Lisa Piccirillo

Last updated

Lisa Piccirillo
Born
Greenwood, Maine, U.S.
Education
Known forSolving the Conway knot problem
AwardsMaryam Mirzakhani New Frontiers Prize (2021)
Clay Research Fellow (2021)
Sloan Research Fellow (2021)
Scientific career
Fields
Thesis Knot traces and the slice genus  (2019)
Doctoral advisor John Luecke

Lisa Marie Piccirillo (born 1990 or 1991) [1] is an American mathematician who works on Geometry and low-dimensional topology. In 2020, Piccirillo published a mathematical proof in the journal Annals of Mathematics determining that the Conway knot is not a slice knot, [2] answering an unsolved problem in knot theory first proposed over fifty years prior by English mathematician John Horton Conway. [3] In July 2020, she became an assistant professor of mathematics at Massachusetts Institute of Technology. [4]

Contents

Early life

Piccirillo was raised in Greenwood, Maine, and attended Telstar Regional High School in Bethel, Maine. [5] Her mother was a middle school math teacher. As a child, she had many hobbies, such as riding dressage, being involved in her church's youth group, and participating in drama and band in school. [1]

Education

Piccirillo earned a B.S. in mathematics from Boston College in 2013 and a PhD in low-dimensional topology at the University of Texas at Austin under the supervision of John Luecke in 2019, [6] followed by postdoctoral research at Brandeis University. [3] [7] [8] Boston College professor Elisenda Grigsby 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. [3]

Work

The Conway Knot. Conway knot.png
The Conway Knot.

The Conway knot was named after its discoverer, English mathematician John Horton Conway, who first wrote about the knot in 1970. The Conway knot was determined to be topologically slice in the 1980s; however, the nature of its sliceness, and whether or not it was smoothly slice (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. [3] [9] 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. [2]

Piccirillo first learned of the Conway knot problem in 2018 at a conference on low-dimensional topology and geometry. [3] [10] 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: [9] [11]

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: The Conway knot is not “slice”. [3] A few days later, she met with Cameron Gordon (mathematician), a professor at UT Austin (a senior topologist), and casually mentioned her solution. In her interview with Quanta Magazine, [11] she described her interaction with Gordon in the following way:

And then the following week, I had a meeting with Cameron Gordon, a senior topologist in my department, about something else, and I mentioned it to him there. He was like, "Oh really? You showed that the Conway knot is not slice?". Like, show me. And then I started to put it up and he started asking kind of detailed questions, and then at some point he got, he got very excited.

Lisa Piccirillo, in the same interview, has mentioned that the fact that this problem was still unsolved was "completely ridiculous". As she put it:

Well, I just thought it was completely ridiculous that we didn't know whether this knot was slice or not. We had a lot of tools to do this sort of thing, so I didn't understand like, why for some 11-crossing-knot this would be so difficult.

She followed this statement up with this:

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." [9]

Following the publication of Piccirillo's proof in Annals of Mathematics, she was offered a tenure-track position at the Massachusetts Institute of Technology set to begin fourteen months after the completion of her doctorate. [3] [12]

Recognition

In association with the 2021 Breakthrough Prizes, Piccirillo was awarded one of three 2021 Maryam Mirzakhani New Frontiers Prizes, for early-career achievements by a woman mathematician. The other two winners were Nina Holden and Urmila Mahadev. [13] She was also awarded a 2021 Clay Research Fellowship for "her work in low-dimensional topology" and a 2021 Sloan Research Fellowship. [14]

She was also counted as one of "The world's top 50 thinkers for the Covid-19 age" by UK magazine Prospect. [15]

Related Research Articles

<span class="mw-page-title-main">John Horton Conway</span> English mathematician (1937–2020)

John Horton Conway was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many branches of recreational mathematics, most notably the invention of the cellular automaton called the Game of Life.

<span class="mw-page-title-main">Knot theory</span> Study of mathematical knots

In topology, knot theory is the study of 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 undone, the simplest knot being a ring. In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, . Two mathematical knots are equivalent if one can be transformed into the other via a deformation of upon itself ; these transformations correspond to manipulations of a knotted string that do not involve cutting it or passing it through itself.

<span class="mw-page-title-main">Ciprian Manolescu</span> Romanian-American mathematician

Ciprian Manolescu is a Romanian-American mathematician, working in gauge theory, symplectic geometry, and low-dimensional topology. He is currently a professor of mathematics at Stanford University.

<span class="mw-page-title-main">Conway knot</span> Prime knot named for John Horton Conway

In mathematics, in particular in knot theory, the Conway knot is a particular knot with 11 crossings, named after John Horton Conway.

<span class="mw-page-title-main">Slice knot</span> Knot that bounds an embedded disk in 4-space

A slice knot is a mathematical knot in 3-dimensional space that bounds an embedded disk in 4-dimensional space.

<span class="mw-page-title-main">Maryam Mirzakhani</span> Iranian mathematician (1977–2017)

Maryam Mirzakhani was an Iranian mathematician and a professor of mathematics at Stanford University. Her research topics included Teichmüller theory, hyperbolic geometry, ergodic theory, and symplectic geometry. On 13 August 2014, Mirzakhani was honored with the Fields Medal, the most prestigious award in mathematics, becoming the first woman to win the prize, as well as the first Iranian. The award committee cited her work in "the dynamics and geometry of Riemann surfaces and their moduli spaces".

