User Marion

15 votes

13 answers

6k views

How to explain the formula for the sum of a geometric series without calculus?

asked Mar 11, 2015 at 13:19

12 votes

1 answer

5k views

$S^2=SO(3)/SO(2)$. Does this mean that $S^2 = SU(2)/U(1) $?

differential-geometry algebraic-topology lie-groups

asked Mar 25, 2015 at 17:28

12 votes

1 answer

1k views

Physicist trying to understand GIT quotient

algebraic-geometry quotient-spaces symplectic-geometry geometric-invariant-theory

asked Feb 21, 2017 at 21:44

7 votes

1 answer

371 views

$q$-series and modular forms

number-theory modular-forms reference-works

asked Jul 6, 2018 at 9:36

6 votes

2 answers

1k views

Parallel transport of a vector in hyperbolic space, specifically in $\mathbb{H}$

differential-geometry riemannian-geometry hyperbolic-geometry

asked Jun 23, 2015 at 15:49

6 votes

2 answers

4k views

Fundamental group of $\mathbb{R}^n\backslash \{0\}$

general-topology algebraic-topology

asked Jan 23, 2015 at 17:32

5 votes

2 answers

2k views

Prove that the antipodal mapping is an isometry on $S^n$. Help understanding the proof.

differential-geometry manifolds spheres

asked Jun 16, 2015 at 16:54

5 votes

1 answer

2k views

Liouville's theorem and the Wronskian

ordinary-differential-equations differential-geometry symplectic-geometry

asked Jan 6, 2016 at 19:34

5 votes

0 answers

116 views

Abelian instantons for generic metric

physics mathematical-physics vector-bundles principal-bundles gauge-theory

asked Aug 30, 2017 at 6:44

5 votes

6 answers

530 views

How to explain to a school kid that on a sphere the shortest path between 2 points is given by a great circle?

general-topology geometry education learning spheres

asked Jun 8, 2016 at 14:55

4 votes

0 answers

329 views

When are two line bundles isomorphic?

differential-geometry algebraic-geometry holomorphic-bundles

asked Nov 21, 2016 at 23:22

4 votes

1 answer

892 views

If $\phi: M_1 \to M_2$ a diffeomorphism between diff. manifolds, prove that if $M_2$ is oriented then so is $M_1$

differential-geometry manifolds smooth-manifolds orientation

asked Jun 14, 2015 at 15:43

4 votes

3 answers

378 views

What is the quotient space $\mathbb{C}[x,y,z]/(x^2+y^2)$?

abstract-algebra algebraic-geometry quotient-spaces

asked Dec 17, 2015 at 22:05

4 votes

6 answers

1k views

3 points lie in the same straight line. Then why is this formula valid?

algebra-precalculus

asked Feb 12, 2015 at 13:58

4 votes

3 answers

2k views

Circle to circle homotopic to the constant map?

general-topology functions algebraic-topology

asked Nov 23, 2014 at 20:36

3 votes

1 answer

367 views

Levi-Civita help

tensors

asked Nov 20, 2014 at 12:55

3 votes

0 answers

639 views

What exactly is a conifold for mathematicians?

algebraic-geometry differential-geometry complex-geometry

asked Jun 1, 2015 at 14:53

3 votes

1 answer

206 views

What information can I immediately extract from a Dynkin diagram?

lie-groups lie-algebras dynkin-diagrams

asked Mar 31, 2015 at 9:37

3 votes

1 answer

196 views

Why do we need the $S \otimes L^{1/2}$ bundle product to determine a $Spin_c$ structure?

differential-geometry differential-topology vector-bundles fiber-bundles spin-geometry

asked Apr 26, 2016 at 7:29

3 votes

2 answers

349 views

What exactly does the Hilbert scheme of points parametrize?

complex-analysis algebraic-geometry mathematical-physics schemes

asked Oct 19, 2015 at 10:35

3 votes

0 answers

73 views

Can I split this integral to a sum over three contours?

complex-analysis mathematical-physics contour-integration gauge-theory

asked Oct 27, 2015 at 12:13

3 votes

1 answer

438 views

Is the group of symplectomorphisms of a symplectic manifold the symplectic group?

differential-geometry lie-groups symplectic-geometry

asked Dec 21, 2015 at 21:38

3 votes

1 answer

464 views

What information does a group extension Ext$^1(X,Y)$ convey?

algebraic-geometry abelian-groups sheaf-theory vector-bundles

asked Dec 24, 2016 at 11:56

3 votes

0 answers

123 views

Natural line bundle over $\mathbb{P}^n$

algebraic-geometry sheaf-theory projective-geometry holomorphic-bundles

asked Dec 27, 2016 at 1:28

3 votes

1 answer

482 views

Confusion: line bundles over $\mathbb{P}^1$ and sheaves

algebraic-geometry complex-geometry sheaf-theory vector-bundles fiber-bundles

asked Sep 26, 2016 at 22:00

3 votes

1 answer

369 views

Euler characteristic of a pair of sheaves $(E,F)$?

algebraic-geometry algebraic-topology sheaf-theory

asked Sep 10, 2017 at 11:57

2 votes

0 answers

41 views

Log Sum Exp trick confusion with probability distributions

statistics probability-distributions bayesian gaussian

asked Jul 16, 2021 at 13:14

2 votes

0 answers

81 views

How to write this product function in a compact way?

sequences-and-series summation products

asked Oct 3, 2016 at 11:14

2 votes

0 answers

44 views

Can clustering be implemented as Linear Programming?

optimization linear-programming matlab integer-programming clustering

asked Oct 20, 2021 at 13:01

2 votes

1 answer

228 views

Pullback of a Hamiltonian

differential-geometry classical-mechanics symplectic-geometry hamiltonian-path

asked Dec 22, 2015 at 9:17

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114 Questions

How to explain the formula for the sum of a geometric series without calculus?

$S^2=SO(3)/SO(2)$. Does this mean that $S^2 = SU(2)/U(1) $?

Physicist trying to understand GIT quotient

$q$-series and modular forms

Parallel transport of a vector in hyperbolic space, specifically in $\mathbb{H}$

Fundamental group of $\mathbb{R}^n\backslash \{0\}$

Prove that the antipodal mapping is an isometry on $S^n$. Help understanding the proof.

Liouville's theorem and the Wronskian

Abelian instantons for generic metric

How to explain to a school kid that on a sphere the shortest path between 2 points is given by a great circle?

When are two line bundles isomorphic?

If $\phi: M_1 \to M_2$ a diffeomorphism between diff. manifolds, prove that if $M_2$ is oriented then so is $M_1$

What is the quotient space $\mathbb{C}[x,y,z]/(x^2+y^2)$?

3 points lie in the same straight line. Then why is this formula valid?

Circle to circle homotopic to the constant map?

Levi-Civita help

What exactly is a conifold for mathematicians?

What information can I immediately extract from a Dynkin diagram?

Why do we need the $S \otimes L^{1/2}$ bundle product to determine a $Spin_c$ structure?

What exactly does the Hilbert scheme of points parametrize?

Can I split this integral to a sum over three contours?

Is the group of symplectomorphisms of a symplectic manifold the symplectic group?

What information does a group extension Ext$^1(X,Y)$ convey?

Natural line bundle over $\mathbb{P}^n$

Confusion: line bundles over $\mathbb{P}^1$ and sheaves

Euler characteristic of a pair of sheaves $(E,F)$?

Log Sum Exp trick confusion with probability distributions

How to write this product function in a compact way?

Can clustering be implemented as Linear Programming?

Pullback of a Hamiltonian