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Sam Hopkins

Cambridge, MA

http://mit.edu/~shopkins

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Top Questions
91 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 '16 at 18:55
mathoverflow.net

40 votes

Examples of “unsuccessful” theories with afterlives

soft-question ho.history-overview big-list asked Sep 18 '19 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 '19 at 22:17
mathoverflow.net

20 votes

Cyclic action on Kreweras walks

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

20 votes

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

fields asked Nov 15 '13 at 6:09
mathoverflow.net

19 votes

Counting problems where unlabeled is easier than labeled

co.combinatorics enumerative-combinatorics hyperplane-arrangements asked Mar 6 '16 at 22:04
mathoverflow.net

18 votes

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

soft-question journals asked Aug 23 '18 at 21:38
mathoverflow.net

18 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 '19 at 9:11
mathoverflow.net

17 votes

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

co.combinatorics asked Feb 16 '13 at 1:02
mathoverflow.net

15 votes

Is there a natural notion of completion of a Coxeter system?

gr.group-theory rt.representation-theory coxeter-groups asked Mar 5 '14 at 3:24
mathoverflow.net

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Top Answers
50
Noteworthy, but not so famous conjectures resolved recent years
mathoverflow.net

48
Mathematicians with both “very abstract” and “very applied” achievements
mathoverflow.net

40
Important formulas in combinatorics
mathoverflow.net

40
Every mathematician has only a few tricks
mathoverflow.net

37
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

32
Examples of unexpected mathematical images
mathoverflow.net

31
New grand projects in contemporary math
mathoverflow.net

28
Which popular games have been studied mathematically?
mathoverflow.net

25
“Strange” proofs of existence theorems
mathoverflow.net

23
Open questions about posets
mathoverflow.net

22
PhD dissertations that solve an established open problem
mathoverflow.net

20
trace and involution permutations: Part I
mathoverflow.net

20
Theorems that impeded progress
mathoverflow.net

18
Elementary applications of linear algebra over finite fields
mathoverflow.net

18
Open questions about posets
mathoverflow.net

16
Two questions on the permutohedron
mathoverflow.net

16
What definitions were crucial to further understanding?
mathoverflow.net

15
Is matroid realizability computable?
mathoverflow.net

15
Decision problems for which it is unknown whether they are decidable
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
Why doesn't mathematics collapse even though humans quite often make mistakes in their proofs?
mathoverflow.net

13
What are examples of (collections of) papers which “close” a field?
mathoverflow.net

13
About the definition of E8, and Rosenfeld's “Geometry of Lie groups”
mathoverflow.net

13
Integer but not Laurent sequences
mathoverflow.net

12
Time-saving (technology) tricks for writing papers
mathoverflow.net

12
Explanatory vs Non-explanatory Proofs
mathoverflow.net

11
Fascinating moments: equivalent mathematical discoveries
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11
Enumerating all permutations that are “square roots” of derangements
mathoverflow.net

11
What is the amplituhedron?
mathoverflow.net

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