Concept
Real algebraic geometry
Publications associées (36)
Transportation-based functional ANOVA and PCA for covariance operators
Victor Panaretos, Yoav Zemel, Valentina Masarotto
We consider the problem of comparing several samples of stochastic processes with respect to their second-order structure, and describing the main modes of variation in this second order structure, if present. These tasks can be seen as an Analysis of Vari ...
Inst Mathematical Statistics-Ims2024Persistence and the Sheaf-Function Correspondence
The sheaf-function correspondence identifies the group of constructible functions on a real analytic manifold M with the Grothendieck group of constructible sheaves on M. When M is a finite dimensional real vector space, Kashiwara-Schapira have recently in ...
Cambridge2023Global Frobenius liftability I
We formulate a conjecture characterizing smooth projective varieties in positive characteristic whose Frobenius morphism can be lifted modulo p(2)-we expect that such varieties, after a finite stale cover, admit a toric fibration over an ordinary abelian v ...
EUROPEAN MATHEMATICAL SOC-EMS2021On the Power and Limitations of Branch and Cut
The Stabbing Planes proof system [Paul Beame et al., 2018] was introduced to model the reasoning carried out in practical mixed integer programming solvers. As a proof system, it is powerful enough to simulate Cutting Planes and to refute the Tseitin formu ...
Schloss Dagstuhl - Leibniz-Zentrum für Informatik2021On Sets Defining Few Ordinary Circles
An ordinary circle of a set P of n points in the plane is defined as a circle that contains exactly three points of P. We show that if P is not contained in a line or a circle, then P spans at least ordinary circles. Moreover, we determine the exact minimu ...
Springer2018A semi-algebraic version of Zarankiewicz's problem
A bipartite graph G is semi-algebraic in R-d if its vertices are represented by point sets P,Q subset of R-d and its edges are defined as pairs of points (p,q) epsilon P x Q that satisfy a Boolean combination of a fixed number of polynomial equations and i ...
European Mathematical Soc2017Distinct Distances on Algebraic Curves in the Plane
Let S be a set of n points in R-2 contained in an algebraic curve C of degree d. We prove that the number of distinct distances determined by S is at least c(d)n(4/3), unless C contains a line or a circle. We also prove the lower bound c(d)' min{m(2/3)n(2/ ...
Cambridge Univ Press2017On some algebraic and extremal problems in discrete geometry
Seyed Hossein Nassajianmojarrad
In the present thesis, we delve into different extremal and algebraic problems arising from combinatorial geometry. Specifically, we consider the following problems. For any integer , we define to be the minimum positive integer such that an ...
EPFL2017Few distinct distances implies no heavy lines or circles
We study the structure of planar point sets that determine a small number of distinct distances. Specifically, we show that if a set of n points determines o(n) distinct distances, then no line contains Omega(n (7/8)) points of and no circle contains Omega ...
Springer Heidelberg2016