Amanda L. Folsom (born 1979) is an American mathematician specializing in

analytic number theory In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Diric ...

and its applications in

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many appl ...

. She is a professor of mathematics at

Amherst College Amherst College ( ) is a private liberal arts college in Amherst, Massachusetts. Founded in 1821 as an attempt to relocate Williams College by its then-president Zephaniah Swift Moore, Amherst is the third oldest institution of higher educatio ...

, where she chairs the department of mathematics and statistics.

Education and career

Folsom graduated from the

University of Chicago The University of Chicago (UChicago, Chicago, U of C, or UChi) is a private research university in Chicago, Illinois. Its main campus is located in Chicago's Hyde Park neighborhood. The University of Chicago is consistently ranked among the b ...

with honors in mathematics in 2001. She completed her Ph.D. in 2006 at the

University of California, Los Angeles The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a teachers college then known as the southern branch of the California St ...

. Her dissertation, ''Modular Units'', was supervised by William Duke. After postdoctoral research at the

Max Planck Institute for Mathematics The Max Planck Institute for Mathematics (german: Max-Planck-Institut für Mathematik, MPIM) is a prestigious research institute located in Bonn, Germany. It is named in honor of the German physicist Max Planck and forms part of the Max Planck S ...

from 2006 to 2007, and at the

University of Wisconsin–Madison A university () is an educational institution, institution of higher education, higher (or Tertiary education, tertiary) education and research which awards academic degrees in several Discipline (academia), academic disciplines. Universities ty ...

from 2007 to 2010, she joined the

Yale University Yale University is a private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the wo ...

mathematics faculty in 2010. She moved to Amherst College in 2014. In 2018–2019 she was a von Neumann Fellow at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

Contributions

With

Ken Ono Ken Ono (born March 20, 1968) is a Japanese-American mathematician who specializes in number theory, especially in integer partitions, modular forms, umbral moonshine, the Riemann Hypothesis and the fields of interest to Srinivasa Ramanujan. He ...

, Jan Hendrik Bruinier, and Zach Kent, Folsom participated in the discovery of a

fractal In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illu ...

structure in the partition function that allows any particular value of the function to be computed exactly by a finite formula. Folsom and Ono are the namesakes of the Folsom–Ono grid, constructed from two sequences of Poincaré series that define weak

harmonic Maass form In mathematics, a weak Maass form is a smooth function f on the upper half plane, transforming like a modular form under the action of the modular group, being an eigenfunction of the corresponding hyperbolic Laplace operator, and having at ...

s and

modular form In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the Group action (mathematics), group action of the modular group, and also satisfying a grow ...

s. The coefficients of these series can be arranged in a two-dimensional grid, and in a 2008 paper, Folsom and Ono conjectured that the values in this grid are all integers. This conjecture was later proven by others. Folsom is also known for her research with Ono and R. C. Rhoades refining results of

Srinivasa Ramanujan Srinivasa Ramanujan (; born Srinivasa Ramanujan Aiyangar, ; 22 December 188726 April 1920) was an Indian mathematician. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis ...

mock modular form In mathematics, a mock modular form is the holomorphic part of a harmonic weak Maass form, and a mock theta function is essentially a mock modular form of weight . The first examples of mock theta functions were described by Srinivasa Ramanu ...

s. With

Kathrin Bringmann Kathrin Bringmann (born 8 May 1977) is a German number theorist in the University of Cologne, Germany, who has made fundamental contributions to the theory of mock theta functions. Education and career Kathrin Bringmann was born on 8 May 1977, ...

, Ken Ono, and Larry Rolen, Folsom is one of the authors of the book ''Harmonic Maass Forms and Mock Modular Forms: Theory and Applications'' (Colloquium Publications 64, American Mathematical Society, 2018).

Recognition

Folsom is the winner of the 2021 Mary P. Dolciani Prize for Excellence in Research, given by the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. The award was for "her outstanding record of research in analytic and algebraic number theory, with applications to combinatorics and Lie theory, for her work with undergraduate students, and for her service to the profession, including her work to promote success of women in mathematics". Her book ''Harmonic Maass Forms and Mock Modular Forms'' won the 2018

Prose Award The PROSE Awards (Professional and Scholarly Excellence) are presented by the Association of American Publishers’ (AAP) Professional and Scholarly Publishing (PSP) Division. Presented since 1976, the awards annually recognize distinguished prof ...

for Best Scholarly Book in Mathematics from the

Association of American Publishers The Association of American Publishers (AAP) is the national trade association of the American book publishing industry. AAP lobbies for book, journal, and education publishers in the United States. AAP members include most of the major commercia ...

References

External links

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{{DEFAULTSORT:Folsom, Amanda L. 1979 births Living people 21st-century American mathematicians American women mathematicians Number theorists University of Chicago alumni University of California, Los Angeles alumni Yale University faculty Amherst College faculty 21st-century American women