Lisa Piccirillo
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Lisa Marie Piccirillo (born 1990 or 1991)''The Boston Globe'
A math problem stumped experts for 50 years. This grad student from Maine solved it in days
August 20, 2020; print title: "A Tough Knot to Crack," ''The Boston Globe Magazine'' (August 23, 2020), pp. 23-25.
is an American mathematician who is a Professor and holds the Sid W. Richardson Regents Chair in Mathematics at the
University of Texas at Austin The University of Texas at Austin (UT Austin, UT, or Texas) is a public university, public research university in Austin, Texas, United States. Founded in 1883, it is the flagship institution of the University of Texas System. With 53,082 stud ...
. She works in the fields of
geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
and
low-dimensional topology In mathematics, low-dimensional topology is the branch of topology that studies manifolds, or more generally topological spaces, of four or fewer dimensions. Representative topics are the theory of 3-manifolds and 4-manifolds, knot theory, ...
. She is most well-known for proving that the
Conway knot In mathematics, specifically in knot theory, the Conway knot (or Conway's knot) is a particular knot (mathematics), knot with 11 crossings, named after John Horton Conway. It is related by mutation (knot theory), mutation to the Kinoshita–Te ...
is not smoothly slice, answering an unsolved problem in
knot theory In topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be und ...
first proposed over fifty years prior by English mathematician
John Horton Conway John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician. He was active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many b ...
.


Early life

Piccirillo was raised in
Greenwood Green wood is unseasoned wood. Greenwood or Green wood may also refer to: People * Greenwood (surname) Settlements Australia * Greenwood, Queensland, a locality in the Toowoomba Region * Greenwood, Western Australia, a suburb of Perth ...
,
Maine Maine ( ) is a U.S. state, state in the New England region of the United States, and the northeasternmost state in the Contiguous United States. It borders New Hampshire to the west, the Gulf of Maine to the southeast, and the Provinces and ...
, and attended Telstar Regional High School in
Bethel, Maine Bethel is a town in Oxford County, Maine, United States. The population was 2,504 at the 2020 census. It includes the villages of Bethel and West Bethel. The town is home to Gould Academy, a private preparatory school, and is near the Sund ...
. Her mother was a middle school math teacher. As a child, she had many hobbies, such as riding
dressage Dressage ( or ; , most commonly translated as "training") is a form of horse riding performed in exhibition and competition, as well as an art sometimes pursued solely for the sake of mastery. As an equestrianism, equestrian sport defined by th ...
, being involved in her
church Church may refer to: Religion * Church (building), a place/building for Christian religious activities and praying * Church (congregation), a local congregation of a Christian denomination * Church service, a formalized period of Christian comm ...
's
youth group Youth Group is an Australian rock band based in Newtown, New South Wales. Built around the vocals of singer Toby Martin and production of Wayne Connolly, the sound of Youth Group is reminiscent of indie rock artists such as Teenage Fanclub, ...
, and participating in drama and band in school.


Education

Piccirillo earned a B.S. in mathematics from
Boston College Boston College (BC) is a private university, private Catholic Jesuits, Jesuit research university in Chestnut Hill, Massachusetts, United States. Founded in 1863 by the Society of Jesus, a Catholic Religious order (Catholic), religious order, t ...
in 2013 and a PhD in low-dimensional topology at the
University of Texas at Austin The University of Texas at Austin (UT Austin, UT, or Texas) is a public university, public research university in Austin, Texas, United States. Founded in 1883, it is the flagship institution of the University of Texas System. With 53,082 stud ...
under the supervision of
John Luecke John Frederick Luecke (July 4, 1889 – March 21, 1952) was a politician from the U.S. state of Michigan. Luecke was born in Escanaba, Michigan to German immigrants and attended the public elementary schools. He was employed as a commercial a ...
in 2019, followed by postdoctoral research at
Brandeis University Brandeis University () is a Private university, private research university in Waltham, Massachusetts, United States. It is located within the Greater Boston area. Founded in 1948 as a nonsectarian, non-sectarian, coeducational university, Bra ...
. Boston College professor
Elisenda Grigsby Julia Elisenda (Eli) Grigsby is an American mathematician who works as a professor at Boston College. Her research began with the study of low-dimensional topology, including knot theory and category-theoretic knot invariants. She is currently wo ...
cited Piccirillo's creativity as contributing to her success, adding that Piccirillo did not fit the mold of a "standard golden child math prodigy" during her undergraduate studies.


