Fundamental concepts of infinite group theory, series of subgroups, radicals and residuals, finiteness conditions: finitely generated and finitely presented groups, groups with finite rank, periodic and locally finite groups, maximal and minimal conditions. Solvable and nilpotent groups, properties of upper and lower central series, residually finite groups, generalized nilpotent groups, Engel groups, local theorems and generalized solvable groups.

Textbook: Finiteness conditions and Generalized Solvable groups, Derek Robinson

The course is in English

Fundamental concepts of infinite group theory, series of subgroups, radicals and residuals, finiteness conditions: finitely generated and finitely presented groups, groups with finite rank, periodic and locally finite groups, maximal and minimal conditions. Solvable and nilpotent groups, properties of upper and lower central series, residually finite groups, generalized nilpotent groups, Engel groups, local theorems and generalized solvable groups.

Textbook: Finiteness conditions and Generalized Solvable groups, Derek Robinson

The course is in English

Fundamental concepts of infinite group theory, series of subgroups, radicals and residuals, finiteness conditions: finitely generated and finitely presented groups, groups with finite rank, periodic and locally finite groups, maximal and minimal conditions. Solvable and nilpotent groups, properties of upper and lower central series, residually finite groups, generalized nilpotent groups, Engel groups, local theorems and generalized solvable groups.

Textbook: Finiteness conditions and Generalized Solvable groups, Derek Robinson

The course is in English

Fundamental concepts of infinite group theory, series of subgroups, radicals and residuals, finiteness conditions: finitely generated and finitely presented groups, groups with finite rank, periodic and locally finite groups, maximal and minimal conditions. Solvable and nilpotent groups, properties of upper and lower central series, residually finite groups, generalized nilpotent groups, Engel groups, local theorems and generalized solvable groups.

Textbook: Finiteness conditions and Generalized Solvable groups, Derek Robinson

The course is in English

Fundamental concepts of infinite group theory, series of subgroups, radicals and residuals, finiteness conditions: finitely generated and finitely presented groups, groups with finite rank, periodic and locally finite groups, maximal and minimal conditions. Solvable and nilpotent groups, properties of upper and lower central series, residually finite groups, generalized nilpotent groups, Engel groups, local theorems and generalized solvable groups.

Textbook: Finiteness conditions and Generalized Solvable groups, Derek Robinson

The course is in English

Die Vorlesung wird ausgewählte Konzepte aus der Differentialgeometrie und ihre Rolle bei der Lösung von aktuellen Anwendungsproblemen vorstellen.

Zur den Themen gehören u.a. Krümmungsmaße, geometrische Flüsse, Minimalflächen, harmonische Abbildungen, Paralleltransport, verzweigte Überlagerungen, sowie deren Diskretisierung und algorithmische Umsetzung.

Praxisnahe Probleme kommen z.B. aus den Bereichen geometrisches Design, Geometrieverarbeitung, Visualisierung, Materialwissenschaft, Medizin, Architektur.

Vorkenntnisse: Differentialgeometrie I

The first tute will take place in semester week 2.

Inhalt:

Abstract:

Modeling, Simulation, and Optimization (MSO) is one of the cornerstones of application-oriented mathematics.

It covers a broad spectrum of research activities, ranging from the design of mathematical models for real-world processes, via efficient numerical simulation algorithms, to the solution of optimization problems for finding optimal scenarios or controls for the process under consideration. This lecture will give an overview over the techniques used in MSO and its application in different areas (life science, mobility, energy, sustainability, …). The lecture will be complemented by several pilot projects in which student groups will develop MSO solutions for realistic (but not too complex) application problems.

Zielpublikum:
Master Mathematik

• Brokate and J. Sprekels: Hysteresis and Phase Transitions. Springer (1996)
• K. Deckelnick, G. Dziuk, and Ch.M. Elliott: Computation of geometric partial differential equations and mean curvature flow. Acta Numerica, p. 1-94 (2005)
• G. Dziuk and Ch.M. Elliott: Finite elements on evolving surfaces. IMA J. Numer. Anal. 27, p. 262-292 (2007)
• J.A. Sethian: Level Set Methods and Fast Marching Methods, CambridgeUniversity Press (1999)
• T.J. Willmore: Riemannian Geometry, Clarendon, Oxford (1993)
• Winkelmann, Stefanie, and Christof Schütte. Stochastic dynamics in computational biology. Vol. 645. Berlin/Heidelberg, Germany: Springer, 2020.

Die Vorlesung wird ausgewählte Konzepte aus der Differentialgeometrie und ihre Rolle bei der Lösung von aktuellen Anwendungsproblemen vorstellen.

