Nigel Boston

Nigel Boston is a British-American mathematician renowned for his contributions to algebra, number theory, and coding theory. He is a professor at the University of Wisconsin–Madison, where he conducts research and teaches in the Department of Mathematics.

Dr. Boston's work encompasses areas such as:

Group Theory: He has studied the properties and structures of groups, which are fundamental objects in abstract algebra.

Galois Theory: He has worked on understanding symmetries of solutions to polynomial equations, extending the classical Galois theory.

Number Theory: His research includes investigations into properties of numbers, especially integers, and their relationships.

Coding Theory: He has applied mathematical concepts to improve error-detecting and error-correcting codes, which are crucial in digital communications and data storage.

Throughout his career, Nigel Boston has authored numerous research papers and has been involved in various collaborative projects that bridge pure mathematics and practical applications, such as cryptography and network coding. He is recognized for his ability to connect abstract mathematical theories with real-world problems.

All published works

Action	Title	Year	Authors
+ PDF Chat	The Distribution of the Number of Real Solutions to the Power Flow Equations	2022	Julia Lindberg Alisha Zachariah Nigel Boston Bernard C. Lesieutre
+ PDF Chat	Heuristics for 2-class Towers of Cyclic Cubic Fields	2021	Nigel Boston Michael R. Bush
+	Heuristics for $2$-class Towers of Cyclic Cubic Fields	2020	Nigel Boston Michael R. Bush
+ PDF Chat	Violations of the Ingleton inequality and revising the four-atom conjecture	2020	Nigel Boston Ting-Ting Nan
+	Exploiting Symmetry in the Power Flow Equations Using Monodromy	2020	Julia Lindberg Nigel Boston Bernard C. Lesieutre
+ PDF Chat	Exploiting symmetry in the power flow equations using monodromy	2020	Julia Lindberg Nigel Boston Bernard C. Lesieutre
+	Heuristics for $2$-class Towers of Cyclic Cubic Fields	2020	Nigel Boston Michael R. Bush
+	Exploiting Symmetry in the Power Flow Equations Using Monodromy	2020	Julia Lindberg Nigel Boston Bernard C. Lesieutre
+	The Distribution of the Number of Real Solutions to the Power Flow Equations	2020	Julia Lindberg Alisha Zachariah Nigel Boston Bernard C. Lesieutre
+	HEURISTICS FOR -CLASS TOWERS OF REAL QUADRATIC FIELDS	2019	Nigel Boston Michael R. Bush Farshid Hajir
+	Explicit Universal Deformations of Galois Representations	2018	Nigel Boston Barry Mazur
+ PDF Chat	Exploiting algebraic structure in global optimization and the Belgian chocolate problem	2018	Zachary Charles Nigel Boston
+ PDF Chat	The weight distribution of quasi-quadratic residue codes	2018	Nigel Boston Jing Hao
+	Heuristics for p-class towers of real quadratic fields	2018	Nigel Boston Michael R. Bush Farshid Hajir
+	The 2-Class Tower of $$\mathbb {Q}(\sqrt{-5460})$$Q(-5460)	2018	Nigel Boston Jiuya Wang
+	Exploiting Algebraic Structure in Global Optimization and the Belgian Chocolate Problem	2017	Zachary Charles Nigel Boston
+ PDF Chat	Non-abelian Cohen–Lenstra heuristics over function fields	2017	Nigel Boston Melanie Matchett Wood
+	The $2$-Class Tower of $\mathbb{Q}(\sqrt{-5460})$	2017	Nigel Boston Jiuya Wang
+	The Weight Distribution of Quasi-quadratic Residue Codes	2017	Nigel Boston Jing Hao
+	Exploiting Algebraic Structure in Global Optimization and the Belgian Chocolate Problem	2017	Zachary Charles Nigel Boston
+	Heuristics for p-class towers of imaginary quadratic fields	2016	Nigel Boston Michael R. Bush Farshid Hajir
+ PDF Chat	A Characterization of Deterministic Sampling Patterns for Low-Rank Matrix Completion	2016	Daniel Pimentel-Alarcón Nigel Boston Robert D. Nowak
