Thomas Henry Brylawski (June 17, 1944 – July 18, 2007) was an American mathematician and professor at the

University of North Carolina, Chapel Hill A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States, th ...

. He worked primarily in

matroid theory In combinatorics, a branch of mathematics, a matroid is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid axiomatically, the most significant being in ...

Education and career

Brylawski was born in 1944, and grew up in

Washington, D.C. ) , image_skyline = , image_caption = Clockwise from top left: the Washington Monument and Lincoln Memorial on the National Mall, United States Capitol, Logan Circle, Jefferson Memorial, White House, Adams Morgan, ...

He attended the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

for his undergraduate degree, finishing with a Bachelor of Science in 1966. He then went on to

Dartmouth College Dartmouth College (; ) is a private research university in Hanover, New Hampshire. Established in 1769 by Eleazar Wheelock, it is one of the nine colonial colleges chartered before the American Revolution. Although founded to educate Native A ...

for his graduate work. He completed his

PhD PHD or PhD may refer to: * Doctor of Philosophy (PhD), an academic qualification Entertainment * '' PhD: Phantasy Degree'', a Korean comic series * ''Piled Higher and Deeper'', a web comic * Ph.D. (band), a 1980s British group ** Ph.D. (Ph.D. albu ...

under the direction of

Gian-Carlo Rota Gian-Carlo Rota (April 27, 1932 – April 18, 1999) was an Italian-American mathematician and philosopher. He spent most of his career at the Massachusetts Institute of Technology, where he worked in combinatorics, functional analysis, pro ...

and Robert Norman in 1970. After his PhD, he moved to the

, where he spent the rest of his career. Brylawski was an editor for the ''

Proceedings of the American Mathematical Society ''Proceedings of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. As a requirement, all articles must be at most 15 printed pages. According to the ' ...

'' from 1977 until 1989. Brylawski wrote 40 mathematical publications, and advised 6 PhD students. He died in 2007 of

esophageal cancer Esophageal cancer is cancer arising from the esophagus—the food pipe that runs between the throat and the stomach. Symptoms often include difficulty in swallowing and weight loss. Other symptoms may include pain when swallowing, a hoarse voice ...

at the Duke Hospice inpatient facility in

Hillsborough, North Carolina The town of Hillsborough is the county seat of Orange County, North Carolina, United States and is located along the Eno River. The population was 6,087 in 2010, but it grew rapidly to 9,660 by 2020. Its name was unofficially shortened to "Hillsb ...

Work

Brylawski's early work used ideas and tools from

category theory Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, cate ...

to understand the

Tutte polynomial The Tutte polynomial, also called the dichromate or the Tutte–Whitney polynomial, is a graph polynomial. It is a polynomial in two variables which plays an important role in graph theory. It is defined for every undirected graph G and contai ...

of a matroid. Indeed, this idea already appeared in his thesis, which made constructions in matroid theory similar to the

Grothendieck group In mathematics, the Grothendieck group, or group of differences, of a commutative monoid is a certain abelian group. This abelian group is constructed from in the most universal way, in the sense that any abelian group containing a homomorphic i ...

. He developed similar ideas in two papers in the ''

Transactions of the American Mathematical Society The ''Transactions of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. It was established in 1900. As a requirement, all articles must be more than 15 p ...

''. Another influential early paper of Brylawski's, published in the same journal, described the influence of a

modular Broadly speaking, modularity is the degree to which a system's components may be separated and recombined, often with the benefit of flexibility and variety in use. The concept of modularity is used primarily to reduce complexity by breaking a sy ...

element in the lattice of

flats Flat or flats may refer to: Architecture * Flat (housing), an apartment in the United Kingdom, Ireland, Australia and other Commonwealth countries Arts and entertainment * Flat (music), a symbol () which denotes a lower pitch * Flat (soldier), ...

on the

characteristic polynomial In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues as roots. It has the determinant and the trace of the matrix among its coefficients. The chara ...

of a matroid. Brylawski also contributed expository chapters to several matroid theory books that appeared in the ''Encyclopedia of Mathematics and its Applications'' series published by

Cambridge University Press Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press A university press is an academic publishing hou ...

. The Tutte polynomial chapter (written jointly with James Oxley) has around 500 citations. In addition to his work in matroid theory, Brylawski also had an interest in mathematics in art, particularly in the role of symmetry in art. He gave lectures on mathematics in art on two occasions at the

National Gallery of Art The National Gallery of Art, and its attached Sculpture Garden, is a national art museum in Washington, D.C., United States, located on the National Mall, between 3rd and 9th Streets, at Constitution Avenue NW. Open to the public and free of char ...

Awards and honors

A memorial conference was held in honor of Brylawski in October 2008 at the

, and a special issue of the ''

European Journal of Combinatorics European, or Europeans, or Europeneans, may refer to: In general * ''European'', an adjective referring to something of, from, or related to Europe ** Ethnic groups in Europe ** Demographics of Europe ** European cuisine, the cuisines of Europe ...

'' in 2011 was dedicated as a tribute to the work of Brylawski.

References

{{DEFAULTSORT:Brylawski, Thomas Henry 1944 births 2007 deaths 20th-century American mathematicians 21st-century American mathematicians Massachusetts Institute of Technology School of Science alumni Dartmouth College alumni University of North Carolina at Chapel Hill faculty Combinatorialists Academic journal editors Mathematicians from Washington, D.C. Deaths from cancer in North Carolina