Orthogonal free quantum group factors are strongly 1-bounded

We prove that the orthogonal free quantum group factors $\mathcal{L}(\mathbb{F}O_N)$ are strongly $1$-bounded in the sense of Jung. In particular, they are not isomorphic to free group factors. This result is obtained by establishing a spectral regularity result for the edge reversing operator on the quantum Cayley tree associated to $\mathbb{F}O_N$, and combining this result with a recent free entropy dimension rank theorem of Jung and Shlyakhtenko.Comment: v3: accepted versio

The Abhyankar-Jung Theorem

We show that every quasi-ordinary Weierstrass polynomial P(Z) = Z^d+a_1 (X) Z^{d-1}+...+a_d(X) \in \K[[X]][Z] , $X=(X_1,..., X_n)$, over an algebraically closed field of characterisic zero \K, and satisfying $a_1=0$, is $\nu$-quasi-ordinary. That means that if the discriminant \Delta_P \in \K[[X]] is equal to a monomial times a unit then the ideal $(a_i^{d!/i}(X))_{i=2,...,d}$ is principal and generated by a monomial. We use this result to give a constructive proof of the Abhyankar-Jung Theorem that works for any Henselian local subring of \K[[X]] and the function germs of quasi-analytic families.Comment: 14 pages. The toric case has been added. To be published in Journal of Algebr

Reply to Comment on "Dynamical corrections to the DFT-LDA electron conductance in nanoscale systems"

We reply to the comment by Jung, Bokes, and Godby (arXiv:0706.0140) on our paper Phys. Rev. Lett. 94, 186810 (2005). We show that the results in their comment should not be taken as an indication that the viscosity corrections to the conductance of real nanoscale structures are small. A more accurate treatment of the density and current density distribution and of the electronic correlations may yield much larger corrections in realistic systems.Comment: Reply to the comment by Jung et al (arXiv:0706.0140). 1 page, no figures, to appear in PR

Analysing Student Work Involving Geometric Concepts

Hyunyi Jung reflects on why students struggle to understand trigonometry

Jung and Antisemitism

Paper given at History of Science, Medicine and Technology [E-seminars

Jung and Antisemitism

Paper given at History of Science, Medicine and Technology [E-seminars