+ PDF Chat	A characterization of deterministic sampling patterns for low-rank matrix completion	2015	Daniel Pimentel-Alarcón Nigel Boston Robert D. Nowak
+	A Refined Conjecture for Factorizations of Iterates of Quadratic Polynomials over Finite Fields	2015	Vefa Goksel Shixiang Xia Nigel Boston
+ PDF Chat	Deterministic conditions for subspace identifiability from incomplete sampling	2015	Daniel Pimentel-Alarcón Nigel Boston Robert D. Nowak
+	A Survey of Beauville $$p$$-Groups	2015	Nigel Boston
+	Regular Algebraic Surfaces, Ramification Structures and Projective Planes	2015	Nathan Barker Nigel Boston Norbert Peyerimhoff Alina Vdovina
+	Deterministic Conditions for Subspace Identifiability from Incomplete Sampling	2014	Daniel Pimentel-Alarcón Robert D. Nowak Nigel Boston
+	An Infinite Family of 2-Groups with Mixed Beauville Structures	2014	Nathan Barker Nigel Boston Norbert Peyerimhoff Alina Vdovina
+	On the Algebraic Structure of Linear Trellises	2014	David V. Conti Nigel Boston
+	Deterministic Conditions for Subspace Identifiability from Incomplete Sampling	2014	Daniel Pimentel-Alarcón Robert D. Nowak Nigel Boston
+	On the Algebraic Structure of Linear Trellises	2014	David V. Conti Nigel Boston
+	A Refined Conjecture For Factoring Iterates Of Quadratic Polynomials Over Finite Fields	2013	Vefa Goksel Shixiang Xia Nigel Boston
+	A refinement of the Four-Atom Conjecture	2013	Nigel Boston Ting-Ting Nan
+	An infinite family of 2-groups with mixed Beauville structures	2013	Nathan Barker Nigel Boston Norbert Peyerimhoff Alina Vdovina
+	The Art of Iterating Rational Functions over Finite Fields	2013	Nigel Boston Michael E. Zieve
+	A Refined Conjecture For Factoring Iterates Of Quadratic Polynomials Over Finite Fields	2013	Vefa Goksel Shixiang Xia Nigel Boston
+	An infinite family of 2-groups with mixed Beauville structures	2013	Nathan Barker Nigel Boston Norbert Peyerimhoff Alina Vdovina
+	Large violations of the Ingleton inequality	2012	Nigel Boston Ting-Ting Nan
+	The Factorization Theorem and new algebraic insights into the theory of linear trellises	2012	David V. Conti Nigel Boston
+	On the Belgian chocolate problem and output feedback stabilization: Efficacy of algebraic methods	2012	Nigel Boston
+	A Note on Beauville p-Groups	2012	Nathan Barker Nigel Boston Ben Fairbairn
+ PDF Chat	None	2012	Rafe Jones Nigel Boston Matthew A. Papanikolas
+	Applications of Algebra to Communications, Control, and Signal Processing	2012	Nigel Boston
+	Algebraic Tools	2012	Nigel Boston
+	Emerging Applications to Signal Processing	2012	Nigel Boston
+	Settled polynomials over finite fields	2011	Rafe Jones Nigel Boston
+ PDF Chat	Random pro-$p$ groups, braid groups, and random tame Galois groups	2011	Nigel Boston Jordan S. Ellenberg
+	New examples of Beauville surfaces	2011	Nathan Barker Nigel Boston Norbert Peyerimhoff Alina Vdovina
+	Heuristics for $p$-class towers of imaginary quadratic fields, with an Appendix by Jonathan Blackhurst	2011	Nigel Boston Michael R. Bush Farshid Hajir
+	Regular algebraic surfaces isogenous to a higher product constructed from group representations using projective planes	2011	Nathan Barker Nigel Boston Norbert Peyerimhoff Alina Vdovina
+	A Note on Beauville p-Groups	2011	Nathan Barker Nigel Boston Ben Fairbairn
+	The weight distributions of cyclic codes with two zeros and zeta functions	2010	Nigel Boston Gary McGuire
+ PDF Chat	Spaces of constant rank matrices over GF(2)	2010	Nigel Boston
+	Spaces of constant rank matrices over .	2010	Nigel Boston
+ PDF Chat	Large transitive groups with many elements having fixed points	2010	Nigel Boston
+ PDF Chat	The Image of an Arboreal Galois Representation	2009	Nigel Boston Rafe Jones
+	Pro-$p$ Extensions of Global Fields and pro-$p$ Groups	2007	Nigel Boston John Coates Fritz Grunewald
