## New MATH+/BMS Dirichlet Postdocs 2023

**The Dirichlet Postdoctoral Program offers two-year positions aimed at early-stage postdoctoral researchers worldwide across all mathematical fields. MATH+ and the BMS support their development into independent researchers while helping them further qualify for their future careers and gain international visibility. The three new BMS Dirichlet Postdoctoral Fellows who have taken up their postdoc positions in Berlin are Fabian Lehman, Ioannis Papadopoulos, and Alexandra Wesolek.**

The Dirichlet Postdoctoral Fellows pursue their research agendas and delve into their individual research interests. Berlin’s extensive mathematical environment offers access to the latest advancements in their respective fields. They will receive support in establishing a collaborative network, encompassing both national and international scientific contacts, and benefit from insights provided by research groups in related or diverse fields. Furthermore, the postdoctoral researchers will have abundant opportunities to acquire teaching, supervisory, and mentoring experience within the framework of the BMS and MATH+.

**Fabian Lehmann @ HU Berlin:**

Fabian Lehmann studied mathematics at the *Universität Freiburg*. He earned his PhD from *University College London* with a dissertation on “Families of complete non-compact Spin (7) holonomy manifolds” in 2020. In the past three years, he worked at the *Simons Center for Geometry and Physics* in Stony Brook, New York.

His research interests are at the intersection of geometry and partial differential equations. An essential system of partial differential equations appearing in geometry is Einstein’s equations, which characterize spaces with a particularly interesting curvature. They also appear in the theory of general relativity. He studies these equations on octonionic spaces, which have dimension seven or eight and are modeled on the octonions, which form an eight-dimensional number system. This extra structure gives Einstein’s equations a simpler form.

Even in this setting, finding solutions is challenging. Fabian hopes that his “research at the BMS can contribute to finding such spaces which look like a cone” and continues with regard to MATH+ and the BMS: “The BMS has been a very successful program so far, and I am honored to be part of it.”

**Ioannis Papadopoulos @ WIAS:**

Ioannis Papadopoulos studied mathematics at the *Imperial College London* (B.Sc.) and the *University of Oxford* (M.Sc.). He obtained his PhD from the *University of Oxford* with a thesis on “Computing multiple solutions of topology optimization problems” in 2021. From 2021 to 2023, he held a research associate (postdoc) position at *Imperial College London*.

His main research area is numerical analysis and scientific computing. The research focuses on the interface between PDEs and numerical analysis: spectral and finite element methods for fractional and nonlinear PDEs, nonconvex optimization, preconditioners, and software. During his Dirichlet postdoctoral fellowship, Ioannis wants to explore nonconvex PDE-constrained optimization, sparse *hp*-finite element methods, and preconditioning techniques for nonlinear PDEs and (quasi) variational inequalities. In particular, he is interested in computing multiple solutions of highly nonlinear problems with sparse high order discretizations.

About his upcoming years in Berlin as a Dirichlet postdoc, he said: “It brings me great joy to become a part of the esteemed MATH+/BMS community. I eagerly anticipate engaging in collaborations and embracing what Berlin has to offer.”

**Alexandra Wesolek @ TU Berlin:**

Alexandra Wesolek recently completed her PhD at the *Simon Fraser University* in Vancouver under the guidance of Bojan Mohar. Her primary research focus lies in topological graph theory. This subject is at the intersection of graph theory and topology/geometry. Throughout her graduate studies, Alexandra also went on research visits to France, where she worked on structural graph theory. Prior to joining the BMS, she pursued a 3-month postdoctoral position in Lyon, France, under the mentorship of Nicolas Bousquet and Théo Pierron.

During her time at MATH+ and the BMS, she wants to work further on geometric and structural problems in graph theory. A problem she finds particularly engaging is the cops and robber game. In this game, cops try to catch one robber, while the cops and the robber move at the same speed. The game field can either be a graph or a surface. One is generally interested in the minimum number of cops that can catch the robber on the game field. Played on a graph, the game has many connections to structural graph theory since the structure of a graph determines the game. However, when played on surfaces, the game is influenced by the geometry of the surface.

Regarding her forthcoming years at the BMS in Berlin, she commented: “Being at the BMS and working in the group of Stefan Felsner was my favorite destination for a postdoc, so I was very excited when I got the Dirichlet Postdoctoral Position. I am looking forward to being part of the BMS and to interacting with the students in the program and other postdocs. I am planning to teach a specialized BMS course in graph theory next year, which I am particularly looking forward to.”

**More information on the MATH+ Postdoctoral Program and the BMS Dirichlet Postdoctoral Program**