One hundred years of the mathematician who discovered infinite symmetries | Coffee and theories | Sciences

Today, October 11, marks the 100th anniversary of the birth of one of the most important Indian mathematicians in history. Harish Chandra. He trained as a physicist under the tutelage of two Nobel Prize winners, and began his work in mathematics by studying the spatio-temporal symmetries of Einstein’s theory of relativity. His later pure mathematical work – on the theory of infinite-dimensional representations of so-called quasi-simple sets – was very influential. They were one of the main sources of inspiration in developing Langlands programmean ambitious mathematical research roadmap linking fields such as algebra, number theory, analysis or geometry.

Harish Chandra Mehrotra was born in 1923 in Kanpur, northern India. After graduating from Allahabad University, he continued his studies in physics at the Indian Institute of Science, Bangalore under the supervision of Dr Raman CV – Nobel Prize in Physics in 1930 – and Homi ji bhabha.

He migrated to Cambridge (United Kingdom) in 1945, before Bhabha founded the prestigious university Tata Institute of Fundamental Research – Where the next generations of Indian mathematicians and physicists will be trained. Soon after, he moved to the United States, where he spent the rest of his career. Although he always had the desire to play a greater role in promoting science in India, his poor health and early death prevented this.

He obtained his doctorate in physics while at Cambridge University under the supervision of Dr Paul Dirac He also won the Nobel Prize in Physics in 1933, but after completing that he decided to change his research topic to mathematics. This transfer between specialties is more common than you might think. Fundamental physics has, since the middle of the twentieth century, needed increasingly advanced mathematics to formalize it, which is why many physicists approaching the frontiers of mathematical research decide to go one step further and modify their specialty.

In Harish Chandra’s case, the logical precision required in mathematical proofs was also an argument in favor of the leap. While theoretical physicists rely on intuition that guides their work and allows them to predict phenomena before verifying them experimentally, among them: According to Harish Chandra, he lacked thatHe felt more confident when he could support his results with a rigorous mathematical argument. Without the requisite intuition, he thought his physical search might lead him astray.

During his thesis, Harish Chandra studied the so-called Poincaré groupIt is an algebraic construct that embodies the temporal and spatial symmetries of Einstein’s theory of relativity. Specifically, A Symmetry group A given object – for example, a square – is the set of operations that can be performed on it, without changing its properties. For example, when you rotate a square 90 degrees, it returns to having the same appearance, so this process is part of the square’s set of symmetries.

When considering the Euclidean plane, i.e. the plane with the idea of ​​distance, any rotation belongs to its own set of symmetries, because when the plane rotates, the distance between any pair of points does not change. But when you stretch it, the distance between the points becomes larger, so this process does not fall within the set of plane symmetries.

In Einstein’s theory of relativity, spacetime is considered with the so-called Metric Minkowski -Instead of the usual distance-. The Poincaré set is the set of space-time symmetries, i.e. all transformations that do not change the Minkowski gauge.

In his doctoral thesis, Harish Chandra studied Poincaré group representations of infinite dimensions. Representing a set in a linear space consists of assigning a linear transformation to each element of the set in said space – i.e. a function satisfying certain properties -, which allows the use of linear algebra techniques in the study of sets. Linear space can be finite or infinite; In the case of the Poincaré set, it accepts certain representations of infinite dimension, which cannot be decomposed into finite representations. Although more difficult to deal with than limited ones, they are an essential tool for studying certain groups.

As a mathematician, Harish Chandra has studied infinite representations of other sets, more specifically so-called quasi-simple sets. For his work, he was a strong candidate for the Fields Medal in 1958. However, one member of the jury apparently did not want to award the medal to two mathematicians from the French Bourbaki group – he considered both Harish Chandra and René Thomme to have received the award that year . Harish Chandra was never a member of this group, but his style, with its attention to detail and precision, may have been thought to be close to that associated with the famous group.

After working at Columbia University (New York, USA), in 1963 he was appointed tenured professor at the Institute for Advanced Study in Princeton (USA). Since 1969 he has had several heart attacks, perhaps exacerbated by his intense work schedule – he extended his work day until late into the night. His doctor insisted that he take annual vacations, which he used to encourage his love of painting – in particular, he was a great admirer of Gauguin – and he finally died in 1983 of a heart attack while on his last afternoon walk. A conference day in honor of Emile Borel, his friend and collaborator.

Tomás Gomez de Quiroga He is a scientific researcher at the Supreme Council for Scientific Research at the Institute of Mathematical Sciences (ICMAT).

Coffee and theories It is a section dedicated to mathematics and the environment in which it is created, coordinated by the Institute of Mathematical Sciences (ICMAT), where researchers and members of the center describe the latest developments in this discipline, share the intersections between mathematics, other social sciences and cultural expressions and remember those who contributed to its development and knew how to transform coffee. To theories. The name evokes the definition of Hungarian mathematician Alfred Rennie: “A mathematician is a machine that turns coffee into theorems.”

Editing and formatting: Agata A. Timon J. Longoria (Ekmat).

You can follow Theme in Facebook, s And Instagramor sign up here to receive Our weekly newsletter.