Regular lectures Summer semester 2020: MPI MIS

Please find more information about the lectures at the detail pages.

For rooms at the MPI MiS please note:
Use the entry doors Kreuzstr. 7a (rooms A3 01, A3 02) and Kreustr. 7c (room G3 10), both in the inner court yard, and go to the 3rd. floor.
To reach the Leibniz-Saal (E1 05, 1st. floor) and the Leon-Lichtenstein Room (E2 10, 2nd. floor) use the main entry Inselstr. 22.

Please remember: The doors will be opened 15 minutes before the lecture starts and closed after beginning of the lecture!


Apr 1, 2020	Albert Much IMPRS-Ringvorlesung: Summer semester 2020 About this lectureDue to the rather broad spectrum of topics within the IMPRS, the curriculum consists of a core curriculum to be attended by all students and a variety of more specialized lectures and courses. The heart of our teaching program certainly is the Ringvorlesung. Each semester the Ringvorlesung focuses on one field and is usually delivered by scientific members of the IMPRS who introduce different approaches and visions within this field. Topics In this "Ringvorlesung" we introduce basic concepts of noncommutative geometry and deformation quantization. We begin by introducing the metric aspect and generalizations of commutative concepts to the noncommutative realm, such as differential forms, know as the universal differential algebra. Further on, we will introduce spectral geometry to see applications of the framework. Once these results are established we move on to deformation quantization. First we introduce the conceptual ideas and later we sketch the proof of the famous Kontsevich theorem, for which he obtained the Fields medal. Next, we introduce the more strict (i.e. non-formal) approach to deformation quantization known by the Rieffel Deformation. In the last part of this lecture series we show how noncommutative geometry and Deformation quantization are connected by the example of a simple quantum gravitational toy model.Date and time infoFriday (July 17, July 24, July 31, August 7), 13.00-14.30Keywordsnoncommutative geometry, deformation quantizationAudienceIMPRS studentsLanguageEnglish A. Much I, Video (1080p) A. Much I, Video (720p) A. Much II, Video (1080p) A. Much II, Video (720p) A. Much III, Video (1080p) A. Much III, Video (720p) A. Much IV, Video (1080p) A. Much IV, Video (720p)
Apr 1, 2020	Bogdan Raita An introduction to generalized Young measures In the study of PDEs, one cannot realistically hope for better compactness than in the weak topologies, which reasonably describe measurements of physical quantities. The phenomena that are less understood do not usually lead to linear equations, making the interaction between nonlinear quantities and weakly convergent sequences an ubiquitous theme in the study of nonlinear PDEs. In this course, we will learn about generalized Young measures (GYM), which are especially useful tools to describe the effective limits of nonlinearities applied to weakly convergent sequences in Lebesgue spaces. In particular, these objects efficiently keep track of concentration and oscillation effects, which are the main obstructions to strong convergence. Thus, Young measures are naturally used in many branches of PDE theory, of which we will focus on their role in the Calculus of Variations, where the notion first emerged from the ideas of L.C. Young. We will thoroughly explore the functional analytic and measure theoretic realities of GYM, with a focus on identifying oscillation and concentration effects, or lack thereof. We will use this basic understanding to study weak sequential continuity and lower semi-continuity of energy functionals $$ E[v]=\int_{\Omega} F(v(x))\mathrm{d\,}x $$ on linear PDE constrained subsets of Lebesgue spaces. Such problems arise in elasticity, plasticity, composites, fluids, and electromagnetism, to name a few; more abstract applications arise in differential geometry and geometric measure theory. Time permitting, we will present the main result of my recent preprint arXiv:1912.09190, joint with Jan Kristensen.Date and time infoWednesdays 11.00-12.30

Apr 1, 2020

Albert Much

IMPRS-Ringvorlesung: Summer semester 2020

About this lectureDue to the rather broad spectrum of topics within the IMPRS, the curriculum consists of a core curriculum to be attended by all students and a variety of more specialized lectures and courses. The heart of our teaching program certainly is the Ringvorlesung. Each semester the Ringvorlesung focuses on one field and is usually delivered by scientific members of the IMPRS who introduce different approaches and visions within this field. Topics In this "Ringvorlesung" we introduce basic concepts of noncommutative geometry and deformation quantization. We begin by introducing the metric aspect and generalizations of commutative concepts to the noncommutative realm, such as differential forms, know as the universal differential algebra. Further on, we will introduce spectral geometry to see applications of the framework. Once these results are established we move on to deformation quantization. First we introduce the conceptual ideas and later we sketch the proof of the famous Kontsevich theorem, for which he obtained the Fields medal. Next, we introduce the more strict (i.e. non-formal) approach to deformation quantization known by the Rieffel Deformation. In the last part of this lecture series we show how noncommutative geometry and Deformation quantization are connected by the example of a simple quantum gravitational toy model.Date and time infoFriday (July 17, July 24, July 31, August 7), 13.00-14.30Keywordsnoncommutative geometry, deformation quantizationAudienceIMPRS studentsLanguageEnglish

A. Much I, Video (1080p) A. Much I, Video (720p) A. Much II, Video (1080p) A. Much II, Video (720p) A. Much III, Video (1080p) A. Much III, Video (720p) A. Much IV, Video (1080p) A. Much IV, Video (720p)

Apr 1, 2020

Bogdan Raita

An introduction to generalized Young measures

In the study of PDEs, one cannot realistically hope for better compactness than in the weak topologies, which reasonably describe measurements of physical quantities. The phenomena that are less understood do not usually lead to linear equations, making the interaction between nonlinear quantities and weakly convergent sequences an ubiquitous theme in the study of nonlinear PDEs. In this course, we will learn about generalized Young measures (GYM), which are especially useful tools to describe the effective limits of nonlinearities applied to weakly convergent sequences in Lebesgue spaces. In particular, these objects efficiently keep track of concentration and oscillation effects, which are the main obstructions to strong convergence. Thus, Young measures are naturally used in many branches of PDE theory, of which we will focus on their role in the Calculus of Variations, where the notion first emerged from the ideas of L.C. Young. We will thoroughly explore the functional analytic and measure theoretic realities of GYM, with a focus on identifying oscillation and concentration effects, or lack thereof. We will use this basic understanding to study weak sequential continuity and lower semi-continuity of energy functionals $$ E[v]=\int_{\Omega} F(v(x))\mathrm{d\,}x $$ on linear PDE constrained subsets of Lebesgue spaces. Such problems arise in elasticity, plasticity, composites, fluids, and electromagnetism, to name a few; more abstract applications arise in differential geometry and geometric measure theory. Time permitting, we will present the main result of my recent preprint arXiv:1912.09190, joint with Jan Kristensen.Date and time infoWednesdays 11.00-12.30

Regular lectures Summer semester 2020

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Katharina Matschke