User Learning math

33 votes

8 answers

12k views

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

asked Aug 4, 2015 at 15:22

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?

asked Jun 28, 2013 at 16:35

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?

asked Nov 18, 2013 at 20:18

9 votes

1 answer

810 views

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

asked May 28, 2014 at 0:56

6 votes

0 answers

406 views

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

asked Jul 11, 2015 at 14:01

4 votes

1 answer

197 views

Distance comparison in submanifold versus in the underlying manifold

asked Apr 4, 2016 at 18:00

4 votes

1 answer

137 views

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

asked Aug 18, 2015 at 23:04

4 votes

3 answers

3k views

Is this inequality involving the Frobenius norm right?

asked Nov 17, 2016 at 10:59

4 votes

0 answers

637 views

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

asked Apr 10, 2020 at 18:52

4 votes

1 answer

286 views

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

asked Feb 6, 2023 at 22:57

3 votes

1 answer

149 views

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

asked Jan 4 at 15:41

3 votes

2 answers

265 views

For a closed Riemannian manifold $M$, must the set of points with non-unique closest points to a closed submanifold $S$ of $M$ be of 0 volume measure?

asked Mar 11 at 12:04

3 votes

1 answer

135 views

Geodesic convexity of Dirichlet Fundamental Domains

asked Sep 22 at 0:40

3 votes

1 answer

352 views

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

asked Feb 7, 2020 at 13:57

3 votes

1 answer

493 views

Two minimization problems using singular value decomposition

asked Mar 24, 2016 at 1:48

3 votes

0 answers

341 views

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

asked Feb 12, 2015 at 18:42

3 votes

2 answers

478 views

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

asked Apr 20, 2014 at 17:21

3 votes

2 answers

348 views

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

asked Aug 25, 2013 at 0:35

2 votes

1 answer

608 views

Generalization of the Lie group exponential map and its derivative

asked May 21, 2015 at 11:07

2 votes

0 answers

147 views

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

asked Nov 17, 2016 at 6:24

2 votes

0 answers

2k views

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

asked Jun 22, 2015 at 11:45

2 votes

1 answer

320 views

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

asked Mar 3, 2020 at 17:44

2 votes

1 answer

900 views

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

asked Apr 14, 2020 at 19:12

2 votes

1 answer

210 views

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

asked Mar 11, 2020 at 17:01

2 votes

1 answer

1k views

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

asked Mar 17, 2020 at 21:57

2 votes

1 answer

101 views

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

asked Mar 30, 2020 at 18:52

2 votes

0 answers

182 views

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

asked Jul 18, 2023 at 18:15

1 vote

1 answer

142 views

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

asked Nov 20, 2023 at 17:22

1 vote

1 answer

255 views

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

asked Nov 24, 2023 at 12:52

1 vote

0 answers

126 views

Is there any sufficient or equivalent condition for the invertibility of a regular map, i.e. a self map of $\mathbb{R}^m$ with polynomial components?

asked Dec 11, 2023 at 15:11

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60 Questions

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

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?

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

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

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

Distance comparison in submanifold versus in the underlying manifold

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

Is this inequality involving the Frobenius norm right?

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

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

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

For a closed Riemannian manifold $M$, must the set of points with non-unique closest points to a closed submanifold $S$ of $M$ be of 0 volume measure?

Geodesic convexity of Dirichlet Fundamental Domains

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

Two minimization problems using singular value decomposition

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

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

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

Generalization of the Lie group exponential map and its derivative

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

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

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

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

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

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

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

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

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

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

Is there any sufficient or equivalent condition for the invertibility of a regular map, i.e. a self map of $\mathbb{R}^m$ with polynomial components?