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RANDOM GRAPHS WITH A GIVEN DEGREE SEQUENCE。
Lower Bounds for the Determinantal Complexity of Explicit Low Degree Polynomials
Computational complexity Arithmetic circuits Determinant versus permanent Elementary symmetric polynomial
2012/12/3
The determinantal complexity of a polynomial f (x1, x2, . . . , xn) is the minimum m such that f = detm(L(x1, x2, . . . , xn)), where L(x1, x2, . . . , xn) is a matrix whose entries are affine forms i...
Levinson's theorem and higher degree traces for Aharonov-Bohm operators
Aharonov-Bohm operators scattering theory wave operators index theorem
2011/2/21
We study Levinson type theorems for the family of Aharonov-Bohm models from different
perspectives. The first one is purely analytical involving the explicit calculation of the waveoperators and allo...
We construct a connected, irreducible component of the moduli space of minimal surfaces of general type with $p_g=q=2$ and $K^2=5$, which contains both examples given by Chen-Hacon and the first autho...
Induced subgraphs in sparse random graphs with given degree sequence
Induced subgraphs math
2010/11/22
For any $S\subset [n]$, we compute the probability that the subgraph of $\mathcal{G}_{n,d}$ induced by $S$ is a given graph $H$ on the vertex set $S$. The result holds for any $d=o(n^{1/3})$ and is fu...
Density of rational points on elliptic curves and small transcendence degree
rational points elliptic curves
2010/11/19
In this paper we pursue two goals: (I) We show how Weil restrictions to real subfields can be fruitfully applied to improve transcendence results. (II) We elaborate (I) in the context of algebraic in...
Surfaces with $p_g = 0$, $K^2 = 5$ and bicanonical maps of degree 4
Surfaces bicanonical maps
2010/11/11
Let $S$ be a minimal surface of general type with $p_g(S) = 0, K_S^2 = 5$ and bicanonical map of degree 4. Denote by $\Sigma$ the bicanonical image. If $\Sigma$ is smooth, then $S$ is a Burniat surfa...