Kathrin Bringmann

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Kathrin Bringmann (right), Oberwolfach 2009

Kathrin Bringmann (born May 8, 1977 in Münster ) is a German mathematician who deals with number theory and modular forms .

Bringmann studied mathematics and theology at the University of Würzburg , with the state examination in 2002 and the diploma in mathematics in 2003. In 2004 she received her doctorate with Winfried Kohnen at the University of Heidelberg ( Applications of Poincaré Series on Jacobi Groups ). From 2004 to 2007 she was Assistant Professor at the University of Wisconsin (Madison) with Ken Ono , then at the University of Minnesota (Minneapolis) and since 2008 professor at the University of Cologne .

Together with Ken Ono she developed a theory of the mock theta functions of S. Ramanujan , which the latter communicated to Godfrey Harold Hardy in an (incompletely preserved) letter in the form of some power series expansion formulas as the last of his "problems" before his death . Ono and Bringmann embedded the mock theta functions in the theory of special modular forms ( Maaß wave forms ), of which they showed that there are infinitely many, and thus achieved a breakthrough in a long open problem area, the importance of which was underlined by Freeman Dyson , among others . In particular, they proved a conjecture by George Andrews (1966) about the exact form of the coefficients of the series expansion of the mock theta function. The mock theta functions also have connections to the theory of partitions in number theory; the exact form of the coefficients results in formulas for the number of partitions of even and odd ranks.

In 2009 she won the SASTRA Ramanujan Prize and in 2009 the Alfried Krupp Prize for Young University Teachers .

Fonts (selection)

  • with Ono: The f (q) mock theta function conjecture and partition ranks. Invent. Math. 165 (2006), no. 2, 243-266.
  • with Ono: Arithmetic properties of coefficients of half-integral weight Maass-Poincaré series. Math. Ann. 337 (2007), no. 3, 591-612.
  • with Ono: Dyson's ranks and Maass forms. Ann. of Math. (2) 171 (2010), no. 1, 419-449.
  • with Mahlburg: An extension of the Hardy-Ramanujan circle method and applications to partitions without sequences. Amer. J. Math. 133 (2011), no. 4, 1151-1178.
  • with Guerzhoy, Kent, Ono: Eichler-Shimura theory for mock modular forms. Math. Ann. 355 (2013), no. 3, 1085-1121.

Web links

Individual evidence

  1. ↑ Mock means something like fake in English , but they have some things in common with the usual theta functions.
  2. ↑ Ramanujan almost always shared his results, especially in the famous notebooks he left behind, with no evidence and also without any indication of how he came up with his formulas.
  3. ^ Bringmann, Ono Lifting cusp forms to Maass forms with an application to partitions , Proc. Nat. Acad. Sci., Vol. 104, 2007, p. 3725
  4. ^ Dyson A Walk Through Ramanujan's Garden , in: Ramanujan Centenary Conference, Illinois, 1987
  5. ↑ Eric Klarreich Science News Online, March 10, 2007 , MAA Online 2007
  6. ↑ The Dutch mathematician Sander Zwegers found a connection to real analytical modular forms in his doctoral thesis with Don Zagier
  7. ↑ Bringmann, Ono The f (q) mock theta function conjecture and partition ranks , Inventiones Math., Volume 165, 2006, p. 243
personal data
SURNAME Bringmann, Kathrin
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH May 8, 1977
PLACE OF BIRTH Muenster