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American mathematician
Lauren Kiyomi Williams (born
c. 1978) is an American mathematician known for her work on
cluster algebras ,
tropical geometry ,
algebraic combinatorics ,
amplituhedra , and the positive
Grassmannian .
[1] She is Dwight Parker Robinson Professor of Mathematics at
Harvard University .
[2]
Education
Williams's father is an engineer; her mother is third-generation
Japanese American . She grew up in Los Angeles, where her interest in mathematics was sparked by winning a fourth-grade mathematics contest.
[1] She was the
valedictorian of
Palos Verdes Peninsula High School in 1996,
[2] and while there participated in summer research at the
Massachusetts Institute of Technology with Satomi Okazaki, a student of her eventual advisor,
Richard P. Stanley .
[1] She graduated
magna cum laude from
Harvard University in 2000 with a A.B. in mathematics,
[2] and received her PhD in 2005 at the
Massachusetts Institute of Technology under the supervision of Stanley.
[3] Her dissertation was titled Combinatorial Aspects of Total Positivity.
Work
After postdoctoral positions at the
University of California, Berkeley and Harvard, Williams rejoined the Berkeley mathematics department as an assistant professor in 2009, and was promoted to associate professor in 2013 and then full professor in 2016.
[2]
Starting in the fall of 2018, she rejoined the Harvard mathematics department as a full professor, making her the second ever tenured female math professor at Harvard. The first,
Sophie Morel , left Harvard in 2012.
[4]
Along with colleagues O. Mandelshtam (her former student, now an assistant professor at
University of Waterloo ) and
S. Corteel , in 2018 Williams developed a new characterization of both symmetric and nonsymmetric
Macdonald polynomials using the combinatorial exclusion process.
[5]
Awards
In 2012, she became one of the inaugural
fellows of the
American Mathematical Society .
[6] She is the 2016 winner of the
Association for Women in Mathematics and
Microsoft Research Prize in Algebra and Number Theory.
[7] In 2022 she was awarded a
Guggenheim Fellowship .
[8]
Selected publications
Williams, Lauren K. (2005), "Enumeration of totally positive Grassmann cells",
Advances in Mathematics , 190 (2): 319–342,
arXiv :
math/0307271 ,
doi :
10.1016/j.aim.2004.01.003 ,
MR
2102660 ,
S2CID
15538736
Postnikov, Alex; Reiner, Victor; Williams, Lauren (2008),
"Faces of generalized permutohedra" (PDF) , Documenta Mathematica , 13 : 207–273,
arXiv :
math/0609184 ,
Bibcode :
2006math......9184P ,
doi :
10.4171/dm/248 ,
MR
2520477 ,
S2CID
10679764
Musiker, Gregg; Schiffler, Ralf; Williams, Lauren (2011), "Positivity for cluster algebras from surfaces",
Advances in Mathematics , 227 (6): 2241–2308,
arXiv :
0906.0748 ,
doi :
10.1016/j.aim.2011.04.018 ,
MR
2807089 ,
S2CID
13559804
Kodama, Yuji; Williams, Lauren K. (2011), "KP solitons, total positivity, and cluster algebras",
Proceedings of the National Academy of Sciences of the United States of America , 108 (22): 8984–8989,
arXiv :
1105.4170 ,
Bibcode :
2011PNAS..108.8984K ,
doi :
10.1073/pnas.1102627108 ,
MR
2813307 ,
PMC
3107278 ,
PMID
21562211
Kodama, Yuji; Williams, Lauren K. (2014), "KP solitons and total positivity of the Grassmannian",
Inventiones Mathematicae , 198 (3): 637–699,
arXiv :
1106.0023 ,
Bibcode :
2014InMat.198..637K ,
doi :
10.1007/s00222-014-0506-3 ,
MR
3279534 ,
S2CID
51759294
Ardila, Federico; Rincón, Felipe; Williams, Lauren (2016), "Positroids and non-crossing partitions",
Transactions of the American Mathematical Society , 368 (1): 337–363,
arXiv :
1308.2698 ,
doi :
10.1090/tran/6331 ,
MR
3413866 ,
S2CID
17008394
Corteel, Sylvie ; Mandelshtam, Olya; Williams, Lauren (2022), "From multiline queues to Macdonald polynomials via the exclusion process", American Journal of Mathematics , 144 (2): 395–436,
arXiv :
1811.01024 ,
doi :
10.1353/ajm.2022.0007 ,
MR
4401508
References
^
a
b
c Hartnett, Kevin (December 16, 2020),
"A Mathematician's Unanticipated Journey Through the Physical World" ,
Quanta Magazine
^
a
b
c
d
Lauren K. Williams , retrieved September 23, 2018 .
^
Lauren Williams at the
Mathematics Genealogy Project
^
"Math Dept Hires 2nd-Ever Female Tenured Prof, Ending Six-Year Drought" , The Harvard Crimson , retrieved May 1, 2018
^ Corteel, Sylvie; Mandelshtam, Olya; Williams, Lauren (2018), "From multiline queues to Macdonald polynomials via the exclusion process",
arXiv :
1811.01024 [
math.CO
^
List of Fellows of the American Mathematical Society , retrieved May 31, 2016 .
^
Lauren Williams wins the second AWM-Microsoft Research Prize in Algebra and Number Theory ,
Association for Women in Mathematics , June 3, 2015, retrieved May 31, 2016 .
^ Durrick, Mallory.
"Announcements" . John Simon Guggenheim Memorial Foundation . Retrieved July 4, 2022 .
External links