A. Shankar

Geometry and Topology · with Bhargava · 2010–2017

A researcher in the Science corpus: 7 papers; trusts 17 researchers and is trusted by 9 researchers here, as inferred from the citation graph.

Subfields

• Geometry and Topology — 57 citations into it; #1,554 of 7,422 by trust here, #1,487 by citations
• Mathematical Physics — 35 citations into it; #3,658 of 8,562 by trust here, #3,022 by citations
• Algebra and Number Theory — 31 citations into it; #482 of 2,864 by trust here, #405 by citations
• Information Systems — 16 citations into it
• Computational Theory and Mathematics — 15 citations into it
• Discrete Mathematics and Combinatorics — 8 citations into it; #1,453 of 2,017 by trust here, #1,149 by citations
• Theoretical Computer Science — 6 citations into it

Whom A. Shankar trusts overall

Their strongest outbound trust, strongest first, inferred from their citations.

1. Manjul Bhargava
2. D. R. Heath-Brown
3. Bjorn Poonen
4. Tom A. Fisher
5. Tim Dokchitser
6. M. Young
7. Jorma Jormakka
8. Jacob Tsimerman
9. Vladimir Dokchitser
10. W. Gan

Who trusts A. Shankar overall

1. Manjul Bhargava
2. Alexei Oblomkov
3. Bjorn Poonen
4. Zhiwei Yun
5. B. Gross

Papers from A. Shankar's perspective

Ordered by how strongly the researchers A. Shankar trusts endorse each paper. Same corpus, a different order for every researcher.

1. Random Matrices
2. The average rank of elliptic curves
3. Random maximal isotropic subspaces and Selmer groups
4. The invariants of a genus one curve
5. Bertini theorems over finite fields
6. Integral points on elliptic curves and 3-torsion in class groups
7. The average analytic rank of elliptic curves
8. Reflection Principles and Bounds for Class Group Torsion
9. The number of extensions of a number field with fixed degree and bounded discriminant
10. Fourier coefficients of modular forms on G2

Their papers

• Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves (2017) — 86 citations
• Squarefree values of polynomial discriminants I (2016) — 78 citations
• Geometry-of-numbers methods over global fields I: Prehomogeneous vector spaces (2015) — 68 citations
• The average size of the 5-Selmer group of elliptic curves is 6, and the average rank is less than 1 (2013) — 84 citations
• Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0 (2010) — 167 citations
• Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves (2010) — 239 citations
• On the Davenport–Heilbronn theorems and second order terms (2010) — 150 citations