Related papers: Lectures on Factorization of Birational Maps

As an application of the theory of Lawson homology and morphic cohomology, Walker proved that the Abel-Jacobi map factors through another regular homomorphism. In this note, we give a direct proof of the theorem.

We initiate a study of cohomological aspects of weakly almost periodic group representations on Banach spaces, in particular, isometric representations on reflexive Banach spaces. Using the Ryll-Nardzewski fixed point Theorem, we prove a…

We introduce type-theoretic algebraic weak factorisation systems and show how they give rise to homotopy-theoretic models of Martin-L\"of type theory. This is done by showing that the comprehension category associated to a type-theoretic…

Following the works by Lin et al. (Circuits Syst. Signal Process. 20(6): 601-618, 2001) and Liu et al. (Circuits Syst. Signal Process. 30(3): 553-566, 2011), we investigate how to factorize a class of multivariate polynomial matrices. The…

This paper is an extended version of four lectures at PIMS in Vancouver given June 27 - 30, 2016. The primary goal of these lectures was to publicize the author's recent efforts to extend to representations of linear algebraic groups the…

With the aim of completing the previous study by A. Or{\l}owski and the author concerning intertwining maps between induced representations and conjugation representation, termed here weighted class operators, we compute the latter…

Free-minor closed classes [2] and free-planar graphs [3] are considered. Versions of Kuratowski-like theorem for free-planar graphs and Kuratowski theorem for planar graphs are considered.

We study the model theoretic strength of various lattices that occur naturally in topology, like closed (semi-linear or semi-algebraic or convex) sets. The method is based on weak monadic second order logic and sharpens previous results by…

We are interested in investigating some definitions and assumptions stated in [4], in particular the notions of measurability and atomicity that the two authors used in order to give a representation for multiplicative linear functionals…

These notes grew out of several introductory talks I gave during the years 2003--2005 on motivic integration. They give a short but thorough introduction to the flavor of motivic integration which nowadays goes by the name of geometric…

This is mainly a small exposition on extensions of valuation rings as a filtered union of smooth algebras.

This paper considers the factorization of elliptic symbols which can be represented by matrix-valued functions. Our starting point is a \textit{Fundamental Factorization Theorem}, due to Budjanu and Gohberg. We critically examine the work…

This is a survey of the use of Fourier analysis in additive combinatorics, with a particular focus on situations where it cannot be straightforwardly applied, but needs to be generalized first. Sometimes very satisfactory generalizations…

This text is the English translation, due to Naoufal Bouchareb, of an unpublished manuscript of 1969 (the French version is available on HAL as hal-00384928) inspired by Zariski's theory of saturation. Its publication is justified by the…

This note is an expansion of three lectures given at the workshop "Topology, Complex Analysis and Arithmetic of Hyperbolic Spaces" held at Kyoto University in December of 2006 and will appear in the proceedings for this workshop.

This is a pedagogical introduction covering maps of metric spaces, Gromov-Hausdorff distance and its "physical" meaning, and dilation structures as a convenient simplification of an exhaustive database of maps of a metric space into…

This is an introduction to small divisors problems. The material treated in this book was brought together for a PhD course I tought at the University of Pisa in the spring of 1999. Here is a Table of Contents: Part I One Dimensional Small…

This paper is a continuation of our previous works where we study maps from $X_0(N)$, $N \ge 1$, into $\mathbb P^2$ constructed via modular forms of the same weight and criteria that such a map is birational (see [12]). In the present paper…

We give combinatorial generalizations of the Cayley-Bacharach theorem and induced map.

In a recent preprint, Y. Namikawa proposed a conjecture on Q-factorial terminalizations and their birational geometry of nilpotent orbits. He proved his conjecture for classical simple Lie algebras. In this note, we prove his conjecture for…