## Research topics in Curves and Surfaces [closed]

Closed. This question needs to be more focused. It is not currently accepting answers. Want to improve this question? Update the question so it focuses on one problem only by editing this post. Closed 5 years ago. Improve this question I advance that I’m not a mathematician but I’m an undergraduate student of mathematics. In … Read more

## What are some interesting examples of cooperative games that can be naturally generalised to a stochastic version of it?

In classical, deterministic cooperative game theory, there are $N$ players that can form $2^{N}$ coalitions. Each of these coalitions is assigned a value by means of the characteristic function $v ( \cdot )$ associated with the particular game, such that $v: 2^{N} \to \mathbb{R}$. The game can be “solved” (i.e. the payoffs can be distributed … Read more

## Has the external knit product been used to construct a previously unknown group?

In the Wikipedia article Zappa–Szép product , the knit product (a.k.a. Zappa–Szép product, Zappa–Rédei-Szép product, general product, exact factorization) is defined, and its basic properties are laid out. Within that article lies a section entitled “External Zappa–Szép products” which details how to take groups H and K (when the groups meet certain properties and when … Read more

## 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, jump to the bottom for time-sensitive information. I am looking for references on porting mathematical code to parallel-processing clusters. To limit the field, I … Read more

## What are your common strategies/remedies when your new theory/idea stuck in most cases?

Sorry if this is not a suitable post for MO. Sometimes after reading the origin of a theory/idea in differential topology I put myself in the shoes of that mathematician and ask myself, Did you do the same? Is that a natural theory/idea? Let’s explain my problem with an example. When I read about Morse … Read more

## Maximality without Zorn

When confronted with finding an object that is maximal with regard to some ordering relation, most of us have the reflex to use Zorn’s Lemma. I am interested in instances of proving the existence of maximal objects, where Zorn’s Lemma is explicitly of no use. By that I mean that you can construct chains of … Read more

## A list of locally finitely presentable topoi that are not coherent

Coherent topoi play an important role in topos theory, especially in the interaction with logic. Their most handy characterization is provided by Johnstone. Sketches, D3.3.1. Every coherent topos is locally finitely presentable (Johnstone. Sketches, D3.3.12), but the converse is not true. Since I am not aware of many counterexamples to the converse, I would like … Read more

## The link and equivalence between variant definition of computation model and computational complexity over reals

To unify the numerical computation and classic computability theory, or to pave a foundation for the numerical computation, mathematicians present variant computation model and computational complexity over reals, for example, the one in the book by Blum,Cucker,Shub, and Smale, or the one in Weihrauch’s book Computable Analysis. mathematicians on such topics usually give the definition … Read more

## Very canonical constructions

You have two categories C1 and C2. We call a map of the classes Ob(C1)→Ob(C2) a construction. Sometimes you can find a functor C1→C2 inducing this map, then you call your construction functorical or canonical. Let us all a construction very canonical if there is a functor inducing it and between any two such functors … Read more

## Transfinite induction vs induction in mathematics

What are the nontrivial theorems one can prove about natural numbers which need transfinite induction? By “need transfinite induction” I mean one can show that the statement is not provable in arithmetic which only allows induction up to ω. In particular, are there any statements which only state a claim about natural numbers but which … Read more