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0
votes
0answers
62 views

Reduction argument from a general vertex set V(G) to a prime power in Prof. Keevash's proof on the Existence of Designs

The proof flow of the paper "On the Existence of Designs" by Prof. Keevash as I understand it is the following: -- Reduction from the general case to $V = \mathbb{F}_{p^a}$ (Lemma 6.3) -- Covering ...
18
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2answers
2k views

Open Problems in Algebraic Topology and Homotopy Theory

Some time ago (I see it was initially written before 1999?) Mark Hovey assembled a list of open problems in algebraic topology. The list can be found here. Some of the problems I know about have been ...
5
votes
1answer
465 views

List of open problems of formal languages [closed]

As we know, there are some open problems of formal languages. I am wondering if there is a somehow complete list of open problem of formal languages. If there isn't such a list, can we make it one as ...
15
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10answers
3k views

Open problems in PDEs, dynamical systems, mathematical physics

(This question might not be appropriate for this site. If so, I apologize in advance. I would have posted to mathstack, but I'm looking for advice from active researchers.) I am an undergrad in math ...
0
votes
0answers
267 views

Known and unknown about Ramanujan's tau function

What is a good reference for open problems relating to the Ramanujan tau function? I know about Lehmer's conjecture. I know the following reductions of the problem: the smallest counterexample must ...
14
votes
3answers
958 views

open problems in Seiberg-Witten Theory on 4-Manifolds

What are some of the open problems in Seiberg-Witten Theory on 4-Manifolds.I tried googling but couldn't any. I tried googling it, but couldn't find any resources.The places where I can a survey or ...
11
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7answers
1k views

Open problems in the theory of compact quantum groups

What are the important open problems in the theory of compact quantum groups? Or conjectures? Here is an example from An De Rijdt's Ph.D. thesis: Is every compact quantum group with the fusion rules ...
9
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4answers
1k views

What are the major open problems in design theory nowaday?

I gather that the question whether the Bruck-Chowla-Ryser condition was sufficient used to top the list, but now that that's settled - what is considered the most interesting open question?
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4answers
1k views

Open problems in Birational Geometry, after BCHM

Rencently a breakthrough was made in the context of the Minimal Model Program by the work of Birkar-Cascini-Hacon-McKernan. They proved that the canonical ring of a smooth or mildly singular ...
37
votes
11answers
2k views

Important open problems that have already been reduced to a finite but infeasible amount of computation

Most open problems, when formalized, naturally involve quantification over infinite sets, thereby obviating the possibility, even in principle, of "just putting it on a computer." Some questions ...
5
votes
1answer
277 views

Open problems about CMC hypersurfaces with symmetries?

Recently, Andrews and Li announced a complete classification of CMC ($H=const.$) tori in $S^3$, confirming a conjecture of Pinkall and Sterling. Their main result is that any such torus is ...
1
vote
3answers
532 views

Open problems in sub-Riemannian geometry

What are some open problems in sub-Riemannian geometry? I am interested especially in problems concerning connections and curvature, but any contribution is welcomed.
8
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3answers
952 views

Motivation and unsolved problems of TQFT

I have been studying topological quantum field theory by mainly reading the Turaev's book. I'd like to know if there are unsolved problems that motivate mathematicians to study TQFT, like Riemann's ...
10
votes
1answer
368 views

List of Whitehead-like Problems

Whitehead problem is a rather well known problem: Suppose that $G$ is an abelian group and $\mathrm{Ext}^1(G,\Bbb Z)=0$, is $G$ free? It wasn't long before it was proved that if $G$ is ...
7
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9answers
2k views

Not especially famous, long-open problems which higher mathematics beginners can understand

This is a pair to Not especially famous, long-open problems which anyone can understand So this time I'm asking for open questions so easy to state for students of subjects such as undergraduate ...
37
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30answers
4k views

Fundamental problems whose solution seems completely out of reach [closed]

In many areas of mathematics there are fundamental problems that are embarrasingly natural or simple to state, but whose solution seem so out of reach that they are barely mentioned in the literature ...
144
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79answers
24k views

Not especially famous, long-open problems which anyone can understand

Question: I'm asking for a big list of not especially famous, long open problems that anyone can understand. Community wiki, so one problem per answer, please. Motivation: I plan to use this list ...
25
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1answer
1k views

Important open questions in the field of Tropical geometry

What are some of the important unanswered questions in the field of tropical geometry?
49
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21answers
15k views

Open problems with monetary rewards

Since the old days, many mathematicians have been used to attaching monetary rewards to problems they admit are difficult. Their reasons could be to draw other mathematicians' attention, to express ...
15
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9answers
4k views

Open Questions in Riemannian Geometry

What are some major open problems in Riemannian Geometry? I tried googling it, but couldn't find any resources.
37
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13answers
5k views

What are some of the big open problems in 3-manifold theory?

From what I understand, the geometrization theorem and its proof helped to settle a lot of outstanding questions about the geometry and topology of 3-manifolds, but there still seems to be quite a lot ...