Harald Helfgott

Harald Helfgott, May 2014

Harald Andrés Helfgott (born November 25, 1977 in Lima , Peru ) is a Peruvian mathematician who specializes in number theory and group theory.

life and work

Helfgott graduated summa cum laude from Brandeis University in 1998 and received his doctorate in 2003 from Princeton University under Henryk Iwaniec (and Peter Sarnak ) ( Root numbers and the parity problem ). As a post-doctoral student , he was Gibbs Assistant Professor at Yale University in 2003/2004 and at Montreal University and Concordia University from 2004 to 2006 . From 2006 he was a lecturer and from 2009 a reader at the University of Bristol . He has been researching for the CNRS at the École normal supérieure since 2010 .

He has taught courses in Peru, India, Cuba, Bolivia, and Brazil.

In 2013 he announced a proof of Goldbach's ternary conjecture for sufficiently large numbers, according to which odd numbers can be represented as the sum of three prime numbers. The limit was , considerably lower than in previous proofs and small enough that the remaining cases (the conjecture claims the representability for odd numbers greater than 5) can be done by computer (which he also did with David Platt). The proof uses the circle method of Hardy and Littlewood , estimates of exponential sums by Vinogradov and the big screen after Yuri Linnik . ${\displaystyle 10^{30}}$

He also deals with growth e.g. B. subsets of generators, resolvable subsets in non-commutative groups. With Akshay Venkatesh he gave new estimates for the number of integer points on elliptic curves. In 2014 he was invited speaker at the ICM in Seoul (The ternary Goldbach problem).

In 2008 he received the Philip Leverhulme Prize in Mathematics, the Whitehead Prize in 2010 and the Adams Prize in 2011 (with Tom Sanders ). In 2007 he received an Advanced Research Fellowship from the UK Engineering and Physical Sciences Research Council (EPSRC). Since 2015 he has been working as an Alexander von Humboldt professor at the Georg-August-Universität Göttingen .

Fonts

• The ternary Goldbach problem, Arxiv (presentation of the evidence in book form, 2015)

Web links

• Harald Andrés Helfgott - Vita , at ENS
• link on page at Georg-August-Universität Göttingen
• Videos by Harald Helfgott (English) in the AV portal of the Technical Information Library

Individual evidence

1. ^ Mathematics Genealogy Project .
2. ↑ Dissertation with Arxiv
3. ^ Helfgott: Major arcs for Goldbach's problem , Preprint 2013, Arxiv
4. ^ Helfgott: Minor arcs for Goldbach´s problem , Preprint 2012, Arxiv
5. ↑ Helfgott, D. Platt: Numerical Verification of the Ternary Goldbach Conjecture up to 8.875e30 , Preprint 2013 , Experimental Mathematics, Volume 22, 2013, pp. 406-409
6. ^ Helfgott: Growth and generation in ${\displaystyle SL_{2}(Z/pZ)}$ , Annals of Mathematics, Volume 167, 2008, pp. 601–623, Arxiv
7. ↑ Helfgott: Growth in ${\displaystyle SL_{3}(Z/pZ)}$ , J. European Math. Soc., Volume 13, 2011, pp. 761-851, Arxiv Preprint 2008
8. ↑ Growth in groups. Ideas and Perspectives , Preprint 2013
9. ↑ Helfgott, Venkatesh: Integral points on elliptic curves and 3-torsion in class groups , J. Amer. Math. Soc. 19: 527-550 (2006)
10. ↑ Harald Andrés Helfgott ( Memento of the original from October 26, 2014 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. at humboldt-professur.de; accessed on November 16, 2014.