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Learning math
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33 votes
8 answers
11k views

How is differential geometry used in immediate industrial applications and what are some sources to learn about it?

15 votes
2 answers
4k views

Switching from pure mathematics (e.g. geometry) to more applied areas (e.g imaging) after Ph.D., as postdoc and chance of getting such a postdoc?

10 votes
2 answers
3k views

How difficult will it be for me to switch fields (details below) after my Ph.D. in pure mathematics?

9 votes
1 answer
775 views

Sources to find industrial jobs for mathematicians with a Ph.D., or with advanced backgrounds? (preferably research positions but not necessarily)

6 votes
0 answers
381 views

Difference between parallel transport composed with exponential maps along two different geodesics starting at the same point?

4 votes
1 answer
189 views

Distance comparison in submanifold versus in the underlying manifold

4 votes
1 answer
135 views

Under what hypothesis on the domain is the X-ray transform/John transform operator bounded?

4 votes
3 answers
2k views

Is this inequality involving the Frobenius norm right?

4 votes
1 answer
227 views

Local maxima of the sum of Gaussian functions in *multiple dimensions* are always strict local maxima - prove/disprove/prove conditionally?

3 votes
1 answer
122 views

Homogeneous regular (= polynomial component) maps with odd degree and their being global homeomorphisms in dimensions higher than one?

3 votes
1 answer
304 views

Connection between non-constant completely monotone function and strictly positive definite kernels (Schoenberg characterization)

3 votes
1 answer
471 views

Two minimization problems using singular value decomposition

3 votes
0 answers
340 views

"Parallel translate" of a geodesic in the following sense [closed]

3 votes
2 answers
459 views

Physical and real life interpretation of the concept of regularity used in differential equations?

3 votes
2 answers
344 views

Request for some references exploring the connections of Riemann surfaces with medical imaging

2 votes
1 answer
555 views

Generalization of the Lie group exponential map and its derivative

2 votes
0 answers
128 views

Is the following inequality true for the norm of Moore-Penrose pseudoinverses?

2 votes
0 answers
1k views

Taylor expansions of Riemannian exponential map and Jacobi fields? [closed]

2 votes
1 answer
285 views

Riemannian submanifolds of Euclidean space admitting Lipschitz extension of Lipschitz functions, and converse statement

2 votes
1 answer
758 views

Bound on eigenvalues of sample covariance matrices in terms of $d, n$, where $n=$ sample size, $d=$ dimension of data

2 votes
1 answer
96 views

Characterization of extrinsic distance prevserving embedding (see the definition given!) from low dimensional Euclidean spaces to high dimensions

2 votes
0 answers
445 views

Comparison of concentrations of different $L^p$-norms of (sub) Gaussian distributions

2 votes
1 answer
753 views

Asymptotically tight concentration of norms of subgaussian random vectors with independent coordinates, as the dimension $n \to \infty?$

2 votes
0 answers
125 views

An attempt to define expected value of a Riemannian manifold valued random variable - what'll go wrong?

2 votes
1 answer
170 views

Marcenko-Pastur and Tracy-Widom laws for sample covariance and Gram matrices when the "features" are correlated: references

1 vote
0 answers
114 views

Law of large numbers and Central Limit Theorem for eigenvalues of perturbed matrices

1 vote
0 answers
72 views

Tracy Widom type results for asymptotic distribution of the $k$-th largest eigenvalue of the sample covariance when $n, p \to \infty$?

1 vote
1 answer
134 views

Asymptotics of $\chi_m$-distribution where the degree of freedom $m \to \infty?$

1 vote
1 answer
128 views

Diagonalizability, orthogonal diagonalizability of higher order tensors and their being or not being dense in some suitable topology

1 vote
1 answer
128 views

How do we calculate the gradient of this function defined using the Riemannian logarithm on a Riemannian manifold?