Professor of Number Theory
Research Interests:
Number theory and arithmetic geometry
Publications
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 Fq(X) with two marked points
– Documenta Mathematica
(2019)
24,
1179
$\hat{G}$-local systems on smooth projective curves are potentially automorphic
– Acta Mathematica
(2019)
223,
1
(DOI: 10.4310/ACTA.2019.v223.n1.a1)
On the arithmetic of simple singularities of type E
– Res Number Theory
(2018)
4,
21
(DOI: 10.1007/s40993-018-0110-5)
Potential automorphy and the leopoldt conjecture
– American Journal of Mathematics
(2017)
139,
1205
(DOI: 10.1353/ajm.2017.0030)
Automorphy of some residually
$S_5$
S
5
Galois representations
– Mathematische Zeitschrift
(2017)
286,
399
(DOI: 10.1007/s00209-016-1766-y)
A 2-adic automorphy lifting theorem for unitary groups over CM fields
– Mathematische Zeitschrift
(2017)
285,
1
(DOI: 10.1007/s00209-016-1681-2)
On the GL$_{n}$-eigenvariety and a conjecture of Venkatesh
– Selecta Mathematica, New Series
(2017)
23,
1205
(DOI: 10.1007/s00029-017-0303-0)
Level-raising and symmetric power functoriality, III
– Duke Mathematical Journal
(2017)
166,
325
(DOI: 10.1215/00127094-3714971)
On the $\phi$-Selmer groups of the elliptic curves y$^2$ = x$^3$ - Dx
– Mathematical Proceedings of the Cambridge Philosophical Society
(2017)
163,
71
(DOI: 10.1017/s0305004116000724)
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