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        Questions tagged [big-list]

        Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.

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        34
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        26answers
        4k views

        Examples of simultaneous independent breakthroughs

        I'm looking for examples where, after a long time with little progress, a simultaneous mathematical discovery, solution, or breakthrough was made independently by at least two different people/groups. ...
        14
        votes
        1answer
        377 views

        Legendary extra parameters to simplify a counting problem

        I am reading Proofs and Confirmations, the history behind the alternating sign matrix conjecture, regarding counting $n \times n$ alternating sign matrices. In the introduction, it is written that ...
        5
        votes
        0answers
        107 views

        Where have you encountered “arrangement spaces”?

        I am compiling a paper in which I advertise (and use) the following notion of arrangement spaces (I made up the name, as I found no standard name in the literature). Let $v_i\in\Bbb R^d,i\in N:=\{1,.....
        9
        votes
        0answers
        346 views

        True on stalks, false on affine opens [closed]

        In scheme theory, there are some properties that can be specified purely on the stalks of the structure sheaf but they "lift" to the properties of the values of structure sheaf on affine opens, e.g. ...
        51
        votes
        5answers
        5k views

        Arriving at the same result with the opposite hypotheses

        I am pretty distant from anything analytic, including analytic number theory but I decided to read the Wikipedia page on the Riemann hypothesis (current revision) and there is some pretty interesting ...
        8
        votes
        2answers
        635 views

        Errata for Bott and Tu's book “Differential Forms in Algebraic Topology”

        My book is Differential Forms in Algebraic Topology by Loring W. Tu and Raoul Bott of which An Introduction to Manifolds by Tu is a prequel. Is there a good list of errata for Bott and Tu available? ...
        4
        votes
        1answer
        309 views

        Functors on the category of abelian groups which satisfy $F(G\times H) \cong F(G)\otimes_{\mathbb{Z}} F(H)$

        Edit: According to the comment of Todd Trimble, I revise the question. What are some examples of functors $F$ on the category of Abelian groups or category of rings which satisfy $$F(G\times H)\cong ...
        4
        votes
        1answer
        266 views

        Very canonical constructions

        You have two categories $C_1$ and $C_2$. We call a map of the classes $\mathrm{Ob}(C_1)\rightarrow \mathrm{Ob}(C_2)$ a construction. Sometimes you can find a functor $C_1\rightarrow C_2$ inducing this ...
        7
        votes
        0answers
        135 views

        Examples of automorphic representations to keep in mind

        I have recently started studying the automorphic science and find it somewhat hard to form intuition. Can we have a list of examples of automorphic representations that you usually use to test a new ...
        15
        votes
        1answer
        1k views

        Telling right from left

        I know a lot of people, some of them mathematicians, who have trouble telling right from left. This can lead to problems when you are composing functions, for example. When did this seemingly ...
        5
        votes
        0answers
        232 views

        What arithmetic would you do in parallel?

        This is a post asking for references, and soliciting problems and people interested in accelerated computing. I will add the big-list tag and make it community-wiki. If this interests you strongly, ...
        9
        votes
        5answers
        698 views

        Equivalent forms of the P vs. NP problem

        Many things in math can be formulated quite differently; see the list of statements equivalent to RH here, for example, with RH formulated as a bound on lcm of consecutive integers, as an integral ...
        1
        vote
        1answer
        222 views

        Topological Invariants for Group

        Let $\mathbf{Grp}$ be the category of groups and $\mathbf{Top}$ be the category of topological spaces. To each group $(G, \circ_G)$, we can associate a topological space $(G,\tau_G)$ the basis for ...
        15
        votes
        2answers
        786 views

        Examples of problems where considering “discrete analogues” has provided insight or led to a solution of the original problem

        The Kakeya conjecture posits that any Kakeya set in $\mathbb{R}^n$ has dimension $n$. A discrete (finitized?) version of this problem is the Finite Field Kakeya conjecture, which was proved by Dvir ...
        9
        votes
        2answers
        283 views

        Big list of comonads

        The concept of a monad is very well established, and there are very many examples of monads pertaining almost all areas of mathematics. The dual concept, a comonad, is less popular. What are ...

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