Fundamental questions in the natural and engineering sciences have always inspired mathematicians to search for new mathematical structures and methods. The interaction between mathematics and the sciences forms the central point of research at the Max Planck Institute for Mathematics in the Sciences (MPI MiS).

We are an interdisciplinary research team that carries out research in pure mathematics and explores new approaches to complex systems in a wide range of domains, bringing in the spectrum of mathematical concepts and methods in novel ways.

Pattern Formation, Energy Landscapes, and Scaling Laws

Our research focus is the analysis of continuum models that originate in materials science and fluid mechanics. Our technical expertise is in the calculus of variations and partial differential equations.

The main focus of this group is on rigorous applied mathematics, mainly involving partial differential equations and the calculus of variations. We bridge several mathematical sub-disciplines by applying methods originally developed for differential geometry (Gromov) to fluid dynamics and nonlinear elasticity.

We conduct fundamental research in geometry, group theory, and dynamics, explore applications and interactions with other sciences and engage in communicating mathematics to the broader public.

We explore discrete sets linked to geometric objects, focusing on Riemann surfaces, particularly those formed by gluing polygons. Our research spans number theory, dynamics, transcendental functions, and data science connections.

We are interested in various geometric structures on surfaces and 3-manifolds and the understanding of their geometry and deformations. Some deformations yield dynamical systems on moduli spaces; ergodic theory offers new perspectives on these objects.

Our focus is on the study of stochastic partial differential equations (SPDEs), nonlinear partial differential equations, stochastic dynamics, interacting particle systems, machine learning, and fluid dynamics.

We are dedicated to developing cutting-edge software that serves as a bridge between mathematical fields and interdisciplinary research areas. Our goal is to advance mathematical knowledge and make it more accessible to a wider audience.

We advance key problems in Deep Learning Theory using geometric analysis. Our mission is to consolidate the theoretical foundations for the success of Deep Learning and make them more broadly applicable. We draw on innovative mathematics to streamline progress into new frontiers.

We focus on the mathematical foundations of inference and learning. We develop methodological innovations for inference and learning and apply them to biology, biomedicine, and clinical challenges. Our goal is to advance these fields through rigorous mathematical analysis.

We want to build new bridges between Tropical Geometry and Algebraic Geometry using computational methods. This involves the study of fundamental problems in tropical geometry and the use and development of state-of-the-art software.

Our goal is to explore and broaden the scope of algebraic geometry and its connections with different branches of math & sciences. We are driven by the belief that this field transcends traditional boundaries, promoting collaboration & practical applications.

We use probabilistic and variational techniques to better understand nonlinear partial differential equations. We apply our findings to kinetic theory, statistical physics, materials science, and quantum mechanics. Our projects include optimal transportation, singular stochastic PDEs, effective equations, pattern formation problems, and density functional theory.

We conduct research at the interface of mathematics and theoretical physics, making use of a high degree of cross-fertilization between physical ideas and intuition on the one hand and rigorous mathematical theory on the other.

We explore the topology of random combinatorial and geometric structures. Our research includes percolation models on lattices, configuration spaces, and random simplicial and cubical complexes. We also investigate extremal topological structures and their properties.

We are dedicated to developing advanced algorithms and theory to tackle the ancient problem of solving polynomial equations. In addition, we delve into related problems such as polynomial optimization, variable elimination, and tensor decomposition.

Our director, Bernd Sturmfels, was recently awarded an honorary doctorate by the University of Bern during its Dies Academicus festivities. The recognition comes in light of his remarkable contributions to mathematical research and the promotion of gender diversity.

Das Max-Planck-Institut für Mathematik in den Naturwissenschaften (MPI MiS) sucht zum nächstmöglichen Zeitpunkt einen Content Manager (m/w/d) für die selbständige Inhaltserstellung auf Basis wissenschaftlicher Inputs.

Hanna Tseran successfully defended her PhD thesis on activation functions in neural networks. She continues to work on deep learning theory in the Matsuo Laboratory at the University of Tokyo. Well done Hanna, and our best wishes!

Our director, Anna Wienhard, was recently elected to the German Academy of Sciences, Leopoldina. Acceptance into the Academy is considered one of the highest academic honors. We extend our sincere congratulations!

Following our Chow Lecture series, graduate students, Laura Casabella and Dante Luber, had the opportunity to interview June Huh about his work, winning the Fields Medal, and mathematics in general.

The Max Planck Institute for Mathematics in the Sciences (MPI MiS) invites applications for several Postdoctoral Research Positions to join our community exploring mathematical frontiers in interdisciplinary fields.

The Max Planck Institute for Mathematics in the Sciences (MPI MiS) offers funding for several PhD positions to join our community exploring mathematical frontiers in interdisciplinary fields.

The European Research Council (ERC) has granted a €10 million Synergy Grant to the UNIVERSE+ project. The project aims to develop a new mathematical language to describe physical phenomena at all scales, from particles to the universe's structure.

We extend our congratulations to Markus Tempelmayr on the successful defense of his thesis “Algebraic and probabilistic aspects of regularity structures”! He joins the University of Münster as a postdoctoral researcher.

Our latest Research Brief from the group of Jürgen Jost explores links between algebra and geometry. They discuss connections between Jordan algebras and Lie groups and investigate symmetries in algebraic structures.

Former group leader Angkana Rüland, renowned for her work in applied analysis, is to receive the New Horizons Prize from the Breakthrough Prize Foundation, a $100,000 accolade. Congratulations on this well-deserved recognition!

Samantha Fairchild just launched her Discrete Sets in Geometry group. In our interview, she covers dynamical systems, transcendental theory, and more. She also seeks a postdoc to join her ambitious effort to explore intersections across mathematics.

Join the International Max Planck Research School Mathematics in the Sciences (IMPRS) PhD program. A collaboration between three Leipzig University Institutes and MiS. Our goal: guide students towards exciting research problems in physical and life sciences using a wide range of mathematical fields.

We are committed to innovative fundamental research and transferring concepts from mathematics into other academic fields. We are always seeking new members for our vibrant community. Are you ready to take the next step in your scientific journey as a PhD student, postdoc, or guest scientist?

Research at MPI MiS is as diverse and multifaceted as the people who pursue it. Our Math Planck People portrait series gives a face to our research and introduces the personalities that make up our institute - our scientists & staff.