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Sam Hopkins

Cambridge, MA

http://mit.edu/~shopkins

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Top Questions
99 votes

Why do combinatorial abstractions of geometric objects behave so well?

ag.algebraic-geometry co.combinatorics rt.representation-theory coxeter-groups matroid-theory asked Nov 27, 2016 at 18:55
mathoverflow.net

40 votes

Examples of "unsuccessful" theories with afterlives

soft-question ho.history-overview big-list asked Sep 18, 2019 at 22:06
mathoverflow.net

34 votes

Updates to Stanley's 1999 survey of positivity problems in algebraic combinatorics?

reference-request co.combinatorics open-problems algebraic-combinatorics asked Dec 30, 2019 at 22:17
mathoverflow.net

22 votes

Cyclic action on Kreweras walks

co.combinatorics ds.dynamical-systems posets asked Feb 1, 2020 at 20:12
mathoverflow.net

21 votes

Which fields have multiplicative group isomorphic to additive group times Z/2Z?

fields asked Nov 15, 2013 at 6:09
mathoverflow.net

20 votes

Counting problems where unlabeled is easier than labeled

co.combinatorics enumerative-combinatorics hyperplane-arrangements asked Mar 6, 2016 at 22:04
mathoverflow.net

20 votes

Non-enumerative proof that, in average, less than 50% of tiles in domino tiling of 2-by-n rectangle are vertical?

co.combinatorics enumerative-combinatorics generating-functions tiling fibonacci-numbers asked Sep 9, 2021 at 1:28
mathoverflow.net

19 votes

Why did _Research in the Mathematical Sciences_ change from open access to subscription-based?

soft-question journals asked Aug 23, 2018 at 21:38
mathoverflow.net

19 votes

Is it possible that the GHKK canonical basis for cluster algebras is the Lusztig/Kashiwara dual canonical basis?

co.combinatorics rt.representation-theory grassmannians cluster-algebras canonical-bases asked Jul 5, 2019 at 9:11
mathoverflow.net

17 votes

Is there a n/2 version of the Erdős-Hanani conjecture?

co.combinatorics asked Feb 16, 2013 at 1:02
mathoverflow.net

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Top Answers
59
Mathematicians with both “very abstract” and “very applied” achievements
mathoverflow.net

52
Noteworthy, but not so famous conjectures resolved recent years
mathoverflow.net

43
Every mathematician has only a few tricks
mathoverflow.net

40
Important formulas in combinatorics
mathoverflow.net

40
What's a great christmas present for someone with a PhD in Mathematics?
mathoverflow.net

37
Updates to Stanley's 1999 survey of positivity problems in algebraic combinatorics?
mathoverflow.net

37
Changes forced by the pandemic
mathoverflow.net

36
Examples of unexpected mathematical images
mathoverflow.net

34
New grand projects in contemporary math
mathoverflow.net

32
Who is Mrs. Gerber?
mathoverflow.net

32
Which popular games have been studied mathematically?
mathoverflow.net

30
PhD dissertations that solve an established open problem
mathoverflow.net

27
"Strange" proofs of existence theorems
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23
Open questions about posets
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22
Proofs of theorems that proved more or deeper results than what was first supposed or stated as the corresponding theorem
mathoverflow.net

20
Theorems that impeded progress
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20
Applications of super-mathematics to non-super mathematics
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20
trace and involution permutations: Part I
mathoverflow.net

18
Elementary applications of linear algebra over finite fields
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18
Open questions about posets
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17
Decision problems for which it is unknown whether they are decidable
mathoverflow.net

17
Is matroid realizability computable?
mathoverflow.net

16
What definitions were crucial to further understanding?
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16
Two questions on the permutohedron
mathoverflow.net

15
Important open problems that have already been reduced to a finite but infeasible amount of computation
mathoverflow.net

15
Great polyhedra: What does "great" signify?
mathoverflow.net

14
Why does the number of permutations of $n-1$ adjacent transpositions where the outputs are different equal $2^{n-2}$?
mathoverflow.net

14
Can the numerator in Weyl's character formula be written as a determinant?
mathoverflow.net

14
What are examples of (collections of) papers which "close" a field?
mathoverflow.net

14
Why doesn't mathematics collapse even though humans quite often make mistakes in their proofs?
mathoverflow.net

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