49

Answers

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12

Proofs that require fundamentally new ways of thinking

1

Books you would like to see translated into English.

9

Noteworthy achievements in and around 2010?

9

What is torsion in differential geometry intuitively?

3

What do heat kernels have to do with the Riemann-Roch theorem and the Gauss-Bonnet theorem?

1

Riemannian Geometry Introductory Text

2

Is there a sheaf theoretical characterization of a differentiable manifold?

2

Intuition behind moduli space of curves

1

Determining a surface in $\mathbb{R}^3$ by its Gaussian curvature

4

Torus minimizer of Willmore energy

2

circle action on sphere

1

Why and how are moduli spaces of (semi)stable vector bundles well-behaved?

4

space of geodesics

9

Dirac’s Original Operator and the Hodge--Dirac Operator

2

Definition of a complex structure on a vector bundle

0

What is known about Higgs bundles with sections?

2

Topological results from geometry

2

What are some geometric reasons why a Dirac operator would have a gap in its spectrum?

1

Connection on line bundle on projective curve

2

Is the volume form on an oriented Riemannian manifold parallel?

2

Is there a complete classification of constant mean curvature surfaces?

1

Is there a coordinate-free proof of the hamiltonian character of the geodesic flow?

1

Finding constant curvature metrics on surfaces for the case of positive Euler characteristic

1

Quotient Surface of A Hyperelliptic Involution

2

What is the easiest way to classify all possible smooth orientable closed 2-manifolds?

1

Newlander-Nirenberg for surfaces

0

Is there an intrinsic way to define the group law on Abelian varieties?

0

What is a good way to think about a fundamental field on a principal G-bundle?

4

A question on deformations of Theta divisor in the Jacobian of a complex curve

3

Tweetable way to see that Willmore energy is Möbius invariant?