Asked how she became interested in mathematics, Morel says her mother worked in a school library and brought home high school mathematics textbooks and a mathematics magazine aimed at high school students. When Morel was 14, she read about Andrew Wiles, now chair of the mathematics department at Princeton, who proved Fermat's Last Theorem. She followed the story avidly, learning that Wiles and his former student Richard Taylor, now a member of the Harvard mathematics department, had discovered a fundamental error in the original proof, which they corrected in a 1995 paper.

When I was in the 9th grade, my mother brought home from her high school a maths magazine for high-school students called "Tangente." I liked it very much and immediately subscribed. It had articles about mathematical concepts that were not taught in school, book recommendations, and maths challenges (I won two HP calculators thanks to them). That's also where I heard about the mathematical summer camp of the French Federation of Mathematical Games, and I convinced my parents to send me there. Later (from 11th grade), I asked my parents to buy me college-level and graduate school-level textbooks and read them in my free time. I didn't always understand everything, but it was fun.

I went to the École Normale Supérieure, and that means that I did not have to attend a class in a university until I was almost a graduate student.

It is a pleasure to thank G Laumon, who spent a lot of time in discussions with me, and the reviewers of this thesis, M Harris and R Kottwitz, who corrected or simplified the proofs of certain results in part 4.

It was about calculating the intersection cohomology of singular compactifications of smooth varieties (mostly Shimura varieties). Intersection cohomology (first introduced by Goresky and MacPherson) is a cohomology theory that is the same as Betti or étale cohomology for smooth varieties, but behaves much better for singular varieties; the only problem is that it can be very difficult to calculate in general. I was lucky enough to stumble on a very simple trick that, for the compactifications of Shimura varieties, allows one to easily reduce the calculation to known results about cohomology with compact support of Shimura varieties.

Her doctoral thesis was extremely demanding and stunningly original, solving a problem that had been intractable for more than 20 years.

It is a pleasure to thank G Laumon, who spent a lot of time in discussions with me. I also thank M Harris for his critiques of an early version of my text, and R Kottwitz, who corrected or simplified the proofs of some results in Part 3.

Obviously, Morel has an extraordinary mind, but in Gross's view that's a trait shared by many people. "She was determined to make her mark in mathematics," he says. And Gross believes that young people are key to the field. "They're the ones who bring the really great ideas into the world," he says. "We've made six appointments in the past five or six years, almost all of them people who were in their 20s when we appointed them. They invigorate our department."

The area of mathematics in which Morel has already made contributions is called the Langlands program, initiated by Robert Langlands ... Langlands brought together two fields, number theory and representation theory. "It's a connection that no one doubts," Gross says. "And yet the bridge between them hasn't been completely built." Morel has made significant advances in building that bridge. "It's an extremely exciting area of mathematics," Gross says, "and it requires a vast background of knowledge, because you have to know both subjects plus algebraic geometry."

The Radcliffe Alumnae Professorship - which will allow Morel to spend four semesters at the Radcliffe Institute during her first five years at Harvard - was a critical factor, Gross says, in recruiting her. "Candidates of her calibre get offers from everywhere," he says. "The fact that we can say to a young person like Sophie, 'We're so excited about your research that Radcliffe is going to give you some time to focus on it' is a huge advantage. Helping us attract young faculty members is one of the great things that the Radcliffe Institute does."

This text was written while I was working as a Professor at the Harvard mathematics department and supported by the Clay Mathematics Institute as a Clay Research Fellow.

The purpose of this talk is to present an (apparently) new way to look at the intersection complex of a singular variety over a finite field, or, more generally, at the intermediate extension functor on pure perverse sheaves, and an application of this to the cohomology of noncompact Shimura varieties.

This book studies the intersection cohomology of the Shimura varieties associated to unitary groups of any rank over $\mathbb{Q}$. In general, these varieties are not compact. The intersection cohomology of the Shimura variety associated to a reductive group G carries commuting actions of the absolute Galois group of the reflex field and of the group $G(A_{f})$ of finite adelic points of G. The second action can be studied on the set of complex points of the Shimura variety. In this book, Sophie Morel identifies the Galois action - at good places - on the $G(A_{f})$-isotypical components of the cohomology.

