Gail Letzter

Last updated

Gail Letzter
Born (1960-09-12) September 12, 1960 (age 63)
New York
NationalityAmerican
Alma materB.A., Harvard University
Ph.D., University of Chicago
Known fortheory of quantum symmetric pairs
Scientific career
Fields Mathematics
InstitutionsWayne State University

Virginia Tech

National Security Agency
Doctoral advisor I.N. Herstein

Gail Letzter (born September 12, 1960, in Nyack, New York) is an American mathematician specializing in the representation theory of quantum groups. Letzter is technical director of the mathematics research group of the National Security Agency. [1] [2]

Contents

Education and career

Letzter received her B.A. from Harvard University in 1982 and her Ph.D. in mathematics from the University of Chicago in 1987. Letzter wrote her Ph.D. dissertation under I.N. Herstein and was later awarded a National Science Foundation Postdoctoral Fellowship supported by MIT. [2] [3] She held tenured positions in the mathematics departments at Wayne State University [1] and Virginia Tech. [4] In 2006, Letzter moved to the National Security Agency with the title of applied research mathematician, where she currently[ when? ] serves as technical director of the mathematics research group at the rank of defense intelligence senior level.

She served as Lie algebra editor of the Proceedings of the American Mathematical Society from 2007 - 2011. [5] In 2008 she published a research memoir in the series Memoirs of the American Mathematical Society entitled Invariant Differential Operators for Quantum Symmetric Space. [6] She has been an active member of the Association for Women in Mathematics (AWM), was elected as an at-large member of the executive committee of the association in 2015 and served on that body from 2016 - 2020. [7] She chaired the AWM policy and advocacy committee from 2016 - 2018. [7] She was one of the primary organizers of the 2015 AWM Research Symposium, which was held at the University of Maryland in College Park, Maryland. [8] She was an editor of the proceedings of this research symposium. [9]

Research

1989 marked the beginning of a long collaboration with Anthony Joseph at the Weizmann Institute in Israel. Their joint investigations of quantum groups included the discovery of the locally finite part [10] and other contributions, "which greatly contribute to our understanding of quantized enveloping algebras" according to one reviewer [11] . [12] [13] [14] Subsequently, Letzter began her own seminal analysis of quantum symmetric pairs from the perspective of Hopf algebras, culminating in a complete classification. [15] [16] [6] This work has served as the basis for breakthrough research by others on canonical bases [17] , categorification, and geometric representation theory. [18]

Recognition

Letzter was recognized as a fellow of the Association of Women in Mathematics (AWM) in the class of 2021. Her citation read "For work in government and in AWM on behalf of women in mathematics, leading the AWM Policy and Advocacy Committee to formally establish the Hill visits program to advocate for women and girls with members of Congress, and co-organizing the 2015 AWM symposium and editing its proceedings". [19] [20]

Books

Related Research Articles

<span class="mw-page-title-main">Melanie Wood</span> American mathematician

Melanie Matchett Wood is an American mathematician at Harvard University who was the first woman to qualify for the U.S. International Mathematical Olympiad Team. She completed her PhD in 2009 at Princeton University and is currently Professor of Mathematics at Harvard University, after being Chancellor's Professor of Mathematics at UC Berkeley and Vilas Distinguished Achievement Professor of Mathematics at the University of Wisconsin, and spending 2 years as Szegö Assistant Professor at Stanford University.

In mathematics, the Hall algebra is an associative algebra with a basis corresponding to isomorphism classes of finite abelian p-groups. It was first discussed by Steinitz (1901) but forgotten until it was rediscovered by Philip Hall (1959), both of whom published no more than brief summaries of their work. The Hall polynomials are the structure constants of the Hall algebra. The Hall algebra plays an important role in the theory of Masaki Kashiwara and George Lusztig regarding canonical bases in quantum groups. Ringel (1990) generalized Hall algebras to more general categories, such as the category of representations of a quiver.

Joan Sylvia Lyttle Birman is an American mathematician, specializing in low-dimensional topology. She has made contributions to the study of knots, 3-manifolds, mapping class groups of surfaces, geometric group theory, contact structures and dynamical systems. Birman is research professor emerita at Barnard College, Columbia University, where she has been since 1973.

In the mathematical field of knot theory, a quantum knot invariant or quantum invariant of a knot or link is a linear sum of colored Jones polynomial of surgery presentations of the knot complement.

