(All times BST)
18.30(ish)   Informal Dinner 
8.30  8.45  Registration  
8.45  9.00  Introductory Remarks  
9.00  10.00 
Bethany Marsh — ConwayCoxeter friezes and categorical models
Joint work with Eleonore Faber and Matthew Pressland 

10.00  10.30 
Kirin Martin — Unfolding Universal Partial Cycles
Universal Partial Cycles (or "upcycles") are a generalization of De Bruijn cycles where in addition to alphabet letters one allows a wildcard character (representing all possible letters). My research group has proven the existence of infinite classes of nontrivial such cycles (De Bruijn cycles are a subset using no wildcard characters, and the use of only wildcard characters would also be trivial), but it has yet to be shown whether it is possible to have more than one wildcard character per wordlength. My thesis research is investigating this, but a nice result from my research group that can be shared in twenty minutes would be that perfect necklaces (as defined in 2016 by Alvarez et al.) are precisely the tool required to unfold an upcycle with d wildcard characters per wordlength into an upcycle with fewer than d wildcards per wordlength (such as fully unfolding it into a De Bruijn cycle), and I can show precisely how to do so for a hypothetical d>1 upcycle. 

10.30  11.00  Coffee Break  
11.00  11.30 
Christina Nguyen — An Invitation to Integer Point Enumeration in Graphical Zonotopes
The Ehrhart polynomial for a given integral polytope counts the lattice points inside the polytope for any positive integer dilate. A graphical zonotope is a polytope constructed from the Minkowski sum of the column vectors of a graph's incidence matrix. I will introduce the audience to Ehrhart theory in the context of graphical zonotopes and how the polytope relates to the induced forests of a graph. Then, I will discuss my current work with signed graphs and their polytopes. 

11.30  12.00 
Justus Bruckamp — On the connected blocks polytope
We study the connected blocks polytope, which, apart from its own merits, can be seen as the generalization of certain connectivity based or Eulerian subgraph polytopes. We provide a complete facet description of this polytope, characterize its edges and show that it is Hirsch. We also show that connected blocks polytopes admit a regular unimodular triangulation by constructing a squarefree Gr\"obner basis. In addition, we prove that the polytope is Gorenstein of index 2 and that its $h^\ast$vector is unimodal. 

12.00  14.00  Lunch Break  
14.00  14.30 
Nicholas Anderson — A Closure Operator for Valuated Matroids
Classical matroid theory develops a settheoretical foundation to the study of linear independence, and in doing so, establishes a far more general theory than what is captured in the linear algebra of vectors in Euclidean space. The theory of valuated matroids is a further generalization, where in addition to independence relations we record a weight on each matroid basis, generalizing the data captured by determinants of maximal minors in an (m x n)matrix. Just as in classical matroid theory, the application of valuated matroids depends largely on which of its many definitions we choose to work with. 

14.30  15.00 
Victoria Schleis — Linear degenerate tropical flag varieties
Grassmannians and flag varieties are important moduli spaces in algebraic geometry. Their linear degenerations arise in representation theory as they describe quiver representations and their irreducible modules. As linear degenerations of flag varieties are difficult to analyze algebraically, we describe them in a matroidal setting and further investigate their tropical counterparts. 

15.00  15.30 
Oskar Henriksson — The tropical geometry of parametric polynomial systems
The famous Bernstein’s theorem tells us that the number of isolated roots over $\mathbb{C}^*$ of a square polynomial system with fixed support is at most equal to a mixed volume, and that this bound is attained for generic choices of coefficients. In practice, though, many systems that arise in applications have coefficients that depend on the parameters in such a way that they are algebraically dependent, and in such cases, the mixed volume bound might be far from sharp for generic choices of parameters. 

