Eric O. Korman

Austin, TX

http://www.ma.utexas.edu/users/ekorman

Post-doc at UT Austin.

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Importance of Representation Theory

representation-theory physics asked Jul 24, 2010 at 2:42

math.stackexchange.com

125 votes

What is known about the topological structure of spacetime?

general-relativity spacetime universe differential-geometry topology asked Dec 10, 2010 at 5:55

physics.stackexchange.com

64 votes

Stiefel–Whitney classes in the spirit of Chern-Weil

characteristic-classes dg.differential-geometry asked Jan 17, 2011 at 17:55

mathoverflow.net

61 votes

Areas versus volumes of revolution: why does the area require approximation by a cone?

calculus integration volume area asked Oct 16, 2010 at 20:55

math.stackexchange.com

42 votes

Motivating Example for Algebraic Geometry/Scheme Theory

algebraic-geometry asked Jul 30, 2010 at 17:55

math.stackexchange.com

28 votes

Summation methods for divergent series

divergent-series reference-request asked Mar 24, 2010 at 15:16

mathoverflow.net

26 votes

Local triviality of principal bundles

differential-geometry algebraic-topology fiber-bundles principal-bundles asked Feb 25, 2011 at 17:21

math.stackexchange.com

24 votes

Where is the Atiyah-Singer index theorem used in physics?

mathematical-physics differential-geometry topology quantum-anomalies asked Dec 12, 2010 at 21:16

physics.stackexchange.com

20 votes

How to Characterize Gradient Vector Fields?

differential-geometry differential-topology asked May 19, 2012 at 1:18

math.stackexchange.com

18 votes

Which continuous functions are polynomials?

ag.algebraic-geometry differential-topology asked Aug 3, 2010 at 18:21

mathoverflow.net

Top Answers

Conjectures that have been disproved with extremely large counterexamples?

math.stackexchange.com

Is the vector cross product only defined for 3D?

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Best Algebraic Topology book/Alternative to Allen Hatcher free book?

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Fundamental group of the special orthogonal group SO(n)

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What are the most elegant proofs that you have learned from MO?

mathoverflow.net

Why is the orthogonal group $\operatorname{O}(2n,\mathbb R)$ not the direct product of $\operatorname{SO}(2n, \mathbb R)$ and $\mathbb Z_2$?

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Is the determinant the "only" group homomorphism from $\mathrm{GL}_n(\mathbb R)$ to $\mathbb R^\times$?

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What are defining & fundamental representations?

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No diffeomorphism that takes unit circle to unit square

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Surprising Generalizations

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Intuitive explanation of covariant, contravariant and Lie derivatives

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Why do people care about principal bundles?

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Lie algebra of a quotient of Lie groups

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Show the existence of a polynomial $f$ such that $T^{-1} = f(T)$ for an invertible linear operator $T.$

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Is the Structure Group of a Fibre Bundle Well-Defined?

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Are $x \cdot 0 = 0$, $x \cdot 1 = x$, and $-(-x) = x$ axioms?

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Roadmap to study Atiyah–Singer index theorem

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Two Definitions of the Special Orthogonal Lie Algebra

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Do all representations of finite groups have one-dimensional subrepresentations?

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$\Omega=x\;dy \wedge dz+y\;dz\wedge dx+z\;dx \wedge dy$ is never zero when restricted to $\mathbb{S^2}$

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Why are $3D$ transformation matrices $4 \times 4$ instead of $3 \times 3$?

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Good Physical Demonstrations of Abstract Mathematics

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Conformal-symplectic geometry ?

mathoverflow.net

Showing a vector field is tangent to the 2-sphere

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fundamental group of $U(n)$

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Does the group of Diffeomorphisms act transitively on the space of Riemannian metrics?

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What should be in every grad student's library?

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If there exists a nontrivial vector field $V$ such that $\nabla_{X}V=0$ for any vector field $X$, the manifold must be flat?

mathoverflow.net

Equivalence of Definitions of Principal $G$-bundle

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If $A$ is a subobject of $B$, and $B$ a subobject of $A$, are they isomorphic?

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