The 2018 ICM Noether Lecturer is **Sun-Yung Alice Chang** for her leading contributions to harmonic analysis, geometric analysis,
differential geometry and partial differential equations.

The 2018 ICM Abel Lecturer is**Sir Michael Francis Atiyah** for his fundamental work bringing together topology, geometry and
analysis, and his outstanding contribution to building new bridges between mathematics and theoretical physics.

**Sung-Yung Alice Chang**

With her collaborators, Alice Chang developed a multi-parameter theory to a level comparable to the classical Calderon–Zygmund theory in the one parameter setting, a true milestone in the area of singular integrals. These operators occur in many contexts, from the most pure areas such as complex analysis and Fourier analysis, to partial differential equations, and to some important applications in fields spanning medicine and signal processing. The broad scientific impact of Alice Chang's contributions includes conformal geometry, and in particular her groundbreaking study of Monge–Ampere type equations.

Besides her deep contributions in mathematics, Alice Chang has been a mentor to many young researchers, and served the mathematical community in several capacities, including chairing the Department of Mathematics at Princeton and having been a member of the Program Committee for ICM2014.

Alice Chang earned her PhD from Berkeley in 1974, under the direction of D. Sarason. She held positions at UCLA and Berkeley, and in 1998 she moved to Princeton, where she is now the Eugene Higgins Professor of Mathematics.

Chang was an invited speaker at ICM 1986, a plenary speaker at ICM 2002 and was awarded the Ruth Lyttle Satter Prize by AMS in 1995. She has been a Fellow of the American Academy of Arts and Science since 2008, a Member of the National Academy of Sciences of the USA since 2009, and an Academician of the Academia Sinica, Republic of China, since 2012. She delivered the AMS Colloquium Lectures in 2004. In 2013, she received an honorary degree from the University Pierre and Marie Curie in Paris.

**Sir Michael Francis Atiyah**

Among his numerous groundbreaking achievements, Michael Atiyah, together with Friedrich Hirzebruch, laid the foundations for topological K-theory, a central tool in algebraic topology which permeates many other fields of mathematics. In collaboration with Isadore M. Singer, he proved in 1963 his most celebrated result, the Atiyah–Singer index theorem, which solved the index problem posed by Gelfand. The theorem asserts that, for an elliptic differential operator on a compact manifold, the analytical index and the topological index agree; this result has a wide array of applications both in mathematics and theoretical physics. Special instances of the Atiyah–Singer index theorem include the Hirzebruch–Riemann–Roch and the Chern–Gauss–Bonnet theorems. Some of Michael Atiyah's more recent work was inspired by gauge theory of elementary particles in physics, in particular instantons and monopoles, which play an important role in quantum field theory.

Michael Atiyah earned his PhD from the University of Cambridge in 1955, under W. V. D. Hodge. He has spent most of his academic life in t he United Kingdom at Oxford and Cambridge, and in the United States at the Institute for Advanced Study, in Princeton. From 1995 to 2005, he was the Director of the Isaac Newton Institute for Mathematical Sciences in Cambridge.

Michael Atiyah is a past president of the London Mathematical Society, of the Royal Society and of the Royal Society of Edinburgh, among many other appointments. Since 1997 he has been an honorary professor at the University of Edinburgh. The list of his former students comprises many renowned mathematicians, such as G. Segal, N. Hitchin, F. Kirwan, L. Jeffrey as well as Fields medalist S. Donaldson.

Michael Atiyah's work has been recognized by the most prestigious prizes, including the Fields medal in 1966 and the Abel Prize, jointly with Singer, in 2004. Among so many other distinctions he has received let us mention the Great Cross of the National Order of Scientific Merit of Brazil in 2010.

The 2018 ICM Abel Lecturer is

With her collaborators, Alice Chang developed a multi-parameter theory to a level comparable to the classical Calderon–Zygmund theory in the one parameter setting, a true milestone in the area of singular integrals. These operators occur in many contexts, from the most pure areas such as complex analysis and Fourier analysis, to partial differential equations, and to some important applications in fields spanning medicine and signal processing. The broad scientific impact of Alice Chang's contributions includes conformal geometry, and in particular her groundbreaking study of Monge–Ampere type equations.

Besides her deep contributions in mathematics, Alice Chang has been a mentor to many young researchers, and served the mathematical community in several capacities, including chairing the Department of Mathematics at Princeton and having been a member of the Program Committee for ICM2014.

Alice Chang earned her PhD from Berkeley in 1974, under the direction of D. Sarason. She held positions at UCLA and Berkeley, and in 1998 she moved to Princeton, where she is now the Eugene Higgins Professor of Mathematics.

Chang was an invited speaker at ICM 1986, a plenary speaker at ICM 2002 and was awarded the Ruth Lyttle Satter Prize by AMS in 1995. She has been a Fellow of the American Academy of Arts and Science since 2008, a Member of the National Academy of Sciences of the USA since 2009, and an Academician of the Academia Sinica, Republic of China, since 2012. She delivered the AMS Colloquium Lectures in 2004. In 2013, she received an honorary degree from the University Pierre and Marie Curie in Paris.

Among his numerous groundbreaking achievements, Michael Atiyah, together with Friedrich Hirzebruch, laid the foundations for topological K-theory, a central tool in algebraic topology which permeates many other fields of mathematics. In collaboration with Isadore M. Singer, he proved in 1963 his most celebrated result, the Atiyah–Singer index theorem, which solved the index problem posed by Gelfand. The theorem asserts that, for an elliptic differential operator on a compact manifold, the analytical index and the topological index agree; this result has a wide array of applications both in mathematics and theoretical physics. Special instances of the Atiyah–Singer index theorem include the Hirzebruch–Riemann–Roch and the Chern–Gauss–Bonnet theorems. Some of Michael Atiyah's more recent work was inspired by gauge theory of elementary particles in physics, in particular instantons and monopoles, which play an important role in quantum field theory.

Michael Atiyah earned his PhD from the University of Cambridge in 1955, under W. V. D. Hodge. He has spent most of his academic life in t he United Kingdom at Oxford and Cambridge, and in the United States at the Institute for Advanced Study, in Princeton. From 1995 to 2005, he was the Director of the Isaac Newton Institute for Mathematical Sciences in Cambridge.

Michael Atiyah is a past president of the London Mathematical Society, of the Royal Society and of the Royal Society of Edinburgh, among many other appointments. Since 1997 he has been an honorary professor at the University of Edinburgh. The list of his former students comprises many renowned mathematicians, such as G. Segal, N. Hitchin, F. Kirwan, L. Jeffrey as well as Fields medalist S. Donaldson.

Michael Atiyah's work has been recognized by the most prestigious prizes, including the Fields medal in 1966 and the Abel Prize, jointly with Singer, in 2004. Among so many other distinctions he has received let us mention the Great Cross of the National Order of Scientific Merit of Brazil in 2010.