Research Spotlight
Putting current research center stage
Our institute represents a great variety of research topics that affect current developments both within the natural sciences as well as social and economic life. In our column Research Spotlight MiS scientists are presenting key ideas and giving insights into recent developments of their research in a short video format.
Research Spotlights
06.05.22
Markus Tempelmayr — A diagram-free approach to the stochastic estimates in regularity structures
We explore the version of Hairer's regularity structures based on a greedier index set than trees, as introduced by Otto, Sauer, Smith and Weber.
Research Spotlights
25.08.21
Claudia Fevola — KP Solitons from Tropical Limits
In this talk, we study solutions to the Kadomtsev-Petviashvili equation whose underlying algebraic curves undergo tropical degenerations.
Research Spotlights
25.08.21
Pablo Linares & Markus Tempelmayr — A tree-free construction of the structure group
We present a new approach to regularity structures, and in particular to the construction of the structure group, which replaces the tree-based framework of Hairer by a more Lie-geometric setting.
Research Spotlights
03.08.21
Daniele Agostini — Curves and theta functions: algebra, geometry & physics
In this talk, I present some of the results obtained in my group about theta functions of algebraic curves, and especially how they connect to the physics of water waves through the KP equation.
Research Spotlights
03.08.21
Stefan Hollands — General Relativity and Quantum Theory
In this short overview talk I outline some of my core research interests, ranging from Mathematical General Relativity, to Quantum Field- and Information Theory.
Research Spotlights
19.07.21
Guido Montúfar — Implicit Bias in Wide Neural Networks
We investigate gradient descent training of overparametrized neural networks with rectified linear units and the corresponding implicit bias in function space.
Research Spotlights
19.07.21
Rostislav Matveev — Tropical Probability and Entropic Inequalities
Tropical Probability is a new method to address problems in Information Theory and related fields of research.
Research Spotlights
24.06.21
Wilmer Leal — Exploration of the chemical space
In this talk, we explore large-scale patterns emerging in the last two centuries of chemical history, in particular, on the growth of chemical knowledge, the use of reactants and the synthesis of products, which reveal both conservatism and sharp transitions in the exploration of the chemical space.
Research Spotlights
24.06.21
Noémie Combe — How many Frobenius manifolds are there?
In this talk an overview of my recent results is presented. In a joint work with Yu. Manin (2020) we discovered that an object central to information geometry: statistical manifolds (related to exponential families) have an F-manifold structure.
Research Spotlights
17.06.21
Pavlos Tsatsoulis — Singular SPDEs and Renormalisation
In this short video I will discuss topics on Singular Stochastic Partial Differential Equations (SPDEs) with interesting connections to different fields of mathematics.
Research Spotlights
17.06.21
Simon Telen — Likelihood Equations and Scattering Amplitudes
We identify the scattering equations from particle physics as the likelihood equations for a particular statistical model.
Research Spotlights
10.06.21
Tobias Ried — Optimal Transportation, Monge-Ampère, and the Matching Problem
We present a fully variational approach to the regularity theory for the Monge-Ampère equation, or rather of optimal transportation, with interesting applications to the problem of optimally matching a realisation of a Poisson point process to the Lebesgue measure.
Research Spotlights
10.06.21
Mima Stanojkovski — Groups from determinantal curves
I will explain how to construct, analyze, and distinguish p-groups using tools coming from (algebraic and arithmetic) geometry, number theory, and algebra.
Research Spotlights
03.06.21
Benjamin Gess — Fluctuations in non-equilibrium and stochastic PDE
Macroscopic fluctuation theory provides a general framework for far from equilibrium thermodynamics, based on a fundamental formula for large fluctuations around (local) equilibria.
Research Spotlights
03.06.21
Michael Joswig — What is Mathematical Software
What is Mathematical Software? A short answer to this question is: Mathematical Software is what mathematics receives as a benefit from the digital age. This is relevant because Mathematical Software is useful in many ways.
Research Spotlights
28.05.21
Raffaella Mulas — Spectral theory of hypergraphs
In this talk, we generalize the graph normalized Laplace operators to the case of hypergraphs, and we discuss some properties of their spectra.
Research Spotlights
28.05.21
Matteo Smerlak — Aspects of evolutionary dynamics from viruses to whales
Our interdisciplinary group studies ecological and evolutionary dynamics across scales. In this video I present a selection of recent results that illustrate the role of mathematics in furthering our understanding of biological evolution.
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