3
votes
1answer
157 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
0answers
165 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
1answer
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
0answers
267 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
1answer
312 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
4answers
835 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
2answers
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
0answers
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
1answer
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
1answer
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
1answer
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
0answers
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
1answer
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
5answers
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
1answer
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
1answer
343 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
2answers
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
2answers
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
1answer
594 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
6answers
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
1answer
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
0answers
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
10answers
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
1answer
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
2answers
437 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
3answers
581 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
1answer
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
1answer
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
0answers
231 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
7answers
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
0answers
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
3answers
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
2answers
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
1answer
444 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
1answer
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
1answer
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
2answers
671 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
0answers
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
1answer
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
19answers
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
11answers
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
7answers
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
10answers
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
0answers
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
1answer
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
2answers
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
6answers
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
1answer
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
0answers
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
2answers
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 ...