Bjorn Poonen

Geometry and Topology · 2000–2017

A researcher in the Science corpus: 22 papers; trusts 40 researchers and is trusted by 38 researchers here, as inferred from the citation graph.

Subfields

• Geometry and Topology — 104 citations into it; #523 of 7,422 by trust here, #433 by citations
• Algebra and Number Theory — 60 citations into it; #288 of 2,864 by trust here, #280 by citations
• Mathematical Physics — 57 citations into it; #3,402 of 8,562 by trust here, #2,122 by citations
• Computational Theory and Mathematics — 29 citations into it; #2,869 of 12,182 by trust here, #3,339 by citations
• Discrete Mathematics and Combinatorics — 18 citations into it; #1,944 of 2,017 by trust here, #1,051 by citations
• Information Systems — 11 citations into it; #4,669 of 8,771 by trust here, #5,501 by citations
• Theoretical Computer Science — 10 citations into it
• Applied Mathematics — 9 citations into it; #4,224 of 7,620 by trust here, #4,482 by citations

Whom Bjorn Poonen trusts overall

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

1. Manjul Bhargava
2. Alexei N. Skorobogatov
3. Michael Stoll
4. N. Jones
5. Brian Conrad
6. Robert A. Wilson
7. Ofer Gabber
8. J. Kollár
9. A. Shankar
10. Qing Liu

Who trusts Bjorn Poonen overall

1. Manjul Bhargava
2. Qing Liu
3. Dietrich Burde
4. A. Shankar
5. D. Huybrechts
6. Michael Stoll
7. Alice Fialowski
8. Dino J. Lorenzini
9. Kiran S. Kedlaya
10. Christopher J. Hillar

Papers from Bjorn Poonen's perspective

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

1. Random maximal isotropic subspaces and Selmer groups
2. Independence of rational points on twists of a given curve (Compositio Mathematica)
3. Bertini theorems over finite fields
4. Implementing 2-descent for Jacobians of hyperelliptic curves
5. The average size of the 2-Selmer group of Jacobians of hyperelliptic curves having a rational Weierstrass point
6. The Monster is a Hurwitz group
7. Most hyperelliptic curves over Q have no rational points
8. Pseudo-reductive Groups
9. Mazur’s conjecture on higher Heegner points
10. On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises (Journal of The American Mathematical Society)

Their papers

• Random polynomials having few or no real zeros (2000) — 84 citations
• The Grothendieck ring of varieties is not a domain (2002) — 107 citations
• Most odd degree hyperelliptic curves have only one rational point (2013) — 71 citations
• Rational Points on Varieties (2017) — 300 citations
• A heuristic for boundedness of ranks of elliptic curves (2016) — 81 citations
• ISOMORPHISM TYPES OF COMMUTATIVE ALGEBRAS OF FINITE RANK OVER AN ALGEBRAICALLY CLOSED FIELD (2016) — 75 citations
• Modeling the distribution of ranks, Selmer groups, and Shafarevich-Tate groups of elliptic curves (2013) — 93 citations
• Bertini irreducibility theorems over finite fields (2013) — 64 citations
• Arithmetic of Higher-Dimensional Algebraic Varieties (2012) — 73 citations
• UNDECIDABLE PROBLEMS: A SAMPLER (2012) — 48 citations
• Random maximal isotropic subspaces and Selmer groups (2010) — 118 citations
• Néron–Severi groups under specialization (2009) — 78 citations
• Insufficiency of the Brauer-Manin obstruction applied to étale covers (2008) — 81 citations
• Characterizing integers among rational numbers with a universal-existential formula (2007) — 60 citations
• Gonality of modular curves in characteristic~$p$ (2006) — 76 citations
• The moduli space of commutative algebras of finite rank (2006) — 63 citations
• The Brauer-Manin obstruction for subvarieties of abelian varieties over function fields (2006) — 59 citations
• Twists of X(7) and primitive solutions to x^2+y^3=z^7 (2005) — 107 citations
• Hilbert's Tenth Problem and Mazur's Conjecture for large subrings of $\mathbb{Q}$ (2003) — 53 citations
• Finiteness results for modular curves of genus at least 2 (2002) — 82 citations