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19962022

most citedThe VOLNA code for the numerical modelling of tsunami waves: generation, propagation and inundation

107 citations

researchers with a paper here

Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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20 papers · 1 filter

math.AG2022

New bounds for the number of connected components of fewnomial hypersurfaces

Frédéric Bihan, Tristan Humbert, Sébastien Tavenas

We prove that the number of connected components of a smooth hypersurface in the positive orthant of $R^{n}$ defined by a real polynomial with $d + k + 1$ monomials, where $…

math.AG2022

Motivic Vitushkin invariants

Georges Comte, Immanuel Halupczok

We prove the nonarchimedean counterpart of a real inequality involving the metric entropy and measure geometric invariants $V_{i}$ , called Vitushkin's variations. Our inequality is b…

math.AG2018★ 2 cited

Motivic wave front sets

Michel Raibaut

The concept of wave front set was introduced in 1969-1970 by M. Sato in the hyperfunctions context and by L. Hörmander in the $C^{\infty}$ context. Howe used the theory of…

math.AG2018★ 1 cited

Motivic and analytic nearby fibers at infinity and bifurcation sets

Lorenzo Fantini, Michel Raibaut

In this paper we use motivic integration and non-archimedean analytic geometry to study the singularities at infinity of the fibers of a polynomial map $f\colon \mathbb A^d_\mathbb…

math.AG2018★ 1 cited

Arc spaces, motivic measure and Lipschitz geometry of real algebraic sets

Jean-Baptiste Campesato, Toshizumi Fukui, Krzysztof Kurdyka +1

We investigate connections between Lipschitz geometry of real algebraic varieties and properties of their arc spaces. For this purpose we develop motivic integration in the real al…

math.AG2017★ 10 cited

Distributions and wave front sets in the uniform non-archimedean setting

Raf Cluckers, Immanuel Halupczok, François Loeser +1

We study some constructions on distributions in a uniform $p$ -adic context, and also in large positive characteristic, using model theoretic methods. We introduce a class of distri…

math.AG2015★ 10 cited

Stringy invariants for horospherical varieties of complexity one

Kevin Langlois, Clélia Pech, Michel Raibaut

In this paper we determine the stringy motivic volume of log terminal horospherical $G$ -varieties of complexity one, where $G$ is a connected reductive linear algebraic group. The…

math.AG2015★ 2 cited

Sparse Polynomial Systems with many Positive Solutions from Bipartite Simplicial Complexes

Frédéric Bihan, Pierre-Jean Spaenlehauer

Consider a regular triangulation of the convex-hull $P$ of a set $A$ of $n$ points in $R^{d}$ , and a real matrix $C$ of size $d \times n$ . A version of Viro's method…

math.AG2015★ 28 cited

Curve-rational functions

János Kollár, Wojciech Kucharz, Krzysztof Kurdyka

Let $W$ be a subset of the set of real points of a real algebraic variety $X$ . We investigate which functions $f : W \to R$ are the restrictions of rational functions on $X$ …

math.AG2013★ 18 cited

Stratified-algebraic vector bundles

Wojciech Kucharz, Krzysztof Kurdyka

We investigate stratified-algebraic vector bundles on a real algebraic variety X. A stratification of X is a finite collection of pairwise disjoint, Zariski locally closed subvarie…

math.AG2012★ 1 cited

Reaching generalized critical values of a polynomial

Zbigniew Jelonek, Krzysztof Kurdyka

Let f be a real or complex polynomial. We give an algorithm to compute the set of generalized critical values. The algorithm uses a finite dimensional space of rational arcs along…

math.AG2011★ 4 cited

Grothendieck ring of semialgebraic formulas and motivic real Milnor fibres

Comte Georges, Fichou Goulwen

We define a Grothendieck ring for basic real semialgebraic formulas, that is for systems of real algebraic equations and inequalities. In this ring the class of a formula takes int…

math.AG2009★ 7 cited

Geometrically rational real conic bundles and very transitive actions

Jérémy Blanc, Frédéric Mangolte

In this article we study the transitivity of the group of automorphisms of real algebraic surfaces. We characterize real algebraic surfaces with very transitive automorphism groups…

math.AG2008★ 2 cited

Real singular Del Pezzo surfaces and 3-folds fibred by rational curves, II

Fabrizio Catanese, Frederic Mangolte

Let W -> X be a real smooth projective 3-fold fibred by rational curves. J. Kollár proved that, if W(R) is orientable, then a connected component N of W(R) is essentially either a…

math.AG2007★ 15 cited

The group of automorphisms of a real rational surface is n-transitive

Johannes Huisman, Frédéric Mangolte

Let X be a rational nonsingular compact connected real algebraic surface. Denote by Aut(X) the group of real algebraic automorphisms of X. We show that the group Aut(X) acts n-tran…

math.AG2006

New fewnomial upper bounds from Gale dual polynomial systems

Frederic Bihan, Frank Sottile

We show that there are fewer than (e^2+3) 2^(k choose 2) n^k/4 non-degenerate positive solutions to a fewnomial system consisting of n polynomials in n variables having a total of…

math.AG2005★ 9 cited

Is every toric variety an M-variety?

Frédéric Bihan, Matthias Franz, Clint McCrory +1

A complex algebraic variety X defined over the real numbers is called an M-variety if the sum of its Betti numbers (for homology with closed supports and coefficients in Z/2) coinc…

math.AG2003

Real algebraic morphisms on 2-dimensional conic bundles

Frederic Mangolte

Given two nonsingular real algebraic varieties V and W, we consider the problem of deciding whether a smooth map f: V -> W can be approximated by regular maps in the space of smoot…

math.AG2003★ 7 cited

Every orientable Seifert 3-manifold is a real component of a uniruled algebraic variety

Johannes Huisman, Frédéric Mangolte

We show that any orientable Seifert 3-manifold is diffeomorphic to a connected component of the set of real points of a uniruled real algebraic variety, and prove a conjecture of J…

math.AG1998★ 4 cited

Surfaces elliptiques réelles et inégalité de Ragsdale-Viro

Frédéric Mangolte

On a real regular elliptic surface without multiple fiber, the Betti number $h_{1}$ and the Hodge number $h^{1, 1}$ are related by $h_{1} \leq h^{1, 1}$ . We prove that it's always possibl…