrepancy of collections of points in two dimensions.  This reformulation permitted approaches to the one and higher dimensional problems by geometric-analytic methods.  The subject of geometric discrepancy theory embraces tools and ideas from number theory, lattice theory, ergodic theory and harmonic analysis.  In this talk, we will give a survey of the subject of the subject and discuss some joint work (with D. Bilyk, C. Spencer, X. Ma) in two-dimensional "directional" discrepancy.

                                         Evening Presentation
          7:30 p.m. in Shaw Hall of the Younts Conference Center

              Cryptography:  From Antiquity to a Post-quantum Age
How is it possible to send encrypted information across an insecure channel (like the internet) so that only the intended recipient can decode it, without sharing the secret key in advance?  In 1976, well before this question arose, a new mathematical theory of encryption (public-key cryptography) was invented by Diffie and Hellman, which made digital commerce and finance possible.  The technology advances of the last twenty years bring new and urgent problems, including the need to compute on encrypted data in the cloud and to have cryptography that can withstand the speed-ups of quantum computers.  In this lecture, we will discuss some of the history of cryptography, as well as some of the latest ideas in "lattice" cryptography which appear to be quantum resistant and efficient.
                                       Biographical Information

Jill Pipher is the Elisha Benjamin Andrews Professor of Mathematics at Brown University.  She is the founding director of ICERM, the Institute for Computational and Experimental Research in Mathematics, an NSF-funded mathematics institute based in Providence, Rhode Island.  ICERM brings together some of the world's best minds to explore topics in pure and applied mathematics, computer science, and related disciplines.  Jill was recently installed as the vice president for research at Brown.  Commenting on her appointment to this position, Brown Provost Richard M. Locke said:  "Jill is an accomplished researcher and a dynamic leader with a deep understanding of Brown's collaborative approach to scholarship that transcends disciplinary boundaries."    

Professor Pipher received a B.A. degree from UCLA in 1979 and a Ph.D. from UCLA in 1985.  Her research director was John Garnett.  She taught at the University of Chicago before taking a position at Brown in 1989.  Her primary area of research is harmonic analysis and its application to elliptic partial differential equations with non-smooth coefficients.

Although Jill's primary research is in pure mathematics, she has made significant contributions to applied mathematics as well.  In 1996, Jill and two of her colleagues, Jeffrey Hoffstein and Joseph Silverman, introduced NTRU, a publickey encryption system, which is in wide use today.  This encryption algorithm is based on the shortest vector problem in a lattice and is an alternative to, for example, the RSA and ECC encryption systems.  At that time, Hoffstein, Pipher, and Silverman were not members of the community of cryptographers.  In a 2012 interview, Hoffstein reflected on some of their earlier difficulties in garnering recognition for their work:  "It wasn't hard to convince people that it was new.  If was hard to convince them that it was secure ...  We were all pure mathematicians with little connection to the crypto community.  When we tried to introduce NTRU, all we got was pushback and outright hostility.  In fact, I would say it wasn't until a few years ago that the crypto community finally began to accept the fact that NTRU might be secure." 

In 2008, Hoffstein, Pipher, and Silverman published their book, An Introduction to Mathematical Cryptography.  Jill's outstanding work has not gone unnoticed.  She is the holder of four patents.  In successive years, 1989 and 1990, Jill was awarded an Alfred P. Sloan Research Fellowship and a Presidential Young Investigator Award.  From 2001 to 2013, Jill served as the president of the Association of Women in Mathematics.  In 2012, she became a fellow of the American Mathematical Society.  In 2015 she was selected a member of the American Academy of Arts and Sciences.  This prestigious society is one of our nations oldest learned societies, tracing its roots back to the American Revolution.  She will deliver the Noether Lecture in 2018 at the joint meetings of the American Mathematical Society and the Mathematical Association of America.       

Previous CLANTON Speakers

2016-2017:  William Trotter, Georgia Institute of Technology
2015-2016:  Richarad Karp, University of California, Berkeley
2014-2015:  Bryna Kra, Northwestern University

Avi Wigderson, Institute of Advanced Study, Princeton, NJ
2012-2013: Ken Ono, Emory University
William J. Cook, Georgia Institute of Technology
J. Michael Steele, University of Pennsylvania
2009-2010: Donald Saari, University of California, Irvine
2008-2009: Stephen Stigler, University of Chicago
2007-2008: Colin Clark, University of British Columbia
2006-2007: Barry Mazur, Harvard University
2005-2006: Peter Winkler, Dartmouth College
2003-2004: Jeffrey Weeks, Mathematician and author of The Shape of Space
2002-2003: Frank Morgan, Williams College
2001-2002: George Andrews, Pennsylvania State University
2000-2001: Kenneth Ribet, University of California, Berkeley
1999-2000: Jonathan Borwein, Simon Fraser University
1998-1999: Carolyn Gordon, Dartmouth College
1997-1998: Mary Ellen Rudin, University of Wisconsin
1996-1997: László Lovász, Yale University
1995-1996: Frederick Mosteller, Harvard University
1994-1995: Saunders MacLane, University of Chicago
1993-1994: Persi Diaconis, Harvard University
1992-1993: John H. Conway, Princeton University
1991-1992: Paul Halmos, Santa Clara University
1990-1991: Bradley Efron, Stanford University
1989-1990: Carl Pomerance, University of Georgia
1988-1999: Heinz-Otto Peitgen, University of Bremen
1987-1988: Ronald Graham, AT&T Bell Laboratories


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