+	Arboreal Galois representations	2007	Nigel Boston Rafe Jones
+ PDF Chat	Galois groups of tamely ramified p-extensions	2007	Nigel Boston
+	Summation Invariant and Its Applications to Shape Recognition	2006	Weiyang Lin Nigel Boston Yu Hen Hu
+	Reducing the Fontaine-Mazur Conjecture to Group Theory	2006	Nigel Boston
+ PDF Chat	Pro–<i>p</i>groups and towers of rational homology spheres	2006	Nigel Boston Jordan S. Ellenberg
+	Embedding 2-groups in groups generated by involutions	2006	Nigel Boston
+	Computing Pro-P Galois Groups	2006	Nigel Boston Harris Nover
+	Class numbers of p-groups of a given order	2004	Nigel Boston I. M. Isaacs
+	Strategies for The Weakest Link	2003	Nigel Boston
+ PDF Chat	Genus Two Hyperelliptic Curve Coprocessor	2003	Nigel Boston T. Clancy Y. Liow Jossemia Webster
+	Makhoul's conjecture for p = 2	2002	Nigel Boston
+ PDF Chat	Explicit computation of Galois p-groups unramified at p	2002	Nigel Boston C. R. Leedham-Green
+	Bounding minimum distances of cyclic codes using algebraic geometry	2001	Nigel Boston
+	Maximal 2-Extensions with Restricted Ramification	2000	Nigel Boston David Perry
+ PDF Chat	Characteristic <i>p</i> Galois Representations That Arise from Drinfeld Modules	2000	Nigel Boston David T. Ose
+ PDF Chat	2-groups with few conjugacy classes	2000	Nigel Boston Judy L. Walker
+	Tree representations of Galois groups	2000	Nigel Boston
+	Bounding minimum distances of cyclic codes using algebraic geometry	2000	Nigel Boston
+	Explicit computation of Galois p-groups unramified at p	2000	Nigel Boston C. R. Leedham-Green
+	p-adic Galois Representations and pro-p Galois Groups	2000	Nigel Boston
+	Some Cases of the Fontaine–Mazur Conjecture, II	1999	Nigel Boston
+ PDF Chat	Counterexamples to a conjecture of Lemmermeyer	1999	Nigel Boston C. R. Leedham-Green
+	The Minimum Distance of the Binary Quadratic Residue Code	1999	Nigel Boston D. E. Kuhlman
+	Some cases of the Fontaine-Mazur conjecture, II	1998	Nigel Boston
+	Counterexamples to a conjecture of Lemmermeyer	1998	Nigel Boston C. R. Leedham-Green
+	Characteristic p Galois representations that are produced by Drinfeld	1997	Nigel Boston David T. Ose
+	A probabilistic generalization of the Riemann zeta function	1996	Nigel Boston
+	Quadratics Representing Primes	1995	Nigel Boston Marshall L. Greenwood
+	Quadratics Representing Primes	1995	Nigel Boston Marshall L. Greenwood
+	A refinement of the Faltings–Serre method	1995	Nigel Boston
+	The World's Most Famous Math Problem (The Proof of Fermat's Last Theorem and Other Mathematical Mysteries).	1995	Nigel Boston Andrew Granville Marilyn vos Savant
+	The World's Most Famous Math Problem (The Proof of Fermat's Last Theorem and Other Mathematical Mysteries). By Marilyn vos Savant	1995	Nigel Boston Andrew Granville
+	A Taylor-made Plug for Wiles' Proof	1995	Nigel Boston
+ PDF Chat	The proportion of fixed-point-free elements of a transitive permutation group	1993	Nigel Boston Walter Dabrowski Tuval Foguel Paul J. Gies J. L. Leavitt David T. Ose David A. Jackson
+	Representations related to CM elliptic curves	1993	Nigel Boston Stephen V. Ullom
+	Some cases of the Fontaine-Mazur conjecture	1992	Nigel Boston
+	Families of Galois representations—increasing the ramification	1992	Nigel Boston
+	Explicit deformation of Galois representations	1991	Nigel Boston
+	Perfect Groups.	1991	Nigel Boston Derek F. Holt W. Plesken
+	Quotients of group rings arising from two-dimensional representations	1991	H. W. Lenstra Nigel Boston Kenneth A. Ribet
+	Deformations of Galois Representations Associated to the Cusp Form △	1990	Nigel Boston
+	Deformations of Galois Representations Associated to the Cusp Form Δ	1990	Nigel Boston
+	A class of soluble groups	1984	Nigel Boston

