Pierre Deligne Nirav Patel 10/30/2014

Pierre Deligne was born in Etterbeck, Belgium in 1944. He attended pri- mary school at Shaerbeek and secondary school at Athenee Adolphe Max in Brussels. Deligne’s brother was actually 7 years older than him. His brother taught him the fundamentals of arithmetic including multiplication and di- vision. Although his parents never had an interest in Mathematics, Deligne always had interest in Mathematics and took great pride in the subject. His friend’s father was a High School teacher. His friend’s father gave him books to read such as Set theory by Bourbaki. Eventually, after ﬁnishing school, Deligne attended Free University of Brussels in 1962.

He graduated in 1966 earning his bachelor’s degree in Mathematics. However, during his last year as an undergraduate, he went to Ecole Normale to study more mathematics in Paris. There, he worked with Alexandre Grothendieck. When they initially met, Deligne thought he was a very odd dressed man with a shaved head. However, when he started attending his seminars, Deligne noticed how good of a mathmetician he really was. Deligne used to ask many questions that he even knew the answer to, but wanted to conﬁrm if his ideas were right. Grothendiek was very impressed by Deligne’s interest in Math through his question that he decided to take him in as a student.

During his time in Paris, he realized his interest to study mathematics to a greater extent. In just 2 shorts years, he was able to get a doctorate degree. After receiving the degree, he went back to Institut des Huates Etudes Scientiﬁques at Bures-sur-Yvette in Paris to work under Grothendieck once more.

Howver, this time the stay was permanant. For 14 years he worked with Alexandre Grothendieck learning about algebraic equations and finding so- lution sets for different functions. He looked at Galois theory, Hilbert’s 21st problem, and theory of moduli. All those interested him, but he wanted to actually find solutions to unsolved problems. This is where Grothendieck became more useful.

In 1949, Weil revealed in one of his paper 3 conjectures that have not been

1 proven. These conjectures were known as the Wiel conjectures which involved zeta functions and Reimann Hypothesis. Reimann suggested that zeta functions do exist over a ﬁnite ﬁeld however nobody was really able to solve it. He knew the ideas of which the question involved but didn’t know how to solve it.

Luckily, Grothendieck was able to solve the first 2 conjectures. Under Grothendieck’s guidance, Deligne learned about the conjectures. The idea was using etale cohomology. He figured the way to solve the 3rd part was very similar as solving the first two conjectures but in a different perspective. Grothendieck relied more on finding algebraic cyles that had repeating solutions, while Deligne focused more on topological ways by using the automorphic form. Doing this, Deligne proved that Grothendieck’s way was lacking.

Today, Deligne is known for using the Weil conjectures to prove estimates for exponential sums. He also showed that the Ramanujan-Petersson conjecture is a part of the Weil Conjecture and proved the Lefschetz Thereom. Having done this tasks, Deligne is recognized as one of the greatest modern day mathematics.

For these great accomlishments, he earned Wolf Prize(2008), Fields medal(1978) and Abel Prize(2013). To this day, he is only one of 4 mathematicians to accomplish such feat. Also he was elected as an honorary member of Lon- don Mathematical Society. Since 1984, he has been a professor teaching at Princeton University. When he won the Abel prize, he decided to give major- ity of the prize to Institut des Huates Etudes Scientiﬁques and the Institute for Advanced study at Princeton.

References

[1] ”Pierre Deligne.” Wikipedia. Wikimedia Foundation, 30 Oct. 2014. Web. 30 Oct. 2014. [2] ”Pierre Ren Deligne.” Deligne Biography. N.p., n.d. Web. 30 Oct. 2014. [3] Raussen, Martin, and Christian Skau. ”Interview with Pierre Deligne.” Notices of the American Mathematical Society 61.02 (2014): 1. Web.