Concept

Conjecture

Publications associées (51)

A Crossing Lemma for Multigraphs

Let G be a drawing of a graph with n vertices and e > 4n edges, in which no two adjacent edges cross and any pair of independent edges cross at most once. According to the celebrated Crossing Lemma of Ajtai, Chvatal, Newborn, Szemeredi and Leighton, the nu ...

SPRINGER2020

Nested Convex Bodies are Chaseable

Marek Elias

In the Convex Body Chasing problem, we are given an initial point v0. Rd and an online sequence of n convex bodies F1,..., Fn. When we receive Ft, we are required to move inside Ft. Our goal is to minimize the total distance traveled. This fundamental onli ...

SPRINGER2019

On the Number of Containments in P-free Families

Abhishek Methuku

A subfamily {F-1, F-2, ..., F-vertical bar P vertical bar} subset of F is a copy of the poset P if there exists a bijection i : P -> {F-1, F-2, ..., F-vertical bar P vertical bar}, such that p

Springer2019

A proof of a sumset conjecture of Erdős

Florian Karl Richter

In this paper we show that every set A ⊂ ℕ with positive density contains B + C for some pair B, C of infinite subsets of ℕ , settling a conjecture of Erdős. The proof features two different decompositions of an arbitrary bounded sequence into a structured ...

2019

Efficient Greedy Coordinate Descent for Composite Problems

Martin Jaggi, Sebastian Urban Stich, Anastasiia Koloskova, Sai Praneeth Reddy Karimireddy

Coordinate descent with random coordinate selection is the current state of the art for many large scale optimization problems. However, greedy selection of the steepest coordinate on smooth problems can yield convergence rates independent of the dimension ...

2019

Efficient Greedy Coordinate Descent for Composite Problems

Martin Jaggi, Sebastian Urban Stich, Anastasiia Koloskova, Sai Praneeth Reddy Karimireddy

MICROTOME PUBLISHING2019

Almost tiling of the Boolean lattice with copies of a poset

Istvan Tomon

Let P be a partially ordered set. If the Boolean lattice (2[n],⊂) can be partitioned into copies of P for some positive integer n, then P must satisfy the following two trivial conditions: (1) the size of P is a power of 2, (2) P has a unique maximal and m ...

ELECTRONIC JOURNAL OF COMBINATORICS2018

Two-term, asymptotically sharp estimates for eigenvalue means of the Laplacian

Joachim Stubbe

We present asymptotically sharp inequalities for the eigenvalues mu(k) of the Laplacian on a domain with Neumann boundary conditions, using the averaged variational principle introduced in [14]. For the Riesz mean R-1(z) of the eigenvalues we improve the k ...

EUROPEAN MATHEMATICAL SOC2018

Mirror symmetry for moduli spaces of Higgs bundles via $p$-adic integration

Dimitri Stelio Wyss, Michael Gröchenig

We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type

SL_n

and

PGL_n

. More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generica ...

2017

Non-Normal Very Ample Polytopes - Constructions and Examples

Michal Lason

We answer several questions posed by Beck, Cox, Delgado, Gubeladze, Haase, Hibi, Higashitani, and Maclagan in [Cox et al. 14, Question 3.5 (1),(2), Question 3.6], [Beck et al. 15, Conjecture 3.5(a),(b)], and [Hasse et al. 07, Open question 3 (a),(b) p. 231 ...

Taylor & Francis Inc2017

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Mirror symmetry for moduli spaces of Higgs bundles via $p$-adic integration

Dimitri Stelio Wyss, Michael Gröchenig

We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type

SL_n

and

PGL_n

. More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generica ...

2017