Ira Martin Gessel (born 9 April 1951 in Philadelphia, Pennsylvania) is an American mathematician, known for his work 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 ...

. He is a long-time faculty member at Brandeis University and resides in Arlington, Massachusetts.

Education and career

Gessel studied at Harvard University graduating ''

magna cum laude Latin honors are a system of Latin phrases used in some colleges and universities to indicate the level of distinction with which an academic degree has been earned. The system is primarily used in the United States. It is also used in some So ...

'' in 1973. There, he became a Putnam Fellow in 1972, alongside Arthur Rubin and

David Vogan David Alexander Vogan, Jr. (born September 8, 1954) is a mathematician at the Massachusetts Institute of Technology who works on unitary representations of simple Lie groups. While studying at the University of Chicago, he became a Putnam Fellow ...

. He received his Ph.D. at MIT and was the first student of Richard P. Stanley. He was then a postdoctoral fellow at the

IBM Watson Research Center The Thomas J. Watson Research Center is the headquarters for IBM Research. The center comprises three sites, with its main laboratory in Yorktown Heights, New York, Yorktown Heights, New York (state), New York, U.S., 38 miles (61 km) north ...

and MIT. He then joined Brandeis University faculty in 1984. He was promoted to Professor of Mathematics and Computer Science in 1990, became a chair in 1996–98, and Professor Emeritus in 2015. Gessel is a prolific contributor to

enumerative An enumeration is a complete, ordered listing of all the items in a collection. The term is commonly used in mathematics and computer science to refer to a listing of all of the elements of a set. The precise requirements for an enumeration (f ...

and

algebraic combinatorics Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algeb ...

. He is credited with the invention of quasisymmetric functions in 1984 and foundational work on the Lagrange inversion theorem. As of 2017, Gessel was an advisor of 27 Ph.D. students. Gessel was elected a Fellow of the American Mathematical Society in the inaugural class of 2012. Since 2015, he is an Associate Editor of the '' Digital Library of Mathematical Functions''.

Gessel's lattice path conjecture

Gessel has made significant contributions to an area in combinatorics known as lattice walks, which usually take place on the integer lattice, and are sometimes confined to the upper right quadrant. An excursion is a lattice walk which starts at the origin and returns to the origin. A lattice excursion in the upper right quadrant with four possible steps, up, down, northeast, and southwest, is now known as a Gessel excursion. By 2001 Gessel had noted empirically, and conjectured, that the number of Gessel excursions with 2n steps admit a simple hypergeometric closed form. This closed form counting function equation became known as Gessel's lattice path conjecture. A computer aided proof of Gessel's conjecture by

Manuel Kauers Manuel Kauers (born 20 February 1979 in Lahnstein, West Germany) is a German mathematician and computer scientist. He is working on computer algebra and its applications to discrete mathematics. He is currently professor for algebra at Joha ...

, Christoph Koutschan, and Doron Zeilberger, was published in 2009. The 2022

David P. Robbins Prize The David P. Robbins Prize for papers reporting novel research in algebra, combinatorics, or discrete mathematics is awarded both by the American Mathematical Society (AMS) and by the Mathematical Association of America (MAA). The AMS award reco ...

of the American Mathematical Society will be awarded to Alin Bostan, Irina Kurkova, and Kilian Raschel, for their 2017 paper “A human proof of Gessel's lattice path conjecture.”

Political activism

In 1970, while a senior in high school, Ira Gessel and his brother Michael Gessel started a

grassroots A grassroots movement is one that uses the people in a given district, region or community as the basis for a political or economic movement. Grassroots movements and organizations use collective action from the local level to effect change at t ...

political organization to end pay toilets in America.A. Gordon,
Why Don’t We Have Pay Toilets in America?
''Pacific Standard'', Sep 17, 2014. The movement was largely successful and was disbanded in 1976.

References

External links

Ira Gessel's homepage
* {{DEFAULTSORT:Gessel, Ira 1951 births Living people 20th-century American mathematicians 21st-century American mathematicians Combinatorialists Fellows of the American Mathematical Society 20th-century American Jews Jewish scientists People from Philadelphia Brandeis University faculty Harvard University alumni Massachusetts Institute of Technology alumni 21st-century American Jews Putnam Fellows

Education and career

Gessel's lattice path conjecture

Political activism

See also

References

External links