# Tagged Questions

**42**

votes

**6**answers

4k views

### What is the significance of non-commutative geometry in mathematics?

This is a question that has been winding around my head for a long time and I have not found a convincing answer. The title says everything, but I am going to enrich my question by little more ...

**31**

votes

**1**answer

1k views

### Various flavours of infinitesimals

I'm not sure if this is a soft question, and whether it may be too broad or, on the contrary, too localized. Well, in Mathematics the concept of "infinitesimal" has been of extreme importance for ...

**7**

votes

**0**answers

270 views

### Canonical Time Evolution for Type $II_{1}$-Factors?

This question was spurred by the answer of Steve Huntsman to the MO question here. The Tomita-Takesaki modular automorphism group gives rise to a canonical time evolution on a type $III$ factor ...

**3**

votes

**0**answers

401 views

### Quantized Calculus, the Hilbert Transform and the Upper Half-Plane

Given a *-algebra $\mathcal{A}$ over $\mathbb{C}$, a Fredholm module is a *-representation $\pi$ of $\mathcal{A}$ as operators on a Hilbert space $\mathcal{H}$ along with a self-adjoint operator $F$ ...

**25**

votes

**2**answers

2k views

### How to unify various reconstruction theorems (Gabriel-Rosenberg, Tannaka,Balmers)

What I am talking about are reconstruction theorems for commutative scheme and group from category. Let me elaborate a bit. (I am not an expert, if I made mistake, feel free to correct me)
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**32**

votes

**6**answers

5k views

### The 'real' use of Quantum Algebra, Non-commutative Geometry, Representation Theory, and Algebraic Geometry to Physics

In this question, Orbicular made the following comment to Feb7 and my own answers;
Please keep in mind that - even though it is stated very often - noncommutative geometry does not give "real" ...

**33**

votes

**7**answers

4k views

### “Algebraic” topologies like the Zariski topology?

The fact that a commutative ring has a natural topological space associated with it is still a really interesting coincidence. The entire subject of Algebraic geometry is based on this simple fact.
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