# Tagged Questions

**3**

votes

**1**answer

161 views

### References for von Neumann Algebras

I have some -possibly- simple but broad questions: Where to begin the study of von Neumann Algebras? Which are the important questions in the field that guide current research? I'm interested in ...

**0**

votes

**0**answers

166 views

### Game Theory - need references on analysis of particular game

My hobby AI research have led me to a thorethical game of particular design. As design is pretty simple, I was sure that such game has well-known name. But my question on math.stackexchange, where I ...

**2**

votes

**1**answer

63 views

### Reference to complete derivation of Kossakowski–Lindblad equation and its steady solutions

Are there recommended textbook or good intro-reference to explain with complete stretch of Kossakowski–Lindblad equation especially how is the idea to derive it from ground?
...

**8**

votes

**0**answers

269 views

### Riemann's quote cited by Lakatos: what is the context?

"If only I had the theorems! Then I should find the proofs easily enough."
This quote is generally attributed to Bernhard Riemann. In particular,
on page 9 in Proofs and refutations by Imre ...

**4**

votes

**1**answer

313 views

### Basics on anabelian geometry and Grothendieck's section conjecture

Even I can find similar questions and some answers on that questions, most of them are not quite unsatisfactory to me. Maybe this is a very stupid question, but there is no other place that I can ask ...

**21**

votes

**4**answers

842 views

### What is the definition of a large cardinal axiom?

In different books one can find different implicit definitions for a large cardinal axiom.
My question is that which one of these definitions are more popular or standard amongst set theorists?
Any ...

**18**

votes

**2**answers

2k views

### Where are Georg Cantor's Original Manuscripts?

Georg Cantor is famous for introducing transfinite numbers and set theory.
A main part of his mathematical point of view about this new type of "numbers" and this new "realm of mathematics" cannot be ...

**2**

votes

**0**answers

201 views

### Request for good research mailing list in Dynamical System & Chaos for notification of recent research results, conference, announcements [closed]

Are there some good research-level mathematics mailing list to be recommended in order to be notified of recent research results, news, announcements, conference, etc, particularly in Dynamical System ...

**2**

votes

**1**answer

138 views

### English translation of Gauss' “Principia generalia theoriae figurae fluidorum in statu aequilibri”

I have been unable to locate an English translation of Gauss' work, "Principia generalia theoriae figurae fluidorum in statu aequilibri".
A German translation exists (PDF), but my German is not quite ...

**5**

votes

**1**answer

297 views

### What does it mean for a Deligne-Mumford stack to have trivial generic stabilizers?

I have stumbled upon some literature on Deligne-Mumford stacks, and it seems to me, at least superficially, that there is a strong link between DM-stacks which have "trivial generic stabilizers" and ...

**7**

votes

**1**answer

300 views

### Model structure for cooperads and for coalgebras

I am studying the homotopy theory of (algebraic) operads and I came up with several questions I am unable to answer to. I would like to stress that I don't have applications in mind, I just would like ...

**1**

vote

**0**answers

312 views

### On Mathematicians Who Did Their Masterworks After 40 Years Old [duplicate]

Remark: The idea of this soft question is adopted from the following interesting book.
Timothy Gowers, Mathematics: A Very Short Introduction, Oxford University Press, 2002.
...

**8**

votes

**1**answer

2k views

### What is the source of this E̶r̶d̶ő̶s̶ quote?

Namely, the following one
"All problems appeared once in the [American Mathematical] Monthly."
I remember reading it several years ago... When I first posed the question, I believed that I had ...

**18**

votes

**5**answers

609 views

### Online high quality colloquium talks

In my department we're thinking about showing online lectures one day per week at lunch, as sort of a virtual colloquium appropriate to mathematics undergraduates as well as faculty. To start with ...

**5**

votes

**1**answer

523 views

### What are current trends/questions in algebraic logic?

What are current trends/questions in algebraic logic?I mean the research developed by Paul Halmos.
And anyone could give some reference for overview of it's history?
Also any overview of it's ...

**7**

votes

**1**answer

344 views

### Number theory underlying Euler's theory of music

I've recently been studying Euler's theories on music, and I came across Euler's concept of gradus suavitatis or 'degree of pleasure' of a rational number representing the ratio of two tones. (I found ...

**19**

votes

**2**answers

718 views

### Strict applications of deformation theory in which to dip one's toe

I hesitate to ask a question like this, but I really have tried finding answers to this question on my own and seemed to come up short. I readily admit this is due to my ignorance of algebraic ...

