Discrete Geometry and Convexity have always been intimately related to other parts of mathematics, including algebra, analysis and number theory. During the last couple of decades, through an amalgamation of these classical disciplines with computational geometry, a new field was born which has undergone explosive growth resulting in spectacular breakthroughs such as the solution of the sphere packing problem in 8 dimensions or Erdős's distinct distances problem.

The main goals of the special semester are to bring together a mix of senior and junior colleagues to advance research in Discrete Geometry and Convexity and to foster and enhance the interaction and synergy between the study of purely combinatorial properties of discrete geometric structures and the design of efficient algorithms for their construction.

Convex and Discrete Geometry Summer School: Aug 28, 2023 - Sep 1, 2023

Convex and Discrete Geometry Workshop: Sep 4, 2023 - Sep 8, 2023

Focused Week: Geometric Spanners: Oct 23, 2023 - Oct 29, 2023

For a graph \(G=(V,E)\) with edge weight \(w:E\rightarrow \mathbb{R}^+\), a \(t\)-spanner is a spanning subgraph \(H\) such that for all pair of vertices \(u,v\in V\), we have \(d_H(u,v)\leq t\cdot d_G(u,v)\), where \(d_G(u,v)\) denotes the shortest path distance between vertices \(u\) and \(v\) in \(G\). That is, \(H\) distorts distances in \(G\) by a factor of at most \(t\), which is called the spanning ratio or stretch factor of \(H\). The primary focus of this week lies in the regime \(t=1+\varepsilon\) for arbitrarily small \(\varepsilon>0\). It will explore the asymptotic behavior of graph parameters of geometric \((1+\varepsilon)\)-spanners as \(\varepsilon\) tends to zero.

Graph Drawing and Combinatorial Geometry Workshop: Nov 13, 2023 - Nov 17, 2023