Explore the pioneering research at MPI MiS, where our research groups are dedicated to advancing outward-looking mathematics. Learn more about how our researchers are expanding the frontiers of understanding and seeking innovative solutions to complex challenges.

Jürgen Jost

Geometry and Complex Systems
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.

Felix Otto

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.

Bernd Sturmfels

Nonlinear Algebra
Our research focusses on fundamental problems in algebra, geometry and combinatorics that are relevant for nonlinear models.

László Székelyhidi

Applied Analysis
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.

Anna Wienhard

Geometry, Groups, and Dynamics
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.

Samantha Fairchild

Discrete Sets in Geometry
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.

James Reed Farre

Geometry on Surfaces
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.

Benjamin Gess

Stochastic Partial Differential Equations
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.

Michael Joswig

Mathematical Software
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.

Guido Montúfar

Mathematical Machine Learning
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.

Sayan Mukherjee

Learning and Inference
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.

Marta Panizzut

Tropical Geometry and Computer Algebra
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.

İrem Portakal

Interdisciplinary Frontiers of Algebraic Geometry
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.

Tobias Ried

Probability and Variational Methods in PDEs
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.

Daniel Roggenkamp

Mathematical Structures in Physics
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.

Érika Roldán

Stochastic Topology and its Applications
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.

Simon Telen

Numerical Nonlinear Algebra
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.

Jürgen Jost

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.

Felix Otto

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.

Bernd Sturmfels

Our research focusses on fundamental problems in algebra, geometry and combinatorics that are relevant for nonlinear models.

László Székelyhidi

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.

Anna Wienhard

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.

Samantha Fairchild

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.

James Reed Farre

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.

Benjamin Gess

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.

Michael Joswig

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.

Guido Montúfar

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.

Sayan Mukherjee

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.

Marta Panizzut

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.

İrem Portakal

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.

Tobias Ried

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.

Daniel Roggenkamp

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.

Érika Roldán

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.

Simon Telen

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.

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