**3**

votes

**2**answers

209 views

### Equivalent definitions of ample bundles

M. Atiyah in "VECTOR BUNDLES OVER AN ELLIPTIC CURVE" defined ample line bundle $E$ on $X$ as satisfying the following conditions:
Canonical map $H^0(X, E)\to E_x$ is surjective for any $x\in X$.
...

**3**

votes

**1**answer

595 views

### The shortest mathematical paper [duplicate]

I was looking at the paper Zum Hilbertschen Nullstellensatz [1] and wondered if there was a shorter mathematical paper than this one. A colleague of mine rumored about a number-theoretic paper where ...

**14**

votes

**6**answers

1k views

### Mathematical Paper That Just Links Two Different Fields of Sciences

I have a soft question that is interesting for me in some aspects. I appreciate your answers and comments about it.
Four years ago, one of my friends in MIT, in the biology lab, had working on ...

**1**

vote

**1**answer

799 views

### PhD in operator algebras and non-commutative geometry [closed]

I do not know whether it is a good place to ask this question or not.
I want to PhD in operator algebras and non-commutative geometry. What are the best places in the world for that? I want a good ...

**3**

votes

**0**answers

711 views

### “Must read ”papers on analytic number theory

Question: What would be some must-read
papers for an aspiring analytic number
theorist? In other words, what are the papers that any analytic number theorist would have read? (Background: ...

**19**

votes

**10**answers

1k views

### Learning through guided discovery

I have been working through Kenneth P. Bogart's "Combinatorics Through Guided Discovery". You can download it from this page: http://www.math.dartmouth.edu/news-resources/electronic/kpbogart/
I've ...

**7**

votes

**1**answer

246 views

### Formulating the calculus of varations with exterior calculus

I noticed that a calculus of variations problem is just an integral over a differential form. Therefore, I would think it would be possible to formulate the Euler-Lagrange equations using exterior ...

**7**

votes

**2**answers

438 views

### Examples In Ergodic Theory and Topological Dynamics

I am currently studying basic Ergodic Theory:
Invariant Measures
Poincaré recurrence Theorem
Invariant Measure For Continuous Transformations
The Ergodic Theorems and Applications
Ergodic ...

**4**

votes

**3**answers

582 views

### Meaning of a phrase from “The algebra of grand unified theories”.

Motivated by an answer to this mathoverflow question I've been making an effort to understand Baez and Huerta's article "The algebra of grand unified theories".
As far as I can tell, mathematically, ...

**0**

votes

**1**answer

52 views

### Continuity of an extension map

Suppose $\delta\in (0,1)$ and $r<1+\delta.$ Suppose moreover we are given a sequence of functions $u_m\in H^{1/2,2}(\partial B_r(0))$, where $B_r(0)$ denotes the euclidean $n-$dimensional ball. ...

**22**

votes

**1**answer

1k views

### How should a number theorist learn a modest amount of algebraic geometry?

A little bit vague, but I hope useful for the entire community.
I am, by training, an analytic number theorist. I have managed to learn some algebraic geometry, by reading parts of Silverman's ...

**2**

votes

**0**answers

232 views

### Descriptive set theory on $\mathbb{R}^\mathbb{N}$

The short version of my question is, What is a good source for learning about descriptive set theory on the space $\mathbb{R}^\mathbb{N}$, under the product topology coming from the discrete topology ...

**11**

votes

**7**answers

1k views

### What are some Applications of Teichmüller Theory?

I'm trying to collect some specific examples of applications of Teichmüller Theory. Here are some things I have collected thus far:
No-wandering-domain Theorem (Sullivan)
Theorems of Thurston ...

**3**

votes

**0**answers

229 views

### A Question Regarding Boolean-valued Models

What were the intuitions motivating the creation (or discovery, if you will) of Boolean-valued models? I have searched for the Scott-Solovay paper on the subject, but to no avail. There also seems to ...

**4**

votes

**3**answers

566 views

### Quotations about the power of simple ideas [closed]

I'm looking for quotations about how very simple mathematical ideas can be very powerful. I know of a few, but they're not quite what I'm looking for insofar as they contain criticism of other ...

**4**

votes

**2**answers

254 views

### Is the generalized Baire space complete?

I want to see whether the fact that the Baire space $\omega^\omega$ is a complete (metrizable) space generalizes to $\kappa^\kappa$ being a complete (topological) space. I think this is an easy ...

**3**

votes

**1**answer

446 views

### Request: Kato's article “Lectures on the approach to Iwasawa theory for Hasse-Weil L-functions.” Part II

Hello,
The question (similar to MO.96531) is about the article by Professor Kazuya Kato in this book.
In this article, Professor Kato indicates the contents of the second part.
MathSciNet does not ...

