Sarah Livia Zerbes (, born 2 August 1978) is a German algebraic number theorist at

ETH Zurich (colloquially) , former_name = eidgenössische polytechnische Schule , image = ETHZ.JPG , image_size = , established = , type = Public , budget = CHF 1.896 billion (2021) , rector = Günther Dissertori , president = Joël Mesot , a ...

. Her research interests include

L-function In mathematics, an ''L''-function is a meromorphic function on the complex plane, associated to one out of several categories of mathematical objects. An ''L''-series is a Dirichlet series, usually convergent on a half-plane, that may give ...

modular form In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition. The theory ...

s, ''p''-adic Hodge theory, and

Iwasawa theory In number theory, Iwasawa theory is the study of objects of arithmetic interest over infinite towers of number fields. It began as a Galois module theory of ideal class groups, initiated by (), as part of the theory of cyclotomic fields. In the ...

, and her work has led to new insights towards the

Birch and Swinnerton-Dyer conjecture In mathematics, the Birch and Swinnerton-Dyer conjecture (often called the Birch–Swinnerton-Dyer conjecture) describes the set of rational solutions to equations defining an elliptic curve. It is an open problem in the field of number theory ...

, which predicts the number of rational points on an

elliptic curve In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point . An elliptic curve is defined over a field and describes points in , the Cartesian product of with itself. If ...

by the behavior of an associated L-function.

Education and career

Zerbes read mathematics at the

University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

, earning first class honours in 2001. She completed a Ph.D. at Cambridge in 2005; her dissertation, ''Selmer groups over non-commutative p-adic Lie extensions'', was supervised by

John H. Coates John Henry Coates (26 January 1945 – 9 May 2022) was an Australian mathematician who was the Sadleirian Professor of Pure Mathematics at the University of Cambridge in the United Kingdom from 1986 to 2012. Early life and education Coates ...

. While still a graduate student, she became a Marie Curie Fellow at the Institut Henri Poincaré in Paris, and after completing her doctorate she undertook postdoctoral studies as a Hodge Fellow at the

Institut des Hautes Études Scientifiques The Institut des hautes études scientifiques (IHÉS; English: Institute of Advanced Scientific Studies) is a French research institute supporting advanced research in mathematics and theoretical physics. It is located in Bures-sur-Yvette, ju ...

near Paris, as a Chapman Fellow at

Imperial College London Imperial College London (legally Imperial College of Science, Technology and Medicine) is a public research university in London, United Kingdom. Its history began with Prince Albert, consort of Queen Victoria, who developed his vision for a ...

, and (while working as a lecturer at the

University of Exeter , mottoeng = "We Follow the Light" , established = 1838 - St Luke's College1855 - Exeter School of Art1863 - Exeter School of Science 1955 - University of Exeter (received royal charter) , type = Public , ...

beginning in 2008) as a postdoctoral fellow under the support of the

Engineering and Physical Sciences Research Council The Engineering and Physical Sciences Research Council (EPSRC) is a British Research Council that provides government funding for grants to undertake research and postgraduate degrees in engineering and the physical sciences, mainly to univers ...

. She took another lectureship at

University College London , mottoeng = Let all come who by merit deserve the most reward , established = , type = Public research university , endowment = £143 million (2020) , budget = � ...

in 2012, and was a professor there from 2016 until 2021. Zerbes also serves on the council of the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...

. Since 1 January 2022 she is a full professor of Mathematics at ETH Zürich.

Recognition

Zerbes won a

Philip Leverhulme Prize The Philip Leverhulme Prize is awarded by the Leverhulme Trust to recognise the achievement of outstanding researchers whose work has already attracted international recognition and whose future career is exceptionally promising. The prize schem ...

in 2014, jointly with her husband and frequent research collaborator David Loeffler of the

University of Warwick , mottoeng = Mind moves matter , established = , type = Public research university , endowment = £7.0 million (2021) , budget = £698.2 million (202 ...

. In 2015 Zerbes and Loeffler won the

Whitehead Prize The Whitehead Prize is awarded yearly by the London Mathematical Society to multiple mathematicians working in the United Kingdom who are at an early stage of their career. The prize is named in memory of homotopy theory pioneer J. H. C. Whitehea ...

"for their work in number theory, in particular for their discovery of a new Euler system, and for their applications of this to generalisations of the Birch–Swinnerton-Dyer conjecture."

References

External links

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{{DEFAULTSORT:Zerbes, Sarah Livia 1978 births Living people 21st-century German mathematicians British mathematicians Women mathematicians Number theorists Alumni of the University of Cambridge Academics of the University of Exeter Academics of University College London