Audrey Anne Terras is an American mathematician who works primarily in number theory. Her research has focused on quantum chaos and on various types of zeta functions.

<span class="mw-page-title-main">Sigurður Helgason (mathematician)</span> Icelandic mathematician

Sigurdur Helgason is an Icelandic mathematician whose research has been devoted to the geometry and analysis on symmetric spaces. In particular, he has used new integral geometric methods to establish fundamental existence theorems for differential equations on symmetric spaces as well as some new results on the representations of their isometry groups. He also introduced a Fourier transform on these spaces and proved the principal theorems for this transform, the inversion formula, the Plancherel theorem and the analog of the Paley–Wiener theorem.

Bhama Srinivasan is a mathematician known for her work in the representation theory of finite groups. Her contributions were honored with the 1990 Noether Lecture. She served as president of the Association for Women in Mathematics from 1981 to 1983.

<span class="mw-page-title-main">Kristin Lauter</span> American cryptographer

Kristin Estella Lauter is an American mathematician and cryptographer whose research interest is broadly in application of number theory and algebraic geometry in cryptography. She is particularly known for her work in the area of elliptic curve cryptography. She was a researcher at Microsoft Research in Redmond, Washington, from 1999–2021 and the head of the Cryptography Group from 2008–2021; her group developed Microsoft SEAL. In April 2021, Lauter joined Facebook AI Research (FAIR) as the West Coast Head of Research Science. She became the President-Elect of the Association for Women in Mathematics in February 2014 and served as President February 1, 2015 - January 31, 2017.

Erica Flapan is an American mathematician, the Lingurn H. Burkhead Professor of Mathematics at Pomona College.

<span class="mw-page-title-main">Georgia Benkart</span> American mathematician (1947–2022)

Georgia McClure Benkart was an American mathematician who was known for her work in the structure and representation theory of Lie algebras and related algebraic structures. She published over 130 journal articles and co-authored three American Mathematical Society memoirs in four broad categories: modular Lie algebras; combinatorics of Lie algebra representations; graded algebras and superalgebras; and quantum groups and related structures.

Karen Ellen Smith is an American mathematician, specializing in commutative algebra and algebraic geometry. She completed her bachelor's degree in mathematics at Princeton University before earning her PhD in mathematics at the University of Michigan in 1993. Currently she is the Keeler Professor of Mathematics at the University of Michigan. In addition to being a researcher in algebraic geometry and commutative algebra, Smith with others wrote the textbook An Invitation to Algebraic Geometry.

<span class="mw-page-title-main">Lauren Williams (mathematician)</span> American mathematician

Lauren Kiyomi Williams is an American mathematician known for her work on cluster algebras, tropical geometry, algebraic combinatorics, amplituhedra, and the positive Grassmannian. She is Dwight Parker Robinson Professor of Mathematics at Harvard University.

<span class="mw-page-title-main">Mara Neusel</span> Mathematician

Mara Dicle Neusel was a mathematician, author, teacher and an advocate for women in mathematics. The focus of her mathematical work was on invariant theory, which can be briefly described as the study of group actions and their fixed points.

Suzanne Marie Lenhart is an American mathematician who works in partial differential equations, optimal control and mathematical biology. She is a Chancellor's Professor of mathematics at the University of Tennessee, an associate director for education and outreach at the National Institute for Mathematical and Biological Synthesis, and a part-time researcher at the Oak Ridge National Laboratory.

In mathematics, a quantum or quantized enveloping algebra is a q-analog of a universal enveloping algebra. Given a Lie algebra , the quantum enveloping algebra is typically denoted as . The notation was introduced by Drinfeld and independently by Jimbo.

<span class="mw-page-title-main">Marie A. Vitulli</span> American mathematician

Marie A. Vitulli is an American mathematician and professor emerita at the University of Oregon.

<span class="mw-page-title-main">Emily Riehl</span> American mathematician

Emily Riehl is an American mathematician who has contributed to higher category theory and homotopy theory. Much of her work, including her PhD thesis, concerns model structures and more recently the foundations of infinity-categories. She is the author of two textbooks and serves on the editorial boards of three journals.

Vladimir Georgievich Turaev is a Russian mathematician, specializing in topology.

Michelle Ann Manes is an American mathematician whose research interests span the fields of number theory, algebraic geometry, and dynamical systems. She is a professor of mathematics at the University of Hawaii at Manoa, and has been a program director for algebra and number theory at the National Science Foundation.

