Leila Schneps | |
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| Pen name | Catherine Shaw |
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| Nationality | American |
| Education | PhD |
| Alma mater | University of Paris |
| Subject | Mathematics |
| Children | Coralie Colmez |
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Leila Schneps is an American mathematician and fiction writer at the Centre national de la recherche scientifique working in number theory. Schneps has written general audience math books and, under the pen name Catherine Shaw, has written mathematically themed murder mysteries.
Schneps earned a B.A. in Mathematics, German Language and Literature from Radcliffe College in 1983. [1] She completed a Doctorat de Troisième Cycle in Mathematics at Université Paris-Sud XI-Orsay in 1985 under the supervision of John H. Coates with a thesis on p-adic L-functions attached to elliptic curves, [2] [3] a Ph.D. in Mathematics in 1990 with a thesis on p-Adic L-functions and Galois groups, [4] [5] and Habilitation at Université de Franche-Comté in 1993, with a thesis on the Inverse Galois problem. [6] [1]
Schneps held various teaching assistant positions in France and Germany until the completion of her Ph.D. in 1990, then worked as a postdoctoral assistant at the ETH in Zurich, Switzerland, for one year. In 1991 she was awarded a tenured research position at CNRS, the French National Centre for Scientific Research, at the University of Franche-Comté in Besançon. [1] During the late 1990s Schneps also had short-term visiting researcher assignments at Harvard University, the Institute for Advanced Study at Princeton, and MSRI at Berkeley. [7]
Schneps has published academic papers on various aspects of analytic number theory since the late 1980s. Her early work explored p-adic L-functions, [8] which became the topic of her first thesis, and around 2010 she was continuing to work on the related fields of zeta functions. [9]
Since the late 1990s she focused on aspects of Galois theory, including Galois groups, geometric Galois actions, and the inverse Galois problem, [10] and has been described by Jordan Ellenberg as "the arithmetic geometer ... who taught me most of what I know about Galois actions on fundamental groups of varieties". [11] Her work led to her study of the related Grothendieck–Teichmüller group, [12] [13] [14] [15] and she has become a member of a group preserving the works and history of Grothendieck. In the early 2010s she published research investigating various aspects of Lie algebras. [16] [17] [18]
Schneps has also edited and contributed to several mathematics textbooks in number theory. She edited a series of lecture notes on Grothendieck's theory of dessins d'enfants [19] and contributed an article to the series, [20] was an editor for a text on the Inverse Galois Problem, [10] and edited a book on Galois groups. [21] She was a co-author of a text on Field Theory [22] and co-editor of another on Galois–Teichmüller Theory. [23]
In 2013, Schneps and her daughter, mathematician Coralie Colmez, published the book Math on Trial: How Numbers Get Used and Abused in the Courtroom . [24] Targeted at a general audience, the book uses ten historical legal cases to show how mathematics, especially statistics, can affect the outcome of criminal proceedings, especially when incorrectly applied or interpreted. The mathematical concepts covered include statistical independence (discussed using the examples of the Sally Clark case and the murder of Meredith Kercher), Simpson's paradox (UC Berkeley gender bias case) and statistical modeling using a binomial distribution (Howland will forgery trial). [24]
While not written as a textbook, some reviewers found it suitable for students, as an introduction to the topic and to "get them thinking, talking and even arguing about the issues involved", [25] with another agreeing that, "they have struck the right balance of providing enough mathematics for the specialist to check out the details, but not so much as to overwhelm the general reader", [26] and another finding the book suitable "for parents trying to support teenagers in their studies of mathematics – or in fact, law". [27]
