Full-revivals in 2-D Quantum Walks

Recurrence of a random walk is described by the Polya number. For quantum walks, recurrence is understood as the return of the walker to the origin, rather than the full-revival of its quantum state. Localization for two dimensional quantum walks is known to exist in the sense of non-vanishing probability distribution in the asymptotic limit. We show on the example of the 2-D Grover walk that one can exploit the effect of localization to construct stationary solutions. Moreover, we find full-revivals of a quantum state with a period of two steps. We prove that there cannot be longer cycles for a four-state quantum walk. Stationary states and revivals result from interference which has no counterpart in classical random walks

Fibrations on four-folds with trivial canonical bundles

Four-folds with trivial canonical bundles are divided into six classes according to their holonomy group. We consider examples that are fibred by abelian surfaces over the projective plane. We construct such fibrations in five of the six classes, and prove that there is no such fibration in the sixth class. We classify all such fibrations whose generic fibre is the Jacobian of a genus two curve.Comment: 28 page

On Sasaki-Einstein manifolds in dimension five

We prove the existence of Sasaki-Einstein metrics on certain simply connected 5-manifolds where until now existence was unknown. All of these manifolds have non-trivial torsion classes. On several of these we show that there are a countable infinity of deformation classes of Sasaki-Einstein structures.Comment: 18 pages, Exposition was expanded and a reference adde

Graph hypersurfaces and a dichotomy in the Grothendieck ring

The subring of the Grothendieck ring of varieties generated by the graph hypersurfaces of quantum field theory maps to the monoid ring of stable birational equivalence classes of varieties. We show that the image of this map is the copy of Z generated by the class of a point. Thus, the span of the graph hypersurfaces in the Grothendieck ring is nearly killed by setting the Lefschetz motive L to zero, while it is known that graph hypersurfaces generate the Grothendieck ring over a localization of Z[L] in which L becomes invertible. In particular, this shows that the graph hypersurfaces do not generate the Grothendieck ring prior to localization. The same result yields some information on the mixed Hodge structures of graph hypersurfaces, in the form of a constraint on the terms in their Deligne-Hodge polynomials.Comment: 8 pages, LaTe

A high fibered power of a family of varieties of general type dominates a variety of general type

We prove the following theorem: Fibered Power Theorem: Let X\rar B be a smooth family of positive dimensional varieties of general type, with $B$ irreducible. Then there exists an integer $n>0$, a positive dimensional variety of general type $W_n$, and a dominant rational map X^n_B \das W_n.Comment: Latex2e (in latex 2.09 compatibility mode). To get a fun-free version change the `FUN' variable to `n' on the second line (option dedicated to my friend Yuri Tschinkel). Postscript file with color illustration available on http://math.bu.edu/INDIVIDUAL/abrmovic/fibered.p

Mono- and double carbonylation of aryl iodides with amine nucleophiles in the presence of recyclable palladium catalysts immobilised on a supported dicationic ionic liquid phase

Silica modified with organic dicationic moieties proved to be an excellent support for palladium catalysts used in the aminocarbonylation of aryl iodides. By an appropriate choice of the reaction conditions, the same catalyst could be used for selective mono- or double carbonylations leading to amide and [small alpha]-ketoamide products, respectively. The best catalyst could be recycled for at least 10 consecutive runs with a loss of palladium below the detection limit. By the application of the new support, efficient catalyst recycling could be achieved under mild reaction conditions (under low pressure and in a short reaction time). Palladium-leaching data support a mechanism with dissolution-re-precipitation of the active palladium species

The Role of Surgical Expertise and Surgical Access in Retroperitoneal Sarcoma Resection - A Retrospective Study.

Background Retroperitoneal sarcoma (RPS) is a rare disease often requiring multi-visceral and wide margin resections for which a resection in a sarcoma center is advised. Midline incision seems to be the access of choice. However, up to now there is no evidence for the best surgical access. This study aimed to analyze the oncological outcome according to the surgical expertise and also the incision used for the resection. Methods All patients treated for RPS between 2007 and 2018 at the Department of Visceral Surgery and Medicine of the University Hospital Bern and receiving a RPS resection in curative intent were included. Patient- and treatment specific factors as well as local recurrence-free, disease-free and overall survival were analyzed in correlation to the hospital type where the resection occurred. Results Thirty-five patients were treated for RPS at our center. The majority received their primary RPS resection at a sarcoma center (SC = 23) the rest of the resection were performed in a non-sarcoma center (non-SC = 12). Median tumor size was 24 cm. Resections were performed via a midline laparotomy (ML = 31) or flank incision (FI = 4). All patients with a primary FI (n = 4) were operated in a non-SC (p = 0.003). No patient operated at a non-SC received a multivisceral resection (p = 0.004). Incomplete resection (R2) was observed more often when resection was done in a non-SC (p = 0.013). Resection at a non-SC was significantly associated with worse recurrence-free survival and disease-free survival after R0/1 resection (2 vs 17 months; Log Rank p-value = 0.02 respectively 2 vs 15 months; Log Rank p-value < 0.001). Conclusions Resection at a non-SC is associated with more incomplete resection and worse outcome in RPS surgery. Inadequate access, such as FI, may prevent complete resection and multivisceral resection if indicated and demonstrates the importance of surgical expertise in the outcome of RPS resection

Termination of (many) 4-dimensional log flips

We prove that any sequence of 4-dimensional log flips that begins with a klt pair (X,D) such that -(K+D) is numerically equivalent to an effective divisor, terminates. This implies termination of flips that begin with a log Fano pair and termination of flips in a relative birational setting. We also prove termination of directed flips with big K+D. As a consequence, we prove existence of minimal models of 4-dimensional dlt pairs of general type, existence of 5-dimensional log flips, and rationality of Kodaira energy in dimension 4.Comment: 13 pages; a minor change in the proof of Thm.4.

Differential Forms on Log Canonical Spaces

The present paper is concerned with differential forms on log canonical varieties. It is shown that any p-form defined on the smooth locus of a variety with canonical or klt singularities extends regularly to any resolution of singularities. In fact, a much more general theorem for log canonical pairs is established. The proof relies on vanishing theorems for log canonical varieties and on methods of the minimal model program. In addition, a theory of differential forms on dlt pairs is developed. It is shown that many of the fundamental theorems and techniques known for sheaves of logarithmic differentials on smooth varieties also hold in the dlt setting. Immediate applications include the existence of a pull-back map for reflexive differentials, generalisations of Bogomolov-Sommese type vanishing results, and a positive answer to the Lipman-Zariski conjecture for klt spaces.Comment: 72 pages, 6 figures. A shortened version of this paper has appeared in Publications math\'ematiques de l'IH\'ES. The final publication is available at http://www.springerlink.co