## Energy-based modeling, simulation, and control. Mathematical theory and algorithms for the solution of real-world problems – Volker Mehrmann (Technische Universität Berlin)

Energy based modeling via port-Hamiltonian systems is a relatively new paradigm in all areas of science and engineering. These systems have wonderful mathematical properties, concerning their analytic, geometric and algebraic properties, but also…

## Motilità biologica e robot bio-ispirati: nuove sfide e opportunità e per la matematica – Antonio DeSimone (Scuola Superiore Sant’Anna)

La biologia è una ricca fonte di ispirazione, anche per la ricerca di nuovi materiali, nuove forme e strategie di movimento, dispositivi mobili e adattabili con nuove funzionalità, strutture architettoniche biomorfe. Di straordinario interesse sono…

## From the liquid drop model for nuclei to the ionization conjecture for atoms – Rupert Frank (Mathematics Institute, University of Munich)

The liquid drop model is an isoperimetric problem with a competing non-local term. It was originally introduced in the nuclear physics literature in 1930 and has received a lot of attention recently as an interesting problem in the calculus of…

## Categorical resolutions of singularities – Alexander Kuznetsov (Steklov Mathematical Institute and HSE, Moscow, Russia)

In the talk, I will try to explain the definition of acategorical resolution of singularities and describe several related constructionsthat show the advantages of this notion over the geometric one. Youtube Channel:https://youtu.be/Y2Im3B7olxY…

## Liouville type theorems and local behaviour of solutions to degenerate or singular problems – Susanna Terracini (Università di Torino)

We consider an equation in divergence form with a singular-degenerate weight $-\mathrm{div}(y^a A(x,y)\ abla u)=y^a f(x,y,u)\; \quad\textrm{or}\; \textrm{div}(y^aF(x,y,u))\;,$ We first study the regularity of the nodal sets of solutions in the…

## Gromov-hyperbolicity and beyond – Alessandro Sisto (ETH Zurigo)

The protagonists of the talk are (Gromov-)hyperbolicity and mapping class groups, both of which I will introduce during the talk. Hyperbolicity is a central notion in geometric group theory which captures the large-scale geometry of negatively…

## Mathematical problems in modern machine learning – Andrea Montanari (Stanford University)

The last fifteen years have witnessed dramatic advances in machine learning. This progress was mainly driven by engineering advances: greater computing power, and larger availability of training data. Not only the collection of methods that emerged…

## Flows of vector fields: classical and modern – Camillo De Lellis (Institute for Advanced Study, Princeton, and University of Zuerich)

Consider a (possibly time-dependent) vector field $v$ on the Euclidean space. The classical Cauchy-Lipschitz (also named Picard-Lindel\”of) Theorem states that, if the vector field $v$ is Lipschitz in space, for every initial datum $x$ there is a…

Abstract TBA…

## Notions of complexity for minimal subvarieties – Alessandro Carlotto (ETH Zurich – Department of Mathematics )

Notions of complexity for minimal subvarieties…

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