category stringclasses 7
values | title stringlengths 4 376 | abstract stringlengths 17 9.32k |
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Math | Quantum-sl(2) action on a divided-power quantum plane at even roots of unity | We describe a nonstandard version of the quantum plane, the one in the basis of divided powers at an even root of unity $q=e^{i\pi/p}$. It can be regarded as an extension of the "nearly commutative" algebra $C[X,Y]$ with $X Y =(-1)^p Y X$ by nilpotents. For this quantum plane, we construct a Wess--Zumino-type de Rham c... |
Math | The tau constant and the edge connectivity of a metrized graph | The tau constant is an important invariant of a metrized graph, and it has applications in arithmetic properties of curves. We show how the tau constant of a metrized graph changes under successive edge contractions and deletions. We discover identities which we call "contraction", "deletion", and "contraction-deletion... |
Math | The Logarithmic Sobolev Inequality for Gibbs measures on infinite product of Heisenberg groups | We are interested in the $q$ Logarithmic Sobolev inequality for probability measures on the infinite product of Heisenberg groups. We assume that the one site boundary free measure satisfies either a $q$ Log-Sobolev inequality or a U-Bound inequality, and we determine conditions so that the infinite dimensional Gibbs m... |
Math | Models of PA: Standard Systems without Minimal Ultrafilters | We prove that bold N, the standard model of arithmetic, has an uncountable elementary extension N such that there is no ultrafilter on the Boolean Algebra of subsets of bold N represented in N which is minimal (i.e. as in Rudin-Keisler order for partitions represented in N). |
Math | The Calabi-Yau equation, symplectic forms and almost complex structures | We discuss a conjecture of Donaldson on a version of Yau's Theorem for symplectic forms with compatible almost complex structures and survey some recent progress on this problem. We also speculate on some future possible directions, and use a monotonicity formula for harmonic maps to obtain a new local estimate in the ... |
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