Karl Mahlburg is an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

whose research interests lie in the areas of

modular form In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition. The theory o ...

s, partitions,

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 a ...

and

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Ma ...

. He submitted a paper to

Proceedings of the National Academy of Sciences ''Proceedings of the National Academy of Sciences of the United States of America'' (often abbreviated ''PNAS'' or ''PNAS USA'') is a peer-reviewed multidisciplinary scientific journal. It is the official journal of the National Academy of S ...

(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 (; born Srinivasa Ramanujan Aiyangar, ; 22 December 188726 April 1920) was an Indian mathematician. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, ...

and later detailed by

Freeman Dyson Freeman John Dyson (15 December 1923 – 28 February 2020) was an English-American theoretical physicist and mathematician known for his works in quantum field theory, astrophysics, random matrices, mathematical formulation of quantum m ...

, George Andrews,

Frank Garvan Francis G. Garvan (born March 9, 1955) is an Australian-born mathematician who specializes in number theory and combinatorics. He holds the position Professor of Mathematics at the University of Florida. He received his Ph.D. from Pennsylvania St ...

, and Mahlburg's advisor

Ken Ono Ken Ono (born March 20, 1968) is a Japanese-American mathematician who specializes in number theory, especially in integer partitions, modular forms, umbral moonshine, the Riemann Hypothesis and the fields of interest to Srinivasa Ramanujan. He ...

called the crank having to do with congruence patterns in

partitions Partition may refer to: Computing Hardware * Disk partitioning, the division of a hard disk drive * Memory partition, a subdivision of a computer's memory, usually for use by a single job Software * Partition (database), the division of ...

. Until recently such congruence patterns were only known to occur for 5, 7, and 11. Mahlburg's result extends this to all

prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...

s. Mahlburg was an undergraduate at

Harvey Mudd College Harvey Mudd College (HMC) is a private college in Claremont, California, focused on science and engineering. It is part of the Claremont Colleges, which share adjoining campus grounds and resources. The college enrolls 902 undergraduate students ...

, where he graduated with highest distinction in 2001 with a B.S. in Mathematics. In 2006, he graduated from the

University of Wisconsin–Madison 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 Stat ...

with a Ph.D. in Mathematics. He was an associate professor at LSU.

References

External links

Mahlburg makes math history
* * {{DEFAULTSORT:Mahlburg, Karl Year of birth missing (living people) Living people 21st-century American mathematicians Combinatorialists Number theorists Harvey Mudd College alumni University of Wisconsin–Madison College of Letters and Science alumni Louisiana State University faculty