**3**

votes

**1**answer

533 views

### Convenient definition of “category of Riemannian manifolds”?

Has a notion of "category of Riemannian manifolds" been defined and used in the literature?
For which reasons is it or would it (not) be a useful notion?
I think the objects should be all (perhaps ...

**9**

votes

**1**answer

207 views

### Is there a Dedekind-Frobenius group determinant for infinite groups?

If $G$ is a finite group and $\lbrace x_{g} \rbrace_{g\in G}$ are commuting formal variables, then one can form a matrix whose $(g,h)$ entry is $x_{gh^{-1}}$. The determinant of this matrix is a ...

**6**

votes

**2**answers

674 views

### Road to Solovay's Land.

In the first semester of 2012 I took a course in General Topology and Set Theory, at undergraduate level. For topology, I was instructed to use Engelking's General Topology; albeit I had a great ...

**8**

votes

**0**answers

181 views

### Fixed marginals of joint distribution: status

One of the well-known problems of classical probability theory is the determination of the set of all extreme points in the convex set of all probability distributions in a product Borel space $\left ...

**0**

votes

**1**answer

110 views

### Reference: DaPrato and Grisvard parabolic PDEs.

Has anyone read G. DaPrato and P. Grisvard Equations d'evolution abstraites nonlineaires de type parabolique?
It's not available in my library. I am wondering if it's worth me acquiring it: is it ...

**16**

votes

**19**answers

2k views

### History Question: AUTObiography of Mathematicians

According to Wikipedia, an autobiography is an account of the life of a person, written by that person sometimes with a collaborator.
An autobiography offers the author the ability to recreate ...

**28**

votes

**11**answers

5k views

### “Must read” papers in numerical analysis

In 1993, Prof. L.N. Trefethen published a NA-net posting with a list of thirteen paper he used for teaching the seminar Classic Papers in Numerical Analysis.
In Trefethen's words, ... this course ...

**6**

votes

**7**answers

1k views

### Incidences of rigorous proofs used in legal proceedings

Motivation: Loius Pojman mentions in What Can We Know? (2001) of a certain Carneades (ca. 214-129 B.C>) who must have been a "remarkable dialectician"because " in 155BC he was sent on a diplomatic ...

**7**

votes

**10**answers

3k views

### Music: mathematical point of view (revised) [closed]

Mathematical analysis of music started when Pythagoras made his observations about consonant intervals and ratios of string lengths.
ADDED:
In the paper Mathematical Music Theory -- Status Quo 2000, ...

**8**

votes

**0**answers

367 views

### Composition of two formal series

There are two formal semi-infinite Laurent series
$$
f_+(z)=z+\sum_{k=2}^{\infty} a_k z^k
$$
and
$$
f_-(z)=z+\sum_{k=0}^{\infty} b_k z^{-k}
$$
Their composition (we assume that this composition ...

**16**

votes

**1**answer

836 views

### Raoul Bott's quote on Morse Theory cited by Bestvina and Kahle: where is it from?

I wanted to properly cite the following awesome quote:
Every mathematician has a secret weapon. Mine is Morse theory. - Raoul Bott
Now this has been attributed to Bott in precisely two places ...

**3**

votes

**2**answers

1k views

### Papers whose title defines a new terminology [duplicate]

To explain a new signal processing technique based on Fourier Transform, Bogert et al went on to define a new vocabulary. The new terminology was published in a paper with the title:
The Quefrency ...

**31**

votes

**6**answers

2k views

### Status of PL topology

I posted this question on math stackexchange but received no answers. Since I know there are more people knowledgeable in geometric and piecewise-linear (PL) topology here, I'm reposting the question. ...

**17**

votes

**1**answer

1k views

### What has happened to Lang's Files and other political texts?

For some background on Lang and his files, one can read the first part of Lang's obituary in the AMS Notices at http://www.ams.org/notices/200605/fea-lang.pdf.
The book "Challenges" was published in ...

**3**

votes

**0**answers

143 views

### Who defined the Inertia Group $I(M^n)\subset\Theta_n$ of a smooth manifold?

If you're unfamiliar with the definition, for an oriented smooth manifold $M^n$ we define the inertia group $I(M)$ to be the set of (h-coboridsm classes of) homotopy spheres $\Sigma^n$ such that ...

**16**

votes

**2**answers

1k views

### Surveys of Goodwillie Calculus

Is there a good general introduction to Goodwillie calculus out there, like a paper or publication that gives a general overview of the calculus as well as how it is useful and why we are interested ...