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Beyond “dessins d’enfant”, the theory nowadays referred to as Grothendieck-Teichmüller theory (Galois-Teichmüller in Grothendieck’s manuscripts) may well represent the main new theme in the Esquisse d'un Programme, as confirmed in the Promenade à travers une œuvre (which is part of Récoltes et semailles). Simplifying a great deal one may say that Grothendieck’s main ideas were taken up especially by Y. Ihara, V. Drinfeld and P. Deligne in the mid and late eighties.They derive in large part from the elementary remark that the fundamental group remains the only invariant in classical algebraic topology which is not a priori abelian .Making this remark fruitful probably required the genius of Alexandre Grothendieck . The fact is that out of it Grothendieck-Teichmüller theory (on which we will concentrate) and Anabelian Geometry (including the so-called “section conjecture”) were born.In Grothendieck’s Esquisse, he is dealing with the full étale fundamental group, which is profinite almost...

The similarities of quantum fluid dynamics with its classical counterpart are at core of a large body of research that started with cryogenic helium more that 50 years ago and now encompasses a broad range of 3D, 2D as well quasi-2D systems. In this 5 day meeting we wish to discuss different topics related to fluid dynamical approaches versus approaches based on quantum excitations.  We aim to focus on specific themes that we have identified, namely: 1. Classical and Quantum Turbulent statistics and the existence of scaling ranges; 2. Vortex & Wave Dynamics in Quantum Fluids, from individual to collective behaviours; 3. Analog gravity models and the advantages of Quantum Fluids for Cosmology. For this we have adopted an interdisciplinary approach that combines ideas from physics, mathematics, and engineering and brings together computational, experimental, and theoretical experts.  We will cover the exciting developments in this field in this discussion meeting, which will, we hope (a)...

Beyond “dessins d’enfant”, the theory nowadays referred to as Grothendieck-Teichmüller theory (Galois-Teichmüller in Grothendieck’s manuscripts) may well represent the main new theme in the Esquisse d'un Programme, as confirmed in the Promenade à travers une œuvre (which is part of Récoltes et semailles). Simplifying a great deal one may say that Grothendieck’s main ideas were taken up especially by Y. Ihara, V. Drinfeld and P. Deligne in the mid and late eighties.They derive in large part from the elementary remark that the fundamental group remains the only invariant in classical algebraic topology which is not a priori abelian .Making this remark fruitful probably required the genius of Alexandre Grothendieck . The fact is that out of it Grothendieck-Teichmüller theory (on which we will concentrate) and Anabelian Geometry (including the so-called “section conjecture”) were born.In Grothendieck’s Esquisse, he is dealing with the full étale fundamental group, which is profinite almost...

The similarities of quantum fluid dynamics with its classical counterpart are at core of a large body of research that started with cryogenic helium more that 50 years ago and now encompasses a broad range of 3D, 2D as well quasi-2D systems. In this 5 day meeting we wish to discuss different topics related to fluid dynamical approaches versus approaches based on quantum excitations.  We aim to focus on specific themes that we have identified, namely: 1. Classical and Quantum Turbulent statistics and the existence of scaling ranges; 2. Vortex & Wave Dynamics in Quantum Fluids, from individual to collective behaviours; 3. Analog gravity models and the advantages of Quantum Fluids for Cosmology. For this we have adopted an interdisciplinary approach that combines ideas from physics, mathematics, and engineering and brings together computational, experimental, and theoretical experts.  We will cover the exciting developments in this field in this discussion meeting, which will, we hope (a)...

Control theory for partial differential equations (PDEs) deals with the use of inputs to influence the behavior of a system governed by PDEs, to achieve a desired goal. This program is focused on recent outstanding developments on controllability and stabilizability of parabolic, hyperbolic and dispersive PDEs. These PDEs appear naturally as mathematical models in numerous applications in physics, engineering, biology, and medicine. Depending on the type of PDEs, the control aspects of PDEs and the techniques used to study them change significantly. To address this point, there will be a dedicated lecture series (mini courses) on (i) Control of parabolic PDEs, (ii) Control of hyperbolic PDEs, (iii) Control of dispersive PDEs, (iv) Feedback stabilization of PDEs, by experts, who have made exceptional contributions. Most of the talks will have an expository flavor in order to introduce the respective topic to a heterogeneous audience followed by few research talks. Each mini course will ...

No living organism escapes evolutionary change, and evolutionary biology thus connects all biological disciplines. To understand the processes driving evolution, we need a theoretical framework to predict and test evolutionary changes in populations. Population genetic theory provides this basic framework, integrating mathematical and statistical concepts with fundamental biological principles of genetic inheritance, selection, mutation, migration and random genetic drift. Population genetic models allow us to make quantitative predictions that can inform an experimentalist while designing new experiments, and give us a deeper understanding of how evolution works. The ICTS schools on population genetics and evolution, organized biennially since 2014, introduce students to fundamental concepts as well as the latest advances in population genetic theory.In the sixth edition of the school, over 2 intense weeks, students from diverse biological and mathematical backgrounds will learn and t...

Control theory for partial differential equations (PDEs) deals with the use of inputs to influence the behavior of a system governed by PDEs, to achieve a desired goal. This program is focused on recent outstanding developments on controllability and stabilizability of parabolic, hyperbolic and dispersive PDEs. These PDEs appear naturally as mathematical models in numerous applications in physics, engineering, biology, and medicine. Depending on the type of PDEs, the control aspects of PDEs and the techniques used to study them change significantly. To address this point, there will be a dedicated lecture series (mini courses) on (i) Control of parabolic PDEs, (ii) Control of hyperbolic PDEs, (iii) Control of dispersive PDEs, (iv) Feedback stabilization of PDEs, by experts, who have made exceptional contributions. Most of the talks will have an expository flavor in order to introduce the respective topic to a heterogeneous audience followed by few research talks. Each mini course will ...

No living organism escapes evolutionary change, and evolutionary biology thus connects all biological disciplines. To understand the processes driving evolution, we need a theoretical framework to predict and test evolutionary changes in populations. Population genetic theory provides this basic framework, integrating mathematical and statistical concepts with fundamental biological principles of genetic inheritance, selection, mutation, migration and random genetic drift. Population genetic models allow us to make quantitative predictions that can inform an experimentalist while designing new experiments, and give us a deeper understanding of how evolution works. The ICTS schools on population genetics and evolution, organized biennially since 2014, introduce students to fundamental concepts as well as the latest advances in population genetic theory.In the sixth edition of the school, over 2 intense weeks, students from diverse biological and mathematical backgrounds will learn and t...

The upcoming electron-ion collider (EIC) to be built at the Brookhaven National Lab, USA will probe the internal structure of the protons and neutrons to unprecedented details, in terms of the fundamental building blocks, quarks and gluons. The EIC will bombard highly energetic electron beams with proton/heavy ion beam.  Some of the key questions that the EIC will investigate are (i) how the quarks and gluons are distributed inside the nucleon ? (ii) How do the massless gluons and light quarks make up the mass of the bulk of the visible matter in the universe ? (iii) How is the spin (1/2) of the proton made up from the spin of its constituents and what is the role of the orbital angular momentum of the quarks and gluons ? (iv) Does a steady state of gluon saturation occurs in the heavy ion collision, called color glass condenstate ? Due to its high luminosity and wide kinematical coverage, EIC will probe the nucleon to unprecedental level, giving access to information never seen before...