Zur den Themen gehören u.a. Krümmungsmaße, geometrische Flüsse, Minimalflächen, harmonische Abbildungen, Paralleltransport, verzweigte Überlagerungen, sowie deren Diskretisierung und algorithmische Umsetzung.

Praxisnahe Probleme kommen z.B. aus den Bereichen geometrisches Design, Geometrieverarbeitung, Visualisierung, Materialwissenschaft, Medizin, Architektur.

Vorkenntnisse: Differentialgeometrie I

The first tute will take place in semester week 2.

Inhalt:

Abstract:

Modeling, Simulation, and Optimization (MSO) is one of the cornerstones of application-oriented mathematics.

It covers a broad spectrum of research activities, ranging from the design of mathematical models for real-world processes, via efficient numerical simulation algorithms, to the solution of optimization problems for finding optimal scenarios or controls for the process under consideration. This lecture will give an overview over the techniques used in MSO and its application in different areas (life science, mobility, energy, sustainability, …). The lecture will be complemented by several pilot projects in which student groups will develop MSO solutions for realistic (but not too complex) application problems.

Zielpublikum:
Master Mathematik

• Brokate and J. Sprekels: Hysteresis and Phase Transitions. Springer (1996)
• K. Deckelnick, G. Dziuk, and Ch.M. Elliott: Computation of geometric partial differential equations and mean curvature flow. Acta Numerica, p. 1-94 (2005)
• G. Dziuk and Ch.M. Elliott: Finite elements on evolving surfaces. IMA J. Numer. Anal. 27, p. 262-292 (2007)
• J.A. Sethian: Level Set Methods and Fast Marching Methods, CambridgeUniversity Press (1999)
• T.J. Willmore: Riemannian Geometry, Clarendon, Oxford (1993)
• Winkelmann, Stefanie, and Christof Schütte. Stochastic dynamics in computational biology. Vol. 645. Berlin/Heidelberg, Germany: Springer, 2020.

Die Vorlesung wird ausgewählte Konzepte aus der Differentialgeometrie und ihre Rolle bei der Lösung von aktuellen Anwendungsproblemen vorstellen.

Zur den Themen gehören u.a. Krümmungsmaße, geometrische Flüsse, Minimalflächen, harmonische Abbildungen, Paralleltransport, verzweigte Überlagerungen, sowie deren Diskretisierung und algorithmische Umsetzung.

Praxisnahe Probleme kommen z.B. aus den Bereichen geometrisches Design, Geometrieverarbeitung, Visualisierung, Materialwissenschaft, Medizin, Architektur.

Vorkenntnisse: Differentialgeometrie I

The first tute will take place in semester week 2.

Inhalt:

Abstract:

Modeling, Simulation, and Optimization (MSO) is one of the cornerstones of application-oriented mathematics.

It covers a broad spectrum of research activities, ranging from the design of mathematical models for real-world processes, via efficient numerical simulation algorithms, to the solution of optimization problems for finding optimal scenarios or controls for the process under consideration. This lecture will give an overview over the techniques used in MSO and its application in different areas (life science, mobility, energy, sustainability, …). The lecture will be complemented by several pilot projects in which student groups will develop MSO solutions for realistic (but not too complex) application problems.

Zielpublikum:
Master Mathematik

• Brokate and J. Sprekels: Hysteresis and Phase Transitions. Springer (1996)
• K. Deckelnick, G. Dziuk, and Ch.M. Elliott: Computation of geometric partial differential equations and mean curvature flow. Acta Numerica, p. 1-94 (2005)
• G. Dziuk and Ch.M. Elliott: Finite elements on evolving surfaces. IMA J. Numer. Anal. 27, p. 262-292 (2007)
• J.A. Sethian: Level Set Methods and Fast Marching Methods, CambridgeUniversity Press (1999)
• T.J. Willmore: Riemannian Geometry, Clarendon, Oxford (1993)
• Winkelmann, Stefanie, and Christof Schütte. Stochastic dynamics in computational biology. Vol. 645. Berlin/Heidelberg, Germany: Springer, 2020.

Die Vorlesung wird ausgewählte Konzepte aus der Differentialgeometrie und ihre Rolle bei der Lösung von aktuellen Anwendungsproblemen vorstellen.

Zur den Themen gehören u.a. Krümmungsmaße, geometrische Flüsse, Minimalflächen, harmonische Abbildungen, Paralleltransport, verzweigte Überlagerungen, sowie deren Diskretisierung und algorithmische Umsetzung.

Praxisnahe Probleme kommen z.B. aus den Bereichen geometrisches Design, Geometrieverarbeitung, Visualisierung, Materialwissenschaft, Medizin, Architektur.

Vorkenntnisse: Differentialgeometrie I

The first tute will take place in semester week 2.

