**Speaker :**Jean-Marc Deshouillers

**Affiliation :**University of Bordeaux, France.

**Tittle :**RESULTS AND MODELS. AN ILLUSTRATION THROUGH SUMS OF CUBES

**Venue :**Seminar hall, Kerala School of Mathematics

**Date :**24-09-2022

**Time :**3.30 PM – 5 PM

**Abstract :**

RESULTS AND MODELS. AN ILLUSTRATION THROUGH SUMS OF CUBESNumber theory has the knack for phrasing easily understandable statements which are hard to prove.An archetype is Goldbach’s problem (1742), which is still unsolved :every even integer larger than 4 is a sum of two primes.The root of the talk is Waring’s problem (1770), which states – for cubes – thatevery integer is a sum of at most 9 cubes.It has been proved in 1909-1912, but we expect much more, namelyevery sufficiently large integer is a sum of 4 cubes.In the frame of this understandable question, we shall illustrate how mathematiciansproveweaker statements, leadcomputation,buildmodelsto comfort their belief in statements they cannot prove.

**About the speaker**

Professor Jean-Marc Deshouillers, a number theorist who has authored more than hundred research papers and advised seventeen PhD students and is currently Professor at Institut mathématique de Bordeaux, Bordeaux, France. Jean-Marc Deshouillers received his PhD in 1972 at the University Paris VI

In 1985 he showed with Ramachandran Balasubramanian and Francois Dress that, in the case of the fourth powers of Waring’s problem, the least number of fourth powers that is necessary to express any positive integer as a sum of fourth powers is 19.

Zoom Meet link:

https://us06web.zoom.us/j/84175273748?pwd=T2dsNCtaa0MxRHBvZ2hEVGdVVHVSZz09

https://us06web.zoom.us/j/84175273748?pwd=T2dsNCtaa0MxRHBvZ2hEVGdVVHVSZz09

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