15.30  16.00  Coffee Break  
16.00  17.45  Community Discussion  Mathematical Biographies  
19.00   Dinner 
9.00  10.00 
Günter Ziegler — The Math Career Lecture
A Career Path in Mathematics: How I met Convex Polytopes, why books areimportant, why examples are important, what my students contributed,and whether there are still interesting problems to work on… 

10.00  10.30 
Hans Höngesberg — Skew symplectic and orthogonal characters through lattice paths
The skew Schur functions admit many determinantal expressions. Chief among them are the (dual) Jacobi–Trudi formula and the Lascoux–Pragacz formula, which is a skew analogue of the Giambelli identity. Comparatively, the skew characters of the symplectic and orthogonal groups, also known as the skew symplectic and orthogonal Schur functions, have received very little attention in this direction. 

10.30  11.00  Coffee Break  
11.00  11.30 
Claudio Alexandre Piedade — Corefree Degrees of Toroidal Maps
Every group G can be represented as a faithful transitive permutation representation of degree n. Moreover, the stabilizer of a point in this permutation representation is always a corefree subgroup of G. Conversely, the action of a group G on a corefree subgroup H ≤ G is always transitive and faithful, giving a faithful transitive permutation representation on the set of cosets G/H, with degree G : H. These permutation representations are powerful tools in the classification of abstract regular/chiral polytopes and hypertopes. In this talk we list all possible degrees of faithful transitive permutation representations of the toroidal regular/chiral maps {4, 4}, {3, 6} and hypermaps (3, 3, 3). This is a joint work with M. Elisa Fernandes. 

11.30  12.00 
Jupiter Davis — Toward an Algebra of Normal Complexes
The polytope algebra is wellstudied and features several interesting properties. One of these is the nilpotency $([P]1)^{n}$. We seek to define an analogue to the polytope algebra for normal complexes. Normal complexes are polytopal complexes obtained by truncating fans, but unlike the polytope case, the fan is not required to be complete. In the first step towards creating a bijection, we prove that this nilpotency holds in the onedimensional case in the algebra for normal complexes. 

12.00  14.00  Lunch Break  
14.00  14.30 
Alexis LangloisRémillard — Computational complexity of chess domination problems on polycubes
In the long tradition of graphtheoretical problems related to chess, we study domination problems on graphs coming from the multidimensional version of chessboards to polycubes. We study the computational complexity of the problem of finding a maximal coclique inside queen and rook graphs on polycubes. This is a generalisation of the famous nqueens problem. We prove that the problem is NPcomplete for rooks on polycubes of dimension 3 and higher and that it is in P for rooks on polyominoes. We will discuss the problem for queens and also survey the related minimal domination problems for queens and rooks and their history. Our final result is the translation of these problems to an integer linear programming problem and its use in numerical investigations improving known values of domination number of square chessboards. 

14.30  15.00 
William Turner — Local separators of Cayley graphs
Given a group $\Gamma$ and a generating set $S\subseteq\Gamma$, the \emph{Cayley graph} $G=\text{Cay}(\Gamma,S)$ is the graph with vertex set $\Gamma$ and, for every $\alpha\in\Gamma$ and $s\in S$, an edge $(\alpha,s\alpha)$. That is, the Cayley graph maps out the entire group and how the generating elements move the group elements around. Stallings' Theorem (1971) states that a finitelygenerated group splits over a finite subgroup if its Cayley graphs have more than one end. In 2010, Bernhard Kr\""on provided a proof of Stallings' Theorem using separators. In this project, we move towards a finite version of Stallings' Theorem, using socalled \lambdaocal separators'. We show that a finitelygenerated group $\Gamma$ (with bounded nilpotency), having a certain local separator, is necessarily a cycle or decomposes as a direct product of a cycle and an involution. In particular, we assume the existence of an $r$local cutvertex or the existence of an $r$local 2separator, for $r$ bounded below. An \emph{$r$local cutvertex} $x$ is a vertex in a graph that disconnects the subgraph induced by the ball of radius $\frac{r}{2}$ centred at $x$. An $r$local 2separator is defined so that it works in a similarly intuitive way. 

15.00  15.30  Coffee Break  
15.30  17.00  Community Discussion  Community organising  
17.00  17.15  Closing Remarks 