# Autobiography of George Lusztig

I was born in 1946 in Timisoara, Romania. Both my parents were accountants and at home we spoke Hungarian (I learned Romanian at age 3 when I went to kindergarten). My wife, Gongqin Li, was born in Wuhan, China and trained as a mathematician but now works on software development. I have two daughters from my previous marriage: Irene (born in 1974) and Tamar (born in 1982).

I attended elementary school and high school in Timisoara. In 7^{th} grade my favorite subject was chemistry but in 8^{th }grade (1960), after some moderate success in the mathematics Olympiad, I began to spend most of my time solving mathematics problems from a mathematics magazine for high school students and decided to be a mathematician. During my last two years of high school I met Maria Neumann, a professor at the University of Timisoara, who lent me some books on Foundations of Geometry and Non-Euclidean Geometry which we would discuss in our meetings. I think that these discussions were very good for my mathematical development.

When I finished high school (1963), I went to Bucharest and enrolled as a student in the Department of Mathematics at the University of Bucharest. The teacher who most influenced me during the Bucharest years (1963–1968) was Kostake Teleman who was a member of a well-known mathematical family. I attended his course on Linear Algebra, based on Artin’s book Geometric Algebra, and his course on Differential Geometry, which was his main area of expertise. I also attended his more advanced courses: one on the Gelfand–Naimark theory of induced representations (in which I learned about flag manifolds) and one on the Atiyah–Singer index theorem. Both of these were very important for my development.

In 1968 I graduated from Bucharest University and got a job as an assistant in the Universityof Timisoarabut stayed there for only six months. In the summer of 1968, I attended a summer school in pseudodifferential operators in Stresa, Italy, where I met I M Singer. I told him that I had been invited to the University of Warwick for a special term in dynamical systems but that I was really more interested in index theory. He suggested that while in England I should meet M F Atiyah. This I did, and after one month at Warwick, Atiyah arranged for me to go to Oxford. When I first met Atiyah, he explained to me a problem on the semicharacteristic of a closed 4*k* + 1 manifold which he was just discussing with Singer. After several weeks I found a solution to that problem. During my two-month stay at Oxford I also proved some results on the constancy of the holomorphic Lefschetz number in a circle action which Atiyah then used in his work with Hirzebruch on the vanishing of the A-roof genus. Before leaving Oxford I received an invitation from the Institute for Advanced Study, Princeton, N J, based on the recommendation of Atiyah who was about to move there.

In 1969 I went to work with Atiyah at the Institute for Advanced Study, Princeton, N J and stayed there for two years. Since I did not have a PhD, at the end of the first year I asked W Browder whether I could get a PhD from Princeton University based on a paper on Novikov’s higher signatures that I had just completed. He said yes, and in 1971 I received my PhD.

Meanwhile, I became very interested in the representation theory of finite algebraic groups. In 1971 I received an offer of a lectureship from the University of Warwick, UK, which I accepted, due in part to the presence there of J A Green from whom I hoped to learn about representation theory. In the first few years at Warwick I had a collaboration with R Carter which helped me to better understand reductive groups. Also, I succeeded in finding a construction of discrete series for GL(*n*) over a finite field for which previously only the characters were known (by the work of Green).

In the spring of 1974, during a visit to IHES, I started a joint work with P Deligne in which we constructed the generic irreducible representations of reductive groups over a finite field using the étale cohomology of certain algebraic varieties; this was completed in the spring of 1975. Around the middle of 1974 I was promoted to Professor at the University of Warwick and spent the next few years trying to classify all irreducible representations of reductive groups over a finite field.

In 1978 I became a professor at MIT where I continue to be today. Around 1980, after my joint work with Kazhdan, intersection cohomology became one of my main tools. I have used this tool very often, in particular in the theory of character sheaves which I started to develop in the 1980s and I am still concerned with today, and also in the theory of canonical bases arising from quantum groups which I started to develop around 1990.

24 September 2014 Hong Kong