Morel uses the method developed by Langlands, Ihara, and Kottwitz, which is to compare the Grothendieck-Lefschetz fixed point formula and the Arthur-Selberg trace formula. The first problem, that of applying the fixed point formula to the intersection cohomology, is geometric in nature and is the object of the first chapter, which builds on Morel's previous work. She then turns to the group-theoretical problem of comparing these results with the trace formula, when G is a unitary group over $\mathbb{Q}$. Applications are then given. In particular, the Galois representation on a $G(A_{f})$-isotypical component of the cohomology is identified at almost all places, modulo a non-explicit multiplicity. Morel also gives some results on base change from unitary groups to general linear groups.

The main result of this book is a calculation of the trace of Hecke correspondences composed with a power of Frobenius on the intersection cohomology of the Baily-Borel compactification of certain Shimura varieties and the stabilisation of this formula for unitary Shimura varieties. An important application of the theory developed in this book is to computing the local factors of L-functions of the Baily-Borel compactification of unitary Shimura varieties at good primes. ...
...
This book is a research monograph, yet the author takes care in recalling in detail the relevant notation and previous results instead of just referring to the literature. Also, explicit calculations are given, making the book readable not only for experts but also for interested advanced students.

... for her deep and original work in arithmetic geometry and automorphic forms, in particular the study of Shimura varieties, bringing new and unexpected ideas to this field.

I was a Harvard professor for only two and a half years, and I often felt that, as a French person, I did not have the same reverence for Harvard as Americans seem to have. In any case, I never really felt that I was imposing enough for the job; it probably does not help that I look much younger than I am (or so I am told by the people who routinely ask where I go to college). When people outside of work ask me what I do, I usually answer something like "I teach maths" and try to leave it at that, unless provoked. I always felt better at ease with the junior faculty - postdocs, assistant professors and preceptors - and the graduate students than with the other professors; if they were annoyed by my presence, they were gracious enough not to let it show. Maybe that would have changed as I got older, but then I left.

... to highlight to the community outstanding contributions by women in the field and to advance the careers of the prize recipients.

The 2014 AWM-Microsoft Research Prize in Algebra and Number Theory is presented to Professor Sophie Morel, in recognition of her exceptional research in number theory. Professor Morel received her doctorate in 2005 from l'Université Paris-Sud. After appointments at the Institute for Advanced Studies, the Clay Mathematics Institute and Harvard University, she is currently a Professor of Mathematics at Princeton University. Professor Morel is a powerful arithmetic algebraic geometer who has made fundamental contributions to the Langlands program. Her research has been called 'spectacularly original, and technically very demanding.' Her research program has been favourably compared to that of several Fields medalists. She accomplished one of the main goals of the Langlands program by calculating the zeta functions of unitary and symplectic Shimura varieties in terms of the L-functions of the appropriate automorphic forms. To achieve this, she introduced an innovative t-structure on derived categories which had been missed by many experts. Her book 'On the cohomology of certain noncompact Shimura varieties' published in the Annals of Mathematics Studies Series is described as a tour-de-force. Professor Morel found another remarkable application of her results on weighted cohomology. She gave a new geometric interpretation and conceptual proof of Brenti's celebrated but mysterious combinatorial formula for Kazhdan-Lusztig polynomials, which are of central importance in representation theory. We would like to congratulate Professor Morel for her substantial achievements.

I try to work out examples, I make calculations. I actually really enjoy calculations, but sometimes I'm bad about examples (I try to see the general case directly and it's a dangerous thing to do). Or I try to generalise the problem. I try to compare it with other problems I know about, I read up on things I think are related to see if it will give me an idea. When I think a statement might be true, I try to see all the consequences of that statement, until I arrive at obviously false things; if I can't do that, then I will try to prove my statement.

My main activity is probably reading. I like reading novels and learning foreign languages, then reading the same novel in different languages. A few years ago I took up running as a way to keep in shape, then got hooked and started running half marathons and marathons. In the summer, I prefer to hike in the mountains in France (but not in the USA, as I am very afraid of bears).