Karl Mahlburg
Encyclopedia
Karl Mahlburg is an American
mathematician
whose research interests lie in the areas of modular form
s, partitions, combinatorics
and number theory
.
He submitted a paper to Proceedings of the National Academy of Sciences
(PNAS) entitled Partition Congruences and the Andrews-Garvan-Dyson Crank in 2005, and the paper won the PNAS first Paper of the Year prize.
The paper extends a result first conjectured by Srinivasa Ramanujan
and later detailed by Freeman Dyson
, George Andrews, Frank Garvan, and Mahlburg's advisor Ken Ono
called the crank having to do with congruence patterns in partitions. Until recently such congruence patterns were only known to occur for 5, 7, and 11. Mahlburg's result extends this to all prime number
s.
Mahlburg was an undergraduate at Harvey Mudd College
, where he graduated with highest distinction in 2001 with a B.S. in Mathematics. In 2006, he graduated from the University of Wisconsin–Madison
with a Ph.D. in Mathematics.
Mahlburg's Erdős number
is 3.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
whose research interests lie in the areas of modular form
Modular form
In mathematics, a modular form is a analytic function on the upper half-plane satisfying a certain kind of functional equation and growth condition. The theory of modular forms therefore belongs to complex analysis but the main importance of the theory has traditionally been in its connections...
s, partitions, combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
and number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
.
He submitted a paper to Proceedings of the National Academy of Sciences
Proceedings of the National Academy of Sciences
The Proceedings of the National Academy of Sciences of the United States of America, usually referred to as PNAS, is the official journal of the United States National Academy of Sciences...
(PNAS) entitled Partition Congruences and the Andrews-Garvan-Dyson Crank in 2005, and the paper won the PNAS first Paper of the Year prize.
The paper extends a result first conjectured by Srinivasa Ramanujan
Srinivasa Ramanujan
Srīnivāsa Aiyangār Rāmānujan FRS, better known as Srinivasa Iyengar Ramanujan was a Indian mathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series and continued fractions...
and later detailed by Freeman Dyson
Freeman Dyson
Freeman John Dyson FRS is a British-born American theoretical physicist and mathematician, famous for his work in quantum field theory, solid-state physics, astronomy and nuclear engineering. Dyson is a member of the Board of Sponsors of the Bulletin of the Atomic Scientists...
, George Andrews, Frank Garvan, and Mahlburg's advisor Ken Ono
Ken Ono
Ken Ono is an American mathematician who specializes in number theory, especially in integer partitions, modular forms, and the fields of interest to Srinivasa Ramanujan...
called the crank having to do with congruence patterns in partitions. Until recently such congruence patterns were only known to occur for 5, 7, and 11. Mahlburg's result extends this to all prime number
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
s.
Mahlburg was an undergraduate at Harvey Mudd College
Harvey Mudd College
Harvey Mudd College is a private residential liberal arts college of science, engineering, and mathematics, located in Claremont, California. It is one of the institutions of the contiguous Claremont Colleges, which share adjoining campus grounds....
, where he graduated with highest distinction in 2001 with a B.S. in Mathematics. In 2006, he graduated from the University of Wisconsin–Madison
University of Wisconsin–Madison
The University of Wisconsin–Madison is a public research university located in Madison, Wisconsin, United States. Founded in 1848, UW–Madison is the flagship campus of the University of Wisconsin System. It became a land-grant institution in 1866...
with a Ph.D. in Mathematics.
Mahlburg's Erdős number
Erdos number
The Erdős number describes the "collaborative distance" between a person and mathematician Paul Erdős, as measured by authorship of mathematical papers.The same principle has been proposed for other eminent persons in other fields.- Overview :...
is 3.