Common Coauthors

Coauthor	Papers Together
Michael R. Bush	7
Nathan Barker	7
Norbert Peyerimhoff	6
Alina Vdovina	6
Daniel Pimentel-Alarcón	5
Bernard C. Lesieutre	5
Robert D. Nowak	5
Julia Lindberg	5
C. R. Leedham-Green	4
Farshid Hajir	4
Rafe Jones	4
Ting-Ting Nan	3
David V. Conti	3
Zachary Charles	3
Vefa Goksel	3
David T. Ose	3
Shixiang Xia	3
Andrew Granville	2
Ben Fairbairn	2
Jing Hao	2
Jordan S. Ellenberg	2
Jiuya Wang	2
Alisha Zachariah	2
Marshall L. Greenwood	2
Walter Dabrowski	1
Gary McGuire	1
David A. Jackson	1
I. M. Isaacs	1
W. Plesken	1
John Coates	1
Michael E. Zieve	1
Harris Nover	1
Melanie Matchett Wood	1
Nathan Barker	1
D. E. Kuhlman	1
Tuval Foguel	1
Fritz Grunewald	1
Derek F. Holt	1
T. Clancy	1
Yu Hen Hu	1
Marilyn vos Savant	1
Barry Mazur	1
H. W. Lenstra	1
Judy L. Walker	1
Weiyang Lin	1
Kenneth A. Ribet	1
J. L. Leavitt	1
Y. Liow	1
Paul J. Gies	1
David Perry	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	The Magma Algebra System I: The User Language	1997	Wieb Bosma John Cannon Catherine Playoust	16
+	Explicit deformation of Galois representations	1991	Nigel Boston	8
+	Some cases of the Fontaine-Mazur conjecture	1992	Nigel Boston	8
+ PDF Chat	Explicit computation of Galois p-groups unramified at p	2002	Nigel Boston C. R. Leedham-Green	7
+	HANDBOOK OF MAGMA FUNCTIONS	2011	John Cannon Wieb Bosma Claus Fieker Allan Steel	7
+ PDF Chat	Heuristics on class groups of number fields	1984	Henri Cohen H. W. Lenstra	7
+	Beauville surfaces without real structures	2005	Ingrid Bauer Fabrizio Catanese Fritz Grunewald	7
+	Some Cases of the Fontaine–Mazur Conjecture, II	1999	Nigel Boston	6
+	Deforming Galois Representations	1989	Barry Mazur	6
+	Galoissche Theorie der p-Erweiterungen	1970	Hermann Koch	6
+	On the maximal unramified p-extension of an algebraic number field.	1993	Kay Wingberg	6
+	Fibred surfaces, varieties isogenous to a product and related moduli spaces	2000	Fabrizio Catanese	6
+	Group Presentation, p-Adic Analytic Groups and Lattices in SL 2 ( C )	1983	Alexander Lubotzky	6
+	Star Graphs, Projective Planes and Free Subgroups in Small Cancellation Groups	1988	Martin Edjvet James Howie	5
+	New examples of Beauville surfaces	2011	Nathan Barker Nigel Boston Norbert Peyerimhoff Alina Vdovina	5
+	Propri�t�s galoisiennes des points d'ordre fini des courbes elliptiques	1971	Jean-Pierre Serre	5
+ PDF Chat	Computation of Galois groups associated to the 2-class towers of some quadratic fields	2003	Michael R. Bush	5
+	Groups acting simply transitively on the vertices of a building of type� 2, I	1993	Donald I. Cartwright Anna Maria Mantero Tim Steger Anna Zappa	5
+ PDF Chat	The Classification of Surfaces with pg = q = 0 Isogenous to a Product of Curves	2008	Ingrid Bauer Fabrizio Catanese Fritz Grunewald	5
