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We survey the progress (or lack thereof!) that has been made on some questions about the p-adic slopes of modular forms that were raised by the first author in [Buz05], discuss strategies for making further progress, and examine other…
This is an extended abstract of my talk at the Oberwolfach Workshop ''Cluster Algebras and Related Topics'' (December 8 - 14, 2013). It is based on a joint work with A. Zelevinsky (arXiv:1306.3495).
This paper reviews results and techniques from the authors' previous work "Symplectomorphism group relations and degenerations of Landau-Ginzburg models" and applies them in basic examples. The main example is the $A_n$ category where we…
In this note, we observe several properties of arithmetic divisors on the projective line over Z and give their Zariski decompositions.
This is an expository paper about the topics listed in the title.
The aim of this note is to give a quick algebraic proof of (the combinatorial part of) the classification theorem for compact real surfaces, whose classical proofs (as in the Massey book and in the Conway ZIP proof) are based on surgery…
The purpose of this survey is to describe how locally compact groups can be studied as geometric objects. We will emphasize the main ideas and skip or just sketch most proofs, often referring the reader to our much more detailed book…
In this paper multivariate extension of the generalized Durrmeyer sampling type series are considered. We establish a Voronovskaja type formula and a quantitative version. Finally some particular examples are discussed.
We discuss the Bohr compactification of a pseudofinite group, motivated by a question of Boris Zilber. Basically referring to results in the literature we point out (i) the Bohr compactification of an ultraproduct of finite simple groups is…
This is a survey on the various notions of Kodaira dimension in low dimensional topology. The focus is on progress after the 2006 survey [78].
This is a comment on the recent paper by O.V. Selyugin, J.-R. Cudell, and E. Predazzi "Analytic properties of different unitarization schemes" arXiv: 0712.0621v2, [hep-ph]
In this talk I present a review on the theoretical status of polarized fragmentation functions and the prospects for conceivable future semi-inclusive deep-inelastic scattering and proton-proton collision experiments to measure them.
In this survey, we give a short overview of the recent progress on the multidimensional L2 conjecture. It can also serve as an introduction to the subject.
Let J be the jacobian of a reduced projective curve C with nodes only. 1) We give a simple and natural definition for its many compactifications and show the connection with various other definitions appearing in the literature. 2) Among…
This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.
The purpose of this short note is to provide a new and very short proof of a result by Sudakov, offering an important improvement of the classical result by Kolmogorov-Riesz on compact subsets of Lebesgue spaces.
We obtain new results about the representation of almost all residues modulo a prime $p$ by a product of a small integer and also an element of small multiplicative subgroup of $({\mathbb Z}/p{\mathbb Z})^*$. These results are based on some…
The goal of this report is to investigate the variety of Hausdorff compactifications of $\mathbb{R}$. The Alexandroff one-point compactification, the two-point compactification, and the Stone-Cech compactification are all clearly different.…
An expository description of smooth cubic curves in the real or complex projective plane.
This is a survey article about some of the work of Peter Scholze for the Jahresbericht der DMV. No originality is claimed. It is hoped that it can serve as a guideline to an exciting and increasingly large edifice of theory.