While most reviews were positive, there was some criticism concerning its over-simplification of mathematics' influence in complex trial proceedings. One reviewer finds that, while the book's description of the weakness of some mathematics presented in courtrooms is valid, the text magnifies mathematics' role in legal proceedings, which traditionally feature evidentiary analysis at appellate as well as trial stages and have preexisting standards for treating certain types of evidence. [28] Another suggests the book was influenced by the authors' selection of cases to show a "disastrous record of causing judicial error", thus attributing insufficient weight to the counterbalancing traditionally inherent in legal proceedings—as lawyers attack opposing evidence and experts with their own, and appellate judges write to influence the conduct of trial judges faced with various types of ordinary and expert testimony. [29]
Schneps has produced English-language translations of several French-language books and papers, including Invitation to the mathematics of Fermat-Wiles, [30] Galois theory, [31] A Mathematician Grappling With His Century, [32] Hodge Theory and Complex Algebraic Geometry II, [33] p-adic L-Functions and p-Adic Representations, [34] and Renormalization methods : critical phenomena, chaos, fractal structures. [35]
Mathematician Alexander Grothendieck became a recluse in 1991 and removed his published works from circulation. More than a decade later, Schneps and Pierre Lochak located him in a town in the Pyrenees, then carried on a correspondence. Thus they became among "the last members of the mathematical establishment to come into contact with him". [36] Schneps became a founding member of the Grothendieck Circle, a group dedicated to making information by and about Grothendieck available, and created and maintains the Grothendieck Circle website, a repository of information regarding Grothendieck, including his own unpublished writings. [37] She also assisted with the translation of his correspondence with Jean-Pierre Serre. [38]
In 2004, Schneps published (as Catherine Shaw) The Three Body Problem, a Cambridge Mystery, [39] a murder mystery novel involving mathematicians in Cambridge in the late 1800s, working on the three-body problem. The title is a double entendre, referring to both the mathematical problem and the three murder victims. While a mathematician reviewing the book disliked the Victorian writing style, he found the math accurate, and the mathematicians' personalities and sociology "well portrayed". [40] When another reviewer contacted the author, she confirmed that Catherine Shaw was a pseudonym and that she was actually an academic and practicing mathematician but preferred to remain anonymous. [41] It has since been revealed that Catherine Shaw is the pseudonym of Leila Schneps. [42]
Schneps, as Catherine Shaw, has published four historical novels in the series, all featuring the same main character Vanessa Duncan, and all following mathematical themes:
As Shaw, Schneps has also published a non-fiction guide to solving Sudoku and Kakuro puzzles. [53]
Schneps promotes public awareness of the importance of the proper use of mathematics and statistics in criminal proceedings. [24] [54] Schneps is a member of the Bayes and the Law International Consortium. [55]
Coralie Colmez is the daughter of Schneps and Pierre Colmez. [56] [57]
Alexander Grothendieck was a German-born mathematician who became the leading figure in the creation of modern algebraic geometry. His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory, and category theory to its foundations, while his so-called "relative" perspective led to revolutionary advances in many areas of pure mathematics. He is considered by many to be the greatest mathematician of the twentieth century.
Jean-Pierre Serre is a French mathematician who has made contributions to algebraic topology, algebraic geometry and algebraic number theory. He was awarded the Fields Medal in 1954, the Wolf Prize in 2000 and the inaugural Abel Prize in 2003.
Pierre René, Viscount Deligne is a Belgian mathematician. He is best known for work on the Weil conjectures, leading to a complete proof in 1973. He is the winner of the 2013 Abel Prize, 2008 Wolf Prize, 1988 Crafoord Prize, and 1978 Fields Medal.
In mathematics, a dessin d'enfant is a type of graph embedding used to study Riemann surfaces and to provide combinatorial invariants for the action of the absolute Galois group of the rational numbers. The name of these embeddings is French for a "child's drawing"; its plural is either dessins d'enfant, "child's drawings", or dessins d'enfants, "children's drawings".
Yuval Zvi Flicker is an American mathematician. His primary research interests include automorphic representations.