+ PDF Chat	Galois groups of tamely ramified p-extensions	2007	Nigel Boston	4
+	A Simpler Approach to Matrix Completion	2009	Benjamin Recht	4
+	Tamely Ramified Towers and Discriminant Bounds for Number Fields—II	2002	Farshid Hajir Christian Maire	4
+ PDF Chat	The density of prime divisors in the arithmetic dynamics of quadratic polynomials	2008	Rafe Jones	4
+ PDF Chat	Note on <i>p</i>-Groups	1950	Noboru Ιτο	4
+	Maximal 2-Extensions with Restricted Ramification	2000	Nigel Boston David Perry	4
+	Cohen–Lenstra heuristic and roots of unity	2008	Gunter Malle	4
+	Cayley graph expanders and groups of finite width	2011	Norbert Peyerimhoff Alina Vdovina	4
+	Explicit Universal Deformations of Galois Representations	2018	Nigel Boston Barry Mazur	4
+	A Combinatorial Algebraic Approach for the Identifiability of Low-Rank Matrix Completion	2012	Franz J. Király Ryota Tomioka	4
+	Computing Pro-P Galois Groups	2006	Nigel Boston Harris Nover	4
+	Sur les représentations modulaires de degré 2 de Gal(Q¯/Q)	1987	Jean-Pierre Serre	4
+	Heuristics for p-class towers of imaginary quadratic fields	2016	Nigel Boston Michael R. Bush Farshid Hajir	4
+ PDF Chat	Totally disconnected, nilpotent, locally compact groups	1997	George A. Willis	3
+ PDF Chat	Linear Pro-p-Groups of Finite Width	1997	Gundel Klaas C. R. Leedham-Green Wilhelm Plesken	3
+	On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory	1996	David J. Broadhurst	3
+ PDF Chat	Mild pro-p-groups and Galois groups of p-extensions of ℚ	2006	John Labute	3
+ PDF Chat	Counterexamples to a conjecture of Lemmermeyer	1999	Nigel Boston C. R. Leedham-Green	3
+ PDF Chat	Iterated Galois towers, their associated martingales, and the $p$-adic Mandelbrot set	2007	Rafe Jones	3
+ PDF Chat	Low-rank matrix completion using alternating minimization	2013	Prateek Jain Praneeth Netrapalli Sujay Sanghavi	3
+	Introduction to Cyclotomic Fields	1982	Lawrence C. Washington	3
+	On ℓ-adic representations and congruences for coefficients of modular forms (II)	1977	H. P. F. Swinnerton-Dyer	3
+	Galois groups over $$cQ$$ of some iterated polynomials	1992	Michael Stoll	3
+ PDF Chat	Functors of Artin rings	1968	Michael Schlessinger	3
+	Settled polynomials over finite fields	2011	Rafe Jones Nigel Boston	3
+ PDF Chat	On Beauville surfaces	2011	Yolanda Fuertes Gabino González-Diez Andrei Jaikin‐Zapirain	3
+	On Beauville structures on the groups S n and A n	2009	Yolanda Fuertes Gabino González-Diez	3
+ PDF Chat	A class group heuristic based on the distribution of 1-eigenspaces in matrix groups	2014	Michael Adam Gunter Malle	3
+	On Almost Fixed Point Free Automorphisms	1993	Aner Shalev	3
+	A Contribution to the Theory of Groups of Prime-Power Order	1934	P. Hall	3
+	Non-Shannon Information Inequalities in Four Random Variables	2011	Randall Dougherty C. Freiling K. Zeger	3