** Professor of Number Theory **

*Research Interests: *

Number theory and arithmetic geometry

## Publications

Modularity of PGL

_{2}(Fp)-representations over totally real fields – Proceedings of the National Academy of Sciences of the United States of America

(2021)

118,

e2108064118

(DOI: 10.1073/pnas.2108064118)

RAISING THE LEVEL OF AUTOMORPHIC REPRESENTATIONS OF GL(2n) OF UNITARY TYPE

– Journal of the Institute of Mathematics of Jussieu

(2021)

1

(DOI: 10.1017/s1474748020000602)

Automorphy lifting for residually reducible l-adic Galois representations, II

– Compositio Mathematica

(2020)

156,

2399

(DOI: 10.1112/s0010437x20007484)

E8 and the average size of the 3‐Selmer group of the Jacobian of a pointed genus‐2 curve

– Proceedings of the London Mathematical Society

(2020)

122,

678

(DOI: 10.1112/plms.12388)

$\hat{G}$-local systems on smooth projective curves are potentially automorphic

– Acta Mathematica

(2019)

223,

1

(DOI: 10.4310/acta.2019.v223.n1.a1)

Elliptic curves over $\mathbb{Q}_\infty$ are modular

– Journal of the European Mathematical Society

(2019)

21,

1943

(DOI: 10.4171/jems/877)

On the average number of 2-Selmer elements of elliptic curves over F_q(X) with two marked points

– Documenta Mathematica

(2019)

24,

1179

Potential automorphy of $\hat{G}$-local systems

(2018)

On the arithmetic of simple singularities of type E.

– Research in Number Theory

(2018)

4,

21

(DOI: 10.1007/s40993-018-0110-5)

A 2-adic automorphy lifting theorem for unitary groups over CM fields

– Mathematische Zeitschrift

(2017)

285,

1

(DOI: 10.1007/s00209-016-1681-2)

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