20 citations · 67 across the 25 of their papers we have counts for
31 papers
How to read Mathematics? A study guide
Petra Schwer
Reading a math textbook isn't like reading a novel. You've probably already figured that out on your own. But how *do* you read mathematical texts? And how can you actually learn f…
The meaning of doing mathematics
Petra Schwer
Can AI solve all math? What do we actually mean by doing mathematics? How do we communicate mathematics? What is mathematics beyond problem solving? This essay is my attempt to ans…
Conjugator length of locally compact groups of Euclidean isometries
Yuri Santos Rego, Petra Schwer
We consider locally compact subgroups of the full isometry group $\Isom(\E^n)$ of Euclidean -space which respect the splitting into an orthogonal and a translation subgroup.…
The geometry of conjugation in affine Coxeter groups
Elizabeth Milićević, Petra Schwer, Anne Thomas
We develop new and precise geometric descriptions of the conjugacy class and coconjugation set for all…
The geometry of conjugation in Euclidean isometry groups
Elizabeth Milićević, Petra Schwer, Anne Thomas
We describe the geometry of conjugation within any split subgroup of the full isometry group of -dimensional Euclidean space. We prove that for any , the conjug…
Involutions in Coxeter groups
Anna Michael, Yuri Santos Rego, Petra Schwer +1
We combinatorially characterize the number of conjugacy classes of involutions in any Coxeter group in terms of higher rank odd graphs. This notion naturally genera…
The galaxy of Coxeter groups
Yuri Santos Rego, Petra Schwer
In this paper we introduce the galaxy of Coxeter groups -- an infinite dimensional, locally finite, ranked simplicial complex which captures isomorphisms between Coxeter systems. I…
Chimney retractions in affine buildings encode orbits in affine flag varieties
Elizabeth Milićević, Petra Schwer, Anne Thomas
This paper determines the relationship between the geometry of retractions and the combinatorics of folded galleries for arbitrary affine buildings, and so provides a unified frame…
TriCCo -- a cubulation-based method for computing connected components on triangular grids
Aiko Voigt, Petra Schwer, Noam von Rotberg +1
We present a new method to identify connected components on triangular grids used in atmosphere and climate models to discretize the horizontal dimension. In contrast to structured…
Shadows in the wild -- folded galleries and their applications
Petra Schwer
This survey is about combinatorial objects related to reflection groups and their applications in representation theory and arithmetic geometry. Coxeter groups and folded galleries…
Affine Deligne-Lusztig varieties and folded galleries governed by chimneys
Elizabeth Milićević, Petra Schwer, Anne Thomas
We characterize the nonemptiness and dimension problems for an affine Deligne-Lusztig variety in the affine flag variety in terms of galleries that are positively folded w…
Polyhedral compactifications, I
Corina Ciobotaru, Linus Kramer, Petra Schwer
In this work we describe horofunction compactifications of metric spaces and finite dimensional real vector spaces through asymmetric metrics and asymmetric polyhedral norms by mea…
A gallery model for affine flag varieties via chimney retractions
Elizabeth Milićević, Yusra Naqvi, Petra Schwer +1
This paper provides a unified combinatorial framework to study orbits in certain affine flag varieties via the associated Bruhat-Tits buildings. We first formulate, for arbitrary a…
Lecture notes on CAT(0) cube complexes
Petra Schwer
These notes grew out of two lectures I have given on CAT(0) cube complexes. I've tried to keep the material elementary and self-contained in order to keep the material easily acces…
The triangle groups (2,4,5) and (2,5,5) are not systolic
Annette Karrer, Petra Schwer, Koen Struyve
In this paper we provide new examples of hyperbolic but nonsystolic groups by showing that the triangle groups and are not systolic. Along the way we prove some…
Shadows in Coxeter groups
Marius Graeber, Petra Schwer
For a given in a Coxeter group the elements smaller than in Bruhat order can be seen as the end-alcoves of stammering galleries of type in the Coxeter complex $…
A structure theorem for euclidean buildings
Petra Schwer, David Weniger
We prove an affine analog of Scharlau's reduction theorem for spherical buildings. To be a bit more precise let be a euclidean building with spherical building at…
Computing reflection length in an affine Coxeter group
Joel Brewster Lewis, Jon McCammond, T. Kyle Petersen +1
In any Coxeter group, the conjugates of elements in its Coxeter generating set are called reflections and the reflection length of an element is its length with respect to this exp…
Generalized non-crossing Partitions and Buildings
Julia Heller, Petra Schwer
For any finite Coxeter group of rank we show that the order complex of the lattice of non-crossing partitions embeds as a connected chamber subcomplex into…
Root operators, root groups and retractions
Petra Schwer
We prove that the Gaussent--Littelmann root operators on galleries can be expressed purely in terms of retractions of a (Bruhat-Tits) building. In addition we establish a connectio…
Dimensions of affine Deligne-Lusztig varieties: a new approach via labeled folded alcove walks and root operators
Elizabeth Milićević, Petra Schwer, Anne Thomas
Let G be a reductive group over the field F=k((t)), where k is an algebraic closure of a finite field, and let W be the (extended) affine Weyl group of G. The associated affine Del…
Systolizing buildings
Piotr Przytycki, Petra Schwer
We introduce a construction turning some Coxeter and Davis realizations of buildings into systolic complexes. Consequently groups acting geometrically on buildings of triangle type…
The 6-strand braid group is CAT(0)
Thomas Haettel, Dawid Kielak, Petra Schwer
We show that braid groups with at most 6 strands are CAT(0) using the close connection between these groups, the associated non-crossing partition complexes and the embeddability o…
Epimorphisms of pseudo-quadratic polar spaces
Petra Schwer, Koen Struyve
We classify the epimorphisms of the buildings , where l is at least two, of pseudo-quadratic form type. This completes the classification of epimorphisms of…