"Esquisse d'un Programme" is a famous proposal for long-term mathematical research made by the German-born, French mathematician Alexander Grothendieck in 1984. He pursued the sequence of logically linked ideas in his important project proposal from 1984 until 1988, but his proposed research continues to date to be of major interest in several branches of advanced mathematics. Grothendieck's vision provides inspiration today for several developments in mathematics such as the extension and generalization of Galois theory, which is currently being extended based on his original proposal.
In mathematics, a p-adic zeta function, or more generally a p-adic L-function, is a function analogous to the Riemann zeta function, or more general L-functions, but whose domain and target are p-adic. For example, the domain could be the p-adic integersZp, a profinite p-group, or a p-adic family of Galois representations, and the image could be the p-adic numbersQp or its algebraic closure.
Anabelian geometry is a theory in number theory which describes the way in which the algebraic fundamental group G of a certain arithmetic variety X, or some related geometric object, can help to recover X. The first results for number fields and their absolute Galois groups were obtained by Jürgen Neukirch, Masatoshi Gündüz Ikeda, Kenkichi Iwasawa, and Kôji Uchida, prior to conjectures made about hyperbolic curves over number fields by Alexander Grothendieck. As introduced in Esquisse d'un Programme the latter were about how topological homomorphisms between two arithmetic fundamental groups of two hyperbolic curves over number fields correspond to maps between the curves. A first version of Grothendieck's anabelian conjecture was solved by Hiroaki Nakamura and Akio Tamagawa, then completed by Shinichi Mochizuki.
Pierre Colmez is a French mathematician, notable for his work on p-adic analysis.
In mathematics, the André–Oort conjecture is a problem in Diophantine geometry, a branch of number theory, that can be seen as a non-abelian analogue of the Manin–Mumford conjecture, which is now a theorem. The conjecture concerns itself with a characterization of the Zariski closure of sets of special points in Shimura varieties. A special case of the conjecture was stated by Yves André in 1989 and a more general statement was conjectured by Frans Oort in 1995. The modern version is a natural generalization of these two conjectures.
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In anabelian geometry, a branch of algebraic geometry, the section conjecture gives a conjectural description of the splittings of the group homomorphism , where is a complete smooth curve of genus at least 2 over a field that is finitely generated over , in terms of decomposition groups of rational points of . The conjecture was introduced by Alexander Grothendieck in a 1983 letter to Gerd Faltings.
In mathematics, the Grothendieck–Teichmüller groupGT is a group closely related to the absolute Galois group of the rational numbers. It was introduced by Vladimir Drinfeld and named after Alexander Grothendieck and Oswald Teichmüller, based on Grothendieck's suggestion in his 1984 essay Esquisse d'un Programme to study the absolute Galois group of the rationals by relating it to its action on the Teichmüller tower of Teichmüller groupoids Tg,n, the fundamental groupoids of moduli stacks of genus g curves with n points removed. There are several minor variations of the group: a discrete version, a pro-l version, a k-pro-unipotent version, and a profinite version; the first three versions were defined by Drinfeld, and the version most often used is the profinite version.
Coralie Colmez is a French author and tutor in mathematics and mathematics education.
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In mathematics, a Siegel modular variety or Siegel moduli space is an algebraic variety that parametrizes certain types of abelian varieties of a fixed dimension. More precisely, Siegel modular varieties are the moduli spaces of principally polarized abelian varieties of a fixed dimension. They are named after Carl Ludwig Siegel, the 20th-century German number theorist who introduced the varieties in 1943.
In mathematics, a tame topology is a hypothetical topology proposed by Alexander Grothendieck in his research program Esquisse d’un programme under the French name topologie modérée. It is a topology in which the theory of dévissage can be applied to stratified structures such as semialgebraic or semianalytic sets, and which excludes some pathological spaces that do not correspond to intuitive notions of spaces.
Math on Trial: How Numbers Get Used and Abused in the Courtroom is a book on mathematical and statistical reasoning in legal argumentation, for a popular audience. It was written by American mathematician Leila Schneps and her daughter, French mathematics educator Coralie Colmez, and published in 2013 by Basic Books.
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