Inhalt:

Abstract:

Modeling, Simulation, and Optimization (MSO) is one of the cornerstones of application-oriented mathematics.

It covers a broad spectrum of research activities, ranging from the design of mathematical models for real-world processes, via efficient numerical simulation algorithms, to the solution of optimization problems for finding optimal scenarios or controls for the process under consideration. This lecture will give an overview over the techniques used in MSO and its application in different areas (life science, mobility, energy, sustainability, …). The lecture will be complemented by several pilot projects in which student groups will develop MSO solutions for realistic (but not too complex) application problems.

Zielpublikum:
Master Mathematik

• Brokate and J. Sprekels: Hysteresis and Phase Transitions. Springer (1996)
• K. Deckelnick, G. Dziuk, and Ch.M. Elliott: Computation of geometric partial differential equations and mean curvature flow. Acta Numerica, p. 1-94 (2005)
• G. Dziuk and Ch.M. Elliott: Finite elements on evolving surfaces. IMA J. Numer. Anal. 27, p. 262-292 (2007)
• J.A. Sethian: Level Set Methods and Fast Marching Methods, CambridgeUniversity Press (1999)
• T.J. Willmore: Riemannian Geometry, Clarendon, Oxford (1993)
• Winkelmann, Stefanie, and Christof Schütte. Stochastic dynamics in computational biology. Vol. 645. Berlin/Heidelberg, Germany: Springer, 2020.

Die Vorlesung wird ausgewählte Konzepte aus der Differentialgeometrie und ihre Rolle bei der Lösung von aktuellen Anwendungsproblemen vorstellen.

Zur den Themen gehören u.a. Krümmungsmaße, geometrische Flüsse, Minimalflächen, harmonische Abbildungen, Paralleltransport, verzweigte Überlagerungen, sowie deren Diskretisierung und algorithmische Umsetzung.

Praxisnahe Probleme kommen z.B. aus den Bereichen geometrisches Design, Geometrieverarbeitung, Visualisierung, Materialwissenschaft, Medizin, Architektur.

Vorkenntnisse: Differentialgeometrie I

The first tute will take place in semester week 2.

Inhalt:

Abstract:

Modeling, Simulation, and Optimization (MSO) is one of the cornerstones of application-oriented mathematics.

It covers a broad spectrum of research activities, ranging from the design of mathematical models for real-world processes, via efficient numerical simulation algorithms, to the solution of optimization problems for finding optimal scenarios or controls for the process under consideration. This lecture will give an overview over the techniques used in MSO and its application in different areas (life science, mobility, energy, sustainability, …). The lecture will be complemented by several pilot projects in which student groups will develop MSO solutions for realistic (but not too complex) application problems.

Zielpublikum:
Master Mathematik

• Brokate and J. Sprekels: Hysteresis and Phase Transitions. Springer (1996)
• K. Deckelnick, G. Dziuk, and Ch.M. Elliott: Computation of geometric partial differential equations and mean curvature flow. Acta Numerica, p. 1-94 (2005)
• G. Dziuk and Ch.M. Elliott: Finite elements on evolving surfaces. IMA J. Numer. Anal. 27, p. 262-292 (2007)
• J.A. Sethian: Level Set Methods and Fast Marching Methods, CambridgeUniversity Press (1999)
• T.J. Willmore: Riemannian Geometry, Clarendon, Oxford (1993)
• Winkelmann, Stefanie, and Christof Schütte. Stochastic dynamics in computational biology. Vol. 645. Berlin/Heidelberg, Germany: Springer, 2020.

In dem Seminar soll ein Einblick in die vielfältigen Themenfelder der Gender- und teilweise Diversityforschung in bzw. über Informatik erarbeitet werden. Dabei werfen wir exemplarisch einen analytischen Blick auf Ungleichheits- Diskriminierungs- und Exklusionsmechanismen in der Geschichte und Fachkultur der Informatik, in der Entwicklung technischer Artefakte und IT-Systeme sowie deren Nutzung.

Darüber hinaus setzten wir uns diskursiv mit verschiedenen Veränderungsansätzen zu den genannten Aspekten auseinander.

In dem Seminar soll ein Einblick in die vielfältigen Themenfelder der Gender- und teilweise Diversityforschung in bzw. über Informatik erarbeitet werden. Dabei werfen wir exemplarisch einen analytischen Blick auf Ungleichheits- Diskriminierungs- und Exklusionsmechanismen in der Geschichte und Fachkultur der Informatik, in der Entwicklung technischer Artefakte und IT-Systeme sowie deren Nutzung.

Darüber hinaus setzten wir uns diskursiv mit verschiedenen Veränderungsansätzen zu den genannten Aspekten auseinander.