Work

The
Conway knot In mathematics, specifically in knot theory, the Conway knot (or Conway's knot) is a particular knot (mathematics), knot with 11 crossings, named after John Horton Conway. It is related by mutation (knot theory), mutation to the Kinoshita–Te ...
was named after its discoverer, English mathematician
John Horton Conway John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician. He was active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many b ...
, who first wrote about the knot in 1970. The Conway knot was determined to be
topologically slice Topology (from the Greek words , and ) is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, withou ...
in the 1980s; however, whether or not it was smoothly slice (that is whether or not it was a slice of a higher dimensional knot) eluded mathematicians for half a century, making it a long-standing unsolved problem in
knot theory In topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be und ...
. This changed with Lisa Piccirillo's work on the Conway knot, which completed the classification of slice knots with under thirteen crossings, as the Conway knot had been the last outstanding knot in its group fully unclassified. Her proof made use of Rasmussen's s-invariant, and showed that the knot is not a smoothly slice knot. Piccirillo first learned of the Conway knot problem in 2018 at
conference
on low-dimensional topology and geometry. She was a graduate student at the time and spent less than a week working on the knot in her free time to "see what's so hard about this problem" before finding an answer:
''I think the next day, which was a Sunday, I just started trying to run the approach for fun and I worked on it a bit in the evenings just to try to see what's supposed to be hard about this problem.''
Before the week was out, Piccirillo had an answer. A few days later, she met with Cameron Gordon, a professor at UT Austin (a senior topologist), and casually mentioned her solution. She stated later:
''It was quite surprising to me. I mean, it's just one knot. In general, when mathematicians prove things, we like to prove really broad, general statements: All objects like this have some property. And I proved like, one knot has a thing. I don't care about knots. So, I do care about three and four dimensional spaces, though. And it turns out that, when you want to study three and four dimensional spaces, you find yourself studying knots anyway.''
''The Washington Post'' reported that her proof had been "hailed as a thing of mathematical beauty, and her work could point to new ways to understand knots." Following the publication of Piccirillo's proof in ''
Annals of Mathematics The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as t ...
,'' she was offered an assistant professorship at the
Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...
, to begin fourteen months after the completion of her doctorate. From 2020 to 2024, she was an assistant professor of mathematics at the
Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...
.


Recognition

In association with the 2021
Breakthrough Prize The Breakthrough Prizes are a set of international awards bestowed in three categories by the Breakthrough Prize Board in recognition of scientific advances. The awards are part of several "Breakthrough" initiatives founded and funded by Yuri M ...
s, Lisa Piccirillo was awarded one of three 2021
Maryam Mirzakhani New Frontiers Prize The Breakthrough Prize in Mathematics is an annual award of the Breakthrough Prize series announced in 2013. It is funded by Yuri Milner and Mark Zuckerberg and others. The annual award comes with a cash gift of $3 million. The Breakthrough Prize ...
s, for early-career achievements by a woman mathematician. The other two winners were Nina Holden and Urmila Mahadev. She was also awarded a 2021 Clay Research Fellowship for "her work in low-dimensional topology" and a 2021
Sloan Research Fellowship The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide support and recognition to early-career scientists and scholars". This program is one of the oldest of its kind in the United States. ...
. Additionally, Lisa was counted as one of "The world's top 50 thinkers for the Covid-19 age" by UK magazine ''Prospect'' in 2020.


References


External links


Official site
{{DEFAULTSORT:Piccirillo, Lisa 21st-century American mathematicians 21st-century American women mathematicians Morrissey College of Arts & Sciences alumni Living people 1990s births Massachusetts Institute of Technology School of Science faculty American topologists University of Texas at Austin alumni University of Texas at Austin College of Natural Sciences alumni Year of birth missing (living people) Brandeis University faculty People from Greenwood, Maine Mathematicians from Maine