-4
votes
0answers
86 views

Löwenheim–Skolem as an argument for discrete mathematics? [on hold]

At least as far as first-order theories go, one could construe the (downward) Löwenheim–Skolem theorem as an incentive to invest more in discrete models rather than in continuous ones. This would ...
1
vote
0answers
100 views

current status of combinatorial optimization solvers [closed]

What is the current status of the solvers in combinatorial optimization? For example, what is the "usual feasible size" for a traveller sale's man problem, say, how many nodes and edges are "usually ...
2
votes
1answer
79 views

Interpretation of riemannian geodesics in probability

Good morning everybody. My question is, as maybe already hinted in the title, rather philosopic. We know that geometric properties of a riemannian manifold can be interpreted in terms of certain ...
10
votes
4answers
600 views

Soft question: beginners reference to moduli spaces

What is a geometrically intuitive yet reasonably general first introduction to the theory of Moduli spaces? (Possibly introducing stacks also)? I'm looking for something which really gets the pictures ...
0
votes
0answers
43 views

Models for events where position and time are correlated

Apologies in advance if this question is not sufficiently research-level: What are the standard models that are used to describe phenomena in which events that occur at the same time are likely to be ...
5
votes
3answers
257 views

A. Markov's papers?

A. Markov published several papers on his chains, starting in 1906, so it is written, in the journal: (1) Извѣстія Физико-математического общества при Казанском университете I am surprised by the ...
6
votes
0answers
316 views

Any reason to believe that $NP \neq P$ is unprovable in ZFC

We know $NP \neq P$ from a lot of point of view like empirical reason,or theoretical reasons such as finite model theory or descriptive complexity.Although we find so many reasons to believe $NP \neq ...
2
votes
0answers
384 views

Help with my research topic [closed]

I have a masters degree in mathematics and I'm currently a PHD student. Since the beginning of my studies (2 years ago) I haven't progressed and still don't have a research topic. I was a very good ...
3
votes
1answer
132 views

Countable model theory for $\omega$-stable theories?

This is a bit of a fishing expedition, because I'm not sure what I'm looking for. Very vaguely stated, here's the driving question: What conditions on an $\omega$-stable theory make the class of ...
30
votes
2answers
1k views

Do's and don'ts of writing survey papers

I am not sure if this is the appropriate forum to ask as it is not directly related to a research level (math) problem, but I figured it was worth a try. I recently attended a conference and felt that ...
0
votes
0answers
113 views

Why “Fourier”-Mukai? [duplicate]

The Fourier-Mukai functor is one of the most important tools to work with in the derived category. While it is clear why the name of S.Mukai appears there, why does Joseph Fourier appear in the name ...
2
votes
2answers
457 views

Have axioms / axiom schemata of this flavour been proposed or otherwise considered?

With the exception of a few miscellaneous cases, the axioms (and/or schemeta) of ZFC can roughly be divided into two kinds: Those that guarantee the existence of more complicated sets, given that ...
3
votes
1answer
209 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
182 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
91 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? ...
11
votes
2answers
487 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
414 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 ...
22
votes
4answers
1k 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
207 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
145 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
323 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 ...
8
votes
1answer
345 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
331 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
636 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 ...
6
votes
1answer
624 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. Could anyone give some references for the overview of its history? Any overview of its application ...
7
votes
1answer
433 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
760 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
212 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
754 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
890 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 ...
5
votes
0answers
903 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
2k 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
271 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
469 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
591 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, ...
1
vote
1answer
61 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
253 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
2k 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
250 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
576 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
278 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
470 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 ...
5
votes
1answer
611 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
216 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
711 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 ...
7
votes
0answers
185 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 ...