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      Questions tagged [reference-request]

      This tag is used if a reference is needed in a paper or textbook on a specific result.

      1
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      22 views

      Functorial cones

      This is probably more a reference request than a real question. I was studying dg-categories in order to understand how one can derive a functorial cone construction when a triangulated category (...
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      votes
      0answers
      34 views

      Terminology: a certain semicategory with objects mor(C) (not the usual or twisted arrow category)

      I’ve had recent cause to consider the following construction: given a category $\newcommand{\C}{\mathbf{C}}\C$, define a semicategory $M(\C)$, whose objects are arrows of $\C$, and where a map from $f ...
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      votes
      2answers
      506 views

      Books on the History of math research at European universities

      Are there good books that cover the history of math and mathematical science (ex. physics, chemistry, computer science) PhD programs in the Occident? My primary motivation is to figure out how the PhD ...
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      votes
      1answer
      44 views

      References for Evaluating Multiple Sums

      I often run into double and triple sums in solid state physics, and there seems to be a definable suite of mostly analytic tools (Poisson summation, Mellin transforms, theta functions, modular forms ...
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      votes
      1answer
      138 views

      Finite covers of Boolean algebras by their subalgebras

      It is a student exercise that no group can be represented as a set-theoretic union of its two proper subgroups. The same also can be shown for Boolean algebras. On the other hand, it's not hard to ...
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      votes
      1answer
      250 views

      Is there any references on the tensor product of presentable (1-)categories?

      Is there any references on the tensor product of (locally) presentable categories ? All I know about this is Lurie's book that deals with the $\infty$-categorical version, and a few references that ...
      3
      votes
      1answer
      175 views
      +50

      Reference request: Oldest (non-analytic) geometry books with (unsolved) exercises?

      Per the title, what are some of the oldest (non-analytic) geometry books out there with (unsolved) exercises? Maybe there are some hidden gems from before the 20th century out there.
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      votes
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      198 views

      What are the character tables of the finite unitary groups?

      I need to know the (complex) character table of the finite unitary group $U_n(q)$. Lusztig and Srinivasan (1977) provide an abstract description, but parsing it requires a stronger background in ...
      2
      votes
      1answer
      140 views

      Alternating binomial-harmonic sum: evaluation request

      Let $H_k=\sum_{j=1}^k\frac1j$ be the harmonic numbers. QUESTION. Can you find an evaluation of the following sum? $$\sum_{a=1}^b(-1)^a\binom{n}{b-a}\frac{H_{b-a}}a.$$
      1
      vote
      1answer
      25 views

      Reference request: Gaussian almost periodic functions

      Let $X(x),x\in R^d$, be a stationary gaussian process for which the covariance function $E(X(0)X(x))=C(x)$ is "almost periodic". Almost periodic means roughly that $C$ is uniformly approximable by ...
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      votes
      3answers
      154 views

      Real points of reductive groups and connected components

      Let $\mathbf G$ be a connected reductive group over $\mathbb R$, and let $G = \mathbf G(\mathbb R)$. Then $G$ is not necessarily connected as a Lie group, e.g. $\mathbf G = \operatorname{GL}_n$. ...
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      votes
      0answers
      186 views

      Did Grothendieck-Serre write about toric varieties?

      I'm curious if Grothendieck or Serre wrote anything about toric varieties? Were they aware of the notion? I would much appreciate any references.
      2
      votes
      1answer
      157 views

      Reference request: Gauge theory [on hold]

      What are some good introductory texts to gauge theory? I have some basic differential geometry knowledge, but I don’t know any algebraic geometry. Also, as a side question, what intuitively is a ...
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      vote
      0answers
      23 views

      Reference Request: Total Variation Between Dependent and Independent Bernoulli Processes

      Let $X$ be a random variable taking values in $\{0,1\}^n$ with the following distribution. For each coordinate $i$, we have $p_i = P(X_i = 1) = c/\sqrt n$, where $c$ is a (very small) constant. ...
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      votes
      1answer
      78 views

      Non-trivial foliation (excluding the Reeb foliation) [on hold]

      Let $M$ be a closed oriented manifold, an oriented foliation $F$ is said non-trivial, if $F$ is not fibration of $M$, i.e. there does not exist a closed manifold $B$, such that $M\overset{F}{\to} B$. ...

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