<span class="mw-page-title-main">Ribbon knot</span> Type of mathematical knot

In the mathematical area of knot theory, a ribbon knot is a knot that bounds a self-intersecting disk with only ribbon singularities. Intuitively, this kind of singularity can be formed by cutting a slit in the disk and passing another part of the disk through the slit. More precisely, this type of singularity is a closed arc consisting of intersection points of the disk with itself, such that the preimage of this arc consists of two arcs in the disc, one completely in the interior of the disk and the other having its two endpoints on the disk boundary.

In the mathematical theory of knots, a Berge knot or doubly primitive knot is any member of a particular family of knots in the 3-sphere. A Berge knot K is defined by the conditions:

  1. K lies on a genus two Heegaard surface S
  2. in each handlebody bound by S, K meets some meridian disc exactly once.
<span class="mw-page-title-main">Ian Agol</span> American mathematician

Ian Agol is an American mathematician who deals primarily with the topology of three-dimensional manifolds.

<span class="mw-page-title-main">Yitang Zhang</span> Chinese-born American mathematician

YitangZhang is a Chinese-American mathematician primarily working on number theory and a professor of mathematics at the University of California, Santa Barbara since 2015.

The Breakthrough Prize in Mathematics is an annual award of the Breakthrough Prize series announced in 2013.

<span class="mw-page-title-main">Tim Cochran</span> American mathematician

Thomas "Tim" Daniel Cochran was a professor of mathematics at Rice University specializing in topology, especially low-dimensional topology, the theory of knots and links and associated algebra.

<span class="mw-page-title-main">Svetlana Jitomirskaya</span> American mathematician

Svetlana Yakovlevna Jitomirskaya is a Soviet-born American mathematician working on dynamical systems and mathematical physics. She is a distinguished professor of mathematics at Georgia Tech and UC Irvine. She is best known for solving the ten martini problem along with mathematician Artur Avila.

<span class="mw-page-title-main">John Pardon</span> American mathematician

John Vincent Pardon is an American mathematician who works on geometry and topology. He is primarily known for having solved Gromov's problem on distortion of knots, for which he was awarded the 2012 Morgan Prize. He is currently a permanent member of the Simons Center for Geometry and Physics and a full professor of mathematics at Princeton University.

<span class="mw-page-title-main">Maryna Viazovska</span> Ukrainian mathematician (born 1984)

Maryna Sergiivna Viazovska is a Ukrainian mathematician known for her work in sphere packing. She is a full professor and Chair of Number Theory at the Institute of Mathematics of the École Polytechnique Fédérale de Lausanne in Switzerland. She was awarded the Fields Medal in 2022.

Hao Huang is a mathematician known for solving the sensitivity conjecture. Huang is currently an associate professor in the mathematics department at National University of Singapore.

<span class="mw-page-title-main">Andrew Booker (mathematician)</span> British mathematician

Andrew Richard Booker is a British mathematician who is currently Professor of Pure Mathematics at the University of Bristol. He is an analytic number theorist known for his work on L-functions of automorphic forms and his contributions to the sums of three cubes problem.

Maggie Miller is a mathematician and an Assistant Professor in the mathematics department at the University of Texas, Austin. She was also a former Visiting Clay Fellow, and Stanford Science Fellow at Stanford University in the Mathematics Department. Her primary research area is low-dimensional topology.

References

  1. 1 2 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.
  2. 1 2 Piccirillo, Lisa (2020). "The Conway knot is not slice". Annals of Mathematics. 191 (2): 581–591. arXiv: 1808.02923 . doi:10.4007/annals.2020.191.2.5. ISSN   0003-486X. JSTOR   10.4007/annals.2020.191.2.5. S2CID   52398890.
  3. 1 2 3 4 5 6 7 Klarreich, Erica. "Graduate Student Solves Decades-Old Conway Knot Problem". Quanta Magazine . Retrieved May 20, 2020.
  4. ↑ "Lisa Piccirillo - MIT Mathematics" . Retrieved August 12, 2020.
  5. ↑ "Telstar Regional High School Class of 2009". May 15, 2009. Retrieved August 26, 2020.
  6. ↑ Lisa Marie Piccirillo. "Knot traces and the slice genus" (PDF).
  7. ↑ "Curriculum vitae" . Retrieved May 19, 2020.
  8. ↑ "Studying Knots and Four-Dimensional Spaces". University of Texas at Austin . Retrieved May 20, 2020.
  9. 1 2 3 Blakemore, Erin. "Graduate student untangles nature of Conway knot". The Washington Post . Retrieved May 26, 2020.
  10. ↑ Delbert, Caroline (May 22, 2020). "Young Mathematician Solves Old, Famous Knot Problem in Barely a Week". Popular Mechanics. Retrieved May 26, 2020.
  11. 1 2 "2020's Biggest Breakthroughs in Math and Computer Science". Quanta Magazine. December 23, 2020.
  12. ↑ "Lisa Piccirillo Solves Decades-Old Conway Knot Problem – Women In Math". math.mit.edu. Retrieved May 26, 2020.
  13. ↑ "Winners of the 2021 Breakthrough Prizes in life sciences, fundamental physics, and mathematics announced". Breakthrough Prizes. September 10, 2020. Retrieved September 19, 2020.
  14. ↑ "Clay Research Fellows Announced" (PDF). Notices of the American Mathematical Society. 68: 828–829.
  15. ↑ "Prospect Magazine's top 50 thinkers of the Covid-19 age".
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.