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Jan 03, 2014
Combinatorics
Algebraic Topology

The following theorem is a strengthening of the topological Tverberg theorem 3.1 in the case when r is a prime.

Tverberg plus constraints

Many of the strengthenings and extensions of the topological Tverberg theorem can be derived with surprising ease directly from the original theorem:…
Oct 06, 2007
Number Theory
Combinatorics

Dedekind-Carlitz Polynomials as Lattice-Point Enumerators in Rational…

We study higher-dimensional analogs of the Dedekind-Carlitz polynomials c(u,v;a,b) := sum_{k=1..b-1} u^[ka/b] v^(k-1), where u and v are indeterminat…
Nov 30, 2017
Fluid Dynamics

A Moving Boundary Flux Stabilization Method for Cartesian Cut-Cell Gr…

An explicit moving boundary method for the numerical solution of time-dependent hyperbolic conservation laws on grids produced by the intersection of…
Nov 20, 2017
Combinatorics

In this paper, we have established general criteria for hypergraphs H, which guarantee that the uniformly random Maker-strategy is essentially optimal in the biased Maker-Breaker game on H. We have proved that several natural games fall into this ca…

On the optimality of the uniform random strategy

The concept of biased Maker-Breaker games, introduced by Chv\'atal and Erd{\H o}s, is a central topic in the field of positional games, with deep con…
Apr 09, 2015
Analysis of PDEs
Dynamical Systems

Spatially discrete reaction-diffusion equations with discontinuous …

We address the question: Why may reaction-diffusion equations with hysteretic nonlinearities become ill-posed and how to amend this? To do so, we dis…
Oct 14, 2017
Combinatorics
Algebraic Topology
Metric Geometry

Cutting a part from many measures

Holmsen, Kyn\v{c}l and Valculescu recently conjectured that if a finite set $X$ with $\ell n$ points in $\mathbb{R}^d$ that is colored by $m$ differe…
Mar 19, 2015
Geometric Topology

While not all properties of complexified line arrangements carry over, we can note two immediate refinements of the generalized Hironaka theorem that concern properties of the attaching map φ and that still apply. The first concerns the naturality o…

A note on boundary manifolds of arrangements

We note an intimate connection between the Lefschetz Theorem for c-arrangements, and a theorem of Hironaka relating the complement of an arrangement …
Aug 12, 2011
Geometric Topology
Combinatorics

Generic rigidity of frameworks with orientation-preserving crystall…

We extend our generic rigidity theory for periodic frameworks in the plane to frameworks with a broader class of crystallographic symmetry. Along the…
Jun 03, 2010
Combinatorics
Computational Complexity
Discrete Mathematics

The Local Lemma is asymptotically tight for SAT

The Local Lemma is a fundamental tool of probabilistic combinatorics and theoretical computer science, yet there are hardly any natural problems know…
Dec 21, 2017
Dynamical Systems
Differential Geometry
Geometric Topology

Counting periodic trajectories of Finsler billiards

We provide lower bounds on the number of periodic Finsler billiard trajectories inside a quadratically convex smooth closed hypersurface M in a d-dim…
Jun 12, 2017
Combinatorics
Algebraic Topology
Metric Geometry

Thieves can make sandwiches

We prove a common generalization of the Ham Sandwich theorem and Alon's Necklace Splitting theorem. Our main results show the existence of fair distr…
Mar 24, 2015
Dynamical Systems

Global dynamics and asymptotics for monomial scalar field potentials …

We consider a minimally coupled scalar field with a monomial potential and a perfect fluid in flat FLRW cosmology. We apply local and global dynamica…
Mar 18, 2015
Algebraic Topology
Algebraic Geometry

Deligne proved that the k-th cohomology space Hk(X;Q) of every complex algebraic variety X carries a functorial mixed Hodge structure: this is given by an increasing filtration

Rational homotopy of complex projective varieties with normal isolate…

Let X be a complex projective variety of dimension n with only isolated normal singularities. In this paper we prove, using mixed Hodge theory, that …
Jul 11, 2011
Combinatorics
Algebraic Topology

One may ask whether Theorem 1.2 can be reduced to Theorem 1.1 by factorizing the given map f:ΔN→M over Rd,

A tight colored Tverberg theorem for maps to manifolds

We prove that any continuous map of an N-dimensional simplex Delta_N with colored vertices to a d-dimensional manifold M must map r points from disjo…
Oct 31, 2013
Group Theory
Combinatorics
Metric Geometry

Lorentzian Coxeter systems and Boyd-Maxwell ball packings

In the recent study of infinite root systems, fractal patterns of ball packings were observed while visualizing roots in affine space. In this paper,…
May 29, 2008
Algebraic Geometry
Combinatorics

Q-factorial Gorenstein toric Fano varieties with large Picard number

Q-factorial Gorenstein toric Fano varieties X of dimension d with Picard number rho(X) correspond to simplicial reflexive d-polytopes with rho(X)+d v…
Sep 15, 2018
Algebraic Geometry

For both quiver representations and vector bundles, there is a surprising link between the counts of absolutely indecomposable objects over finite fields and the Betti numbers of the (complex) hyperkähler moduli spaces described above. This was firs…

Lectures on the parallels between moduli of quiver representations an…

These are lecture notes for a mini-course at the SCGP in March 2019 for the fourth workshop on the Geometry and Physics of Higgs bundles. In this cou…
Dec 02, 2013
Combinatorics

What is Ramsey-equivalent to a clique?

A graph G is Ramsey for H if every two-colouring of the edges of G contains a monochromatic copy of H. Two graphs H and H' are Ramsey-equivalent if e…
Jun 15, 2016
Combinatorics
Metric Geometry

Two double poset polytopes

To every poset P, Stanley (1986) associated two polytopes, the order polytope and the chain polytope, whose geometric properties reflect the combinat…
Oct 22, 2018
Atmospheric and Oceanic Physics

Statistical investigations of flow structures in different regimes of…

A combination of methods originating from non-stationary timeseries analysis is applied to two datasets of near surface turbulence in order to gain i…
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