Ruth I. Michler was an American-born mathematician of German descent who lived and worked in the United States. She earned her Ph.D. in Mathematics from the University of California, Berkeley, and she was a tenured associate professor at the University of North Texas. She died at the age of 33 while visiting Northeastern University, after which at least three memorial conferences were held in her honor, and the Ruth I. Michler Memorial Prize was established in her memory.

References

  1. 1 2 "AWM Election". Association for Women in Mathematics Newsletter. 45 (6): 12–13. November–December 2015.
  2. 1 2 "Gail Letzter Profile". LinkedIn. LinkedIn Corporation. Retrieved 2020-11-05.
  3. ↑ Gail Letzter at the Mathematics Genealogy Project
  4. ↑ "Board of visitors approves 2005 promotions, tenure". Virginia Tech Daily. Virginia Tech. Retrieved 2020-11-05.
  5. ↑ "Front Matter" (PDF). Proceedings of the American Mathematical Society. 135 (9). Retrieved 2020-11-05.
  6. 1 2 Letzter, Gail (2008), Invariant differential operators for quantum symmetric spaces, Memoirs of the American Mathematical Society, vol. 193, Providence, R.I.: American Mathematical Society, ISBN   978-0-8218-4131-0, MR   2400554
  7. 1 2 "Historical List of AWM Committee Members". Association for Women in Mathematics. Retrieved 2020-11-05.
  8. ↑ "AWM Research Symposium 2015". Association for Women in Mathematics. Retrieved 2020-11-05.
  9. ↑ Martin, Carla; Chambers, Erin; Letzter, Gail; Grigsby, Julia Elisenda; Ryan, Kathleen; Trivisa, Konstantina; Lauter, Kristin; Flournoy, Nancy, eds. (August 19, 2016). Advances in the Mathematical Sciences: Research from the 2015 Association for Women in Mathematics Symposium. Springer International Publishing. ISBN   9783319341392 . Retrieved 2020-11-05.
  10. ↑ Joseph, A.; Letzter, G. (1992). "Local Finiteness of the Adjoint Action for Quantized Enveloping Algebras". Journal of Algebra. 153 (2): 289–318. doi: 10.1016/0021-8693(92)90157-H . MR   1198203.
  11. ↑ (see Math Review 1262429 )
  12. ↑ Joseph, A.; Letzter, G. (1994). "Separation of Variables for Quantized Enveloping Algebras". American Journal of Mathematics. 116 (1): 127–177. doi:10.2307/2374984. JSTOR   2374984. MR   1262429 . Retrieved 2020-11-08.
  13. ↑ Joseph, A.; Letzter, G. (1995). "Verma Module Annihilators for Quantized Enveloping Algebras". Annales Scientifiques de l'École Normale Supérieure. 116 (1): 493–526. doi: 10.24033/ASENS.1723 . MR   1334611.
  14. ↑ Joseph, A.; Letzter, G. (1996). "Rosso's Form and Quantized Kac Moody algebras". Mathematische Zeitschrift. 222 (4): 543–571. doi:10.1007/BF02621883. MR   1406268. S2CID   119874745 . Retrieved 2020-11-08.
  15. ↑ Letzter, Gail (2002), Coideal Subalgebras and Quantum Symmetric Pairs (PDF), Math. Sci. Res. Inst. Publications, vol. 43, Cambridge University Press, pp. 117–166, MR   1913438
  16. ↑ Letzter, G. (2003). "Quantum Symmetric Pairs and Their Zonal Spherical Functions". Transformation Groups. 8 (3): 261–291. arXiv: math/0204103 . doi:10.1007/s00031-003-0719-9. MR   1996417. S2CID   16003181 . Retrieved 2020-11-08.
  17. ↑ "Huanchen Bao and Weiqiang Wang Will Receive the 2020 Chevalley Prize". American Mathematical Society. Retrieved 2020-11-08.
  18. ↑ Weelinck, T.A.N. (2019). "A topological origin of quantum symmetric pairs". Selecta Mathematica. New Series. 25 (51). doi: 10.1007/s00029-019-0497-4 . MR   3984109. S2CID   119143788.
  19. ↑ "The AWM Fellows Program: 2021 Class of AWM Fellows". Association for Women in Mathematics. Retrieved 2020-11-05.
  20. ↑ "Adjunct Professor, Gail Letzer named AWM Fellow". Department of Mathematics. University of Maryland. Retrieved 2020-11-06.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.