Academic Career and Research Areas
Prof. Weltge (b. 1986) works on theoretical questions in discrete mathematics that concern the foundations of mathematical optimization. His research focuses on optimal formulations of optimization problems, which he approaches by applying tools from geometry and theoretical computer science. Professor Weltge has made numerous important contributions to the theory of "extended formulations", demonstrating inter alia the unviability of several popular approaches to solving the famous P versus NP problem.
Prof. Weltge studied Mathematics with a minor in Computer Science at the Otto von Guericke University Magdeburg and completed his studies there with distinction in 2012. After research visits in Tartu (Estonia) and Padua (Italy), he completed his Ph.D. in Magdeburg in 2016. He worked as a postdoctoral researcher at the Institute for Operations Research, ETH Zurich, from 2016 to 2018 and has been at TUM since 2018.
Key Publications (all publications)
Cevallos A, Weltge S, Zenklusen R: "Lifting Linear Extension Complexity Bounds to the Mixed-Integer Setting". Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). New Orleans, Louisiana, USA. 07.-10.01.2018: 788-807.Abstract
Averkov G, Krümpelmann J, Weltge S: "Notions of maximality for integral lattice-free polyhedra: the case of dimension three". Mathematics of Operations Research. 2017; 42(4): 1035-1062.Abstract
Averkov G, Merino BG, Paschke I, Schymura M, Weltge S: "Tight bounds on discrete quantitative Helly numbers". Advances in Applied Mathematics. 2017; 89: 76-101.Abstract
Kaibel V, Weltge S: "A short proof that the extension complexity of the correlation polytope grows exponentially". Discrete & Computational Geometry. 2015; 53(2): 397-401.Abstract
Kaibel V, Weltge S: "Lower bounds on the sizes of integer programs without additional variables". Mathematical Programming. 2015; 154(1-2): 407-425.Abstract