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

Many of the strengthenings and extensions of the topological Tverberg theorem can be derived with surprising ease directly from the original theorem:…

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…

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

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…

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…

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…

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…

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…

We note an intimate connection between the Lefschetz Theorem for c-arrangements, and a theorem of Hironaka relating the complement of an arrangement …

We extend our generic rigidity theory for periodic frameworks in the plane to frameworks with a broader class of crystallographic symmetry. Along the…

The Local Lemma is a fundamental tool of probabilistic combinatorics and theoretical computer science, yet there are hardly any natural problems know…

We provide lower bounds on the number of periodic Finsler billiard trajectories inside a quadratically convex smooth closed hypersurface M in a d-dim…

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…

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…

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

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 …

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

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…

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

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…

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…

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…

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…

To every poset P, Stanley (1986) associated two polytopes, the order polytope and the chain polytope, whose geometric properties reflect the combinat…

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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