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Sander P. Zwegers

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Sander Pieter Zwegers (born 16 April 1975 in Oosterhout) is a Dutch mathematician who made a connection between Maass forms and Srinivasa Ramanujan's mock theta functions in 2002.[1] After a period at the Max-Planck Institute in Bonn, he became assistant professor at the University College Dublin in 2008. Since 2011, he has been is professor of number theory at the University of Cologne.

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Oosterhout

Oosterhout

Oosterhout is a municipality and a city in the southern Netherlands. The municipality had a population of 55,616 in 2019.

Srinivasa Ramanujan

Srinivasa Ramanujan

Srinivasa Ramanujan was an Indian mathematician. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then considered unsolvable. Ramanujan initially developed his own mathematical research in isolation: according to Hans Eysenck: "He tried to interest the leading professional mathematicians in his work, but failed for the most part. What he had to show them was too novel, too unfamiliar, and additionally presented in unusual ways; they could not be bothered". Seeking mathematicians who could better understand his work, in 1913 he began a postal correspondence with the English mathematician G. H. Hardy at the University of Cambridge, England. Recognising Ramanujan's work as extraordinary, Hardy arranged for him to travel to Cambridge. In his notes, Hardy commented that Ramanujan had produced groundbreaking new theorems, including some that "defeated me completely; I had never seen anything in the least like them before", and some recently proven but highly advanced results.

University College Dublin

University College Dublin

University College Dublin is a public research university in Dublin, Ireland, and a member institution of the National University of Ireland. With 33,284 students, it is Ireland's largest university, and amongst the most prestigious universities in the country. Five Nobel Laureates are among UCD's alumni and current and former staff. Additionally, four Irish Taoiseach and three Irish Presidents have graduated from UCD, along with one President of India.

Number theory

Number theory

Number theory 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, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theorists study prime numbers as well as the properties of mathematical objects made out of integers or defined as generalizations of the integers.

University of Cologne

University of Cologne

The University of Cologne is a university in Cologne, Germany. It was established in the year 1388 and is one of the most prestigious and research intensive universities in Germany. It was the sixth university to be established in Central Europe. It closed in 1798 before being re-established in 1919. It is now one of the largest universities in Germany with more than 48,000 students. The University of Cologne was a university of excellence as part of the German Universities Excellence Initiative from 2012 to 2019. As of 2021, 3 Nobel Prize winners have been affiliated with the university.

Research

In 1976, the American mathematician George Andrews found what is nowadays known as the “Lost Notebook” of Ramanujan. It contains many remarkable results, including the mysterious mock theta functions. This notebook contains what many specialists regard as Ramanujan’s deepest work. It was Sander Zwegers who, as a PdD student, had groundbreaking ideas how to fit the mock theta functions into a broader context. His 2002 PhD thesis has led to numerous publications and international conferences.[2]

Zwegers' general area of interest is number theory. More specifically, he studies modular forms and variations thereof, such as Maass forms, mock modular forms, (indefinite) theta functions, and (Maass) Jacobi forms.

Works

  • Zwegers, S. P. (2001), "Mock θ-functions and real analytic modular forms" (PDF), q-series with applications to combinatorics, number theory, and physics (Urbana, IL, 2000), Contemp. Math., vol. 291, Providence, R.I.: American Mathematical Society, pp. 269–277, ISBN 978-0-8218-2746-8, MR 1874536
  • Zwegers, S. P. (2002), Mock Theta Functions, Utrecht PhD thesis, ISBN 90-393-3155-3
  • Zwegers, S. P. (2008), Appell–Lerch sums as mock modular forms (PDF)

Source: "Sander P. Zwegers", Wikipedia, Wikimedia Foundation, (2022, November 25th), https://en.wikipedia.org/wiki/Sander_P._Zwegers.

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References
  1. ^ Don Zagier Ramanujan´s Mock Theta Functions and their Applications (d'après Zwegers and Bringmann-Ono), Séminaire Bourbaki, No. 986, 2007
  2. ^ Peter Lynch, Timely reminder of a mathematical genius, The Irish Times, Dec 6, 2012.
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