# Courses

- Nonlinear Analysis (Navier-Stokes equations), [M,CM,MP,WM], 3 St., Di 12-14, Fr 12-13 SE 40, A. Schlömerkemper
- Exercises in Nonlinear Analysis (Navier-Stokes equations), [M,CM,MP,WM], 1 St., Fr 13-14 SE 40, A. Schlömerkemper

**Bachelor:**

- Exercises in Analysis 2, in groups, 2 hours, Mon 14-16 S0.106, Tue 12-14 S0.106, 14-16, G. Dirr, J. Kortum

**Teacher training courses:**

- Analysis in one Variable (Fundamentals of Analysis 1), 4 hrs, Wed 14-16 Zuse-HS, Thu 10-12, HS 2 (Phil) , F. de Anna
- Exercises in Analysis in one Variable (Fundamentals of Analysis 1), in groups, 2 hours, Mon 12-14 SE 10, 14-16 S0.107, 16-18 S0.102, F. de Anna, J. Kortum

- Advanced Mathematics (Realschule), 3 hours, Wed 16-18, Thu 8-10 HS 4 (until Christmas), J. Ratzkin
- Exercises in Advanced Mathematics (Realschule), n groups, 2 hours, Mon 16-18 S0.106, Tue 10-12 S0.101, J. Ratzkin, M. Dippel

- Mathematics for Computer Scientists 2: 5 hrs, Mon 9-12, Wed 8-10, Zuse-HS, J. Ratzkin
- Exercises on Mathematics for Computer Scientists 2, in groups, 2 hrs, Mon 12-12, 14-16, 16-18; Tues 8-10, 12-14, 16-18, SE I, Tues 14-16 SE 8, J. Ratzkin.

Geometric Analysis, Dr. Jesse Ratzkin

Mathematics for Computer Scientists, Dr. Jesse Ratzkin

Oberseminar Mathematics in the Sciences, after announcement

- Master Seminar Mathematics in the Sciences "Sustainability", Prof. Anja Schlömerkemper
- Mathematics for Computer Scientists, Dr. Jesse Ratzkin
- Oberseminar Mathematics in the Natural Sciences, after announcement

- Mathematical Foundations for MINT Studies (Orientation Studies), Prof. Anja Schlömerkemper
- Seminar Homogenization Theory and Multiscale Methods / Seminar Mathematics in the Natural Sciences, Prof. Anja Schlömerkemper
- Oberseminar Mathematics in the Natural Sciences, after announcement

- Analysis in One Variable (Fundamentals of Analysis 1), Prof. Dr. Anja Schlömekemper
- Mathematical Continuum Mechanics, [M,CM,MP], Prof. Dr. Anja Schlömerkemper
- Mathematical Foundations for MINT Studies (Orientation Studies), Prof. Anja Schlömerkemper
- Oberseminar Mathematics in the Natural Sciences, after announcement

- Linear partial differential equations and nonlinear partial differential equations of the first order, lecturer: Prof. Dr. Anja Schlömerkemper, Assistant: Francesco De Anna (Orientation Part I of the textbook by L.C. Evans, Partial Differential Equations)
- Seminar: Fixed point sets and their applications, Lecturer: Prof. Dr. Anja Schlömerkemper (Orientation Chapter 1 Eberhard Zeidler, Applied Functional Analysis, Vol. 108)
- Oberseminar mathematics in the natural sciences: (details and speakers here)

- Introduction to functional analysis, lecturer: Prof. Dr. Anja Schlömerkemper
- Exercises to introduce functional analysis, Lecturer: Prof. Dr. Anja Schlömerkemper, assistant: Joshua Kortum
- Oberseminar mathematics in the natural sciences: (details and speakers here)

- Advanced analysis, lecturer: Prof. Dr. Anja Schlömerkemper, assistants: Joshua Kortum and PhD Jesse Ratzkin
- Research in Groups: Calculus of Variations, Dozentin: Prof. Dr. Anja Schlömerkemper

- Analysis II, lecturer: Prof. Dr. Anja Schlömerkemper, assistants: Joshua Kortum, Laura Lauerbach and PhD Jesse Ratzkin
- The exercise sheets, brief tips on how to solve the tasks and other general information about the lecture can be found at WueCampus (course: WS18_Analysis2). The lecture is mainly based on Tretter, Christiane: Analysis II, Birkhäuser 2013
- Research Seminar Mathematics in Science (details and speakers here)
- Please notice the lecture series and seminar by Prof. Š. Nečasová on Compressible Navier-Stokes equations and fluid-structure interactions.

*Partial Differential Equations of Mathematical Physics*

The topic of this lecture series is the mathematical analysis of the Navier-Stokes equations. These equations model the motion of viscous fluids. They are used in the modeling of weather, air flow around a wing, ocean currents, flow of viscoelastic materials and many more. Despite their wide range of application, there are still major open mathematical problems. It has not been proven yet that in three dimensions solutions always exist. Further, in case solutions exist, it is not known whether they do not contain any singularities. These are the Navier-Stokes existence and smoothness problems, which were mentioned by the Clay Mathematical Institute as part of the Millennium problems. In this course we will discuss important results in the mathematical theory of the three-dimensional Navier-Stokes equations. The lecture series will be based on the recent monograph by Robinson, Rodrigo and Sadowski: The Three-Dimensional Navier-Stokes Equations, Cambridge University Press, 2016, in particular Chapters 1-8. The book is available as an e-book at the library of the University of Würzburg.

Prerequisites: Basics of functional analysis and partial differential equations. I plan to only recall what is written in Sections 1.1-1.8. If you do not know Lebesgue and Sobolev spaces, it will be useful to study these before the term starts.

*Master/Research seminar Mathematics in the Sciences*

Together with Prof. B. Zwicknagl, Topic: Calculus of variations and applications, for further information click here.

*Oberseminar Mathematik in den Naturwissenschaften*(details and speakers here)

## Summer semester 2017

*Partial Differential Equations of Mathematical Physics*The topic of this lecture series is the mathematical analysis of the Navier-Stokes equations. These equations model the motion of viscous fluids. They are used in the modeling of weather, air flow around a wing, ocean currents, flow of viscoelastic materials and many more. Despite their wide range of application, there are still major open mathematical problems. It has not been proven yet that in three dimensions solutions always exist. Further, in case solutions exist, it is not known whether they do not contain any singularities. These are the Navier-Stokes existence and smoothness problems, which were mentioned by the Clay Mathematical Institute as part of the Millenium problems.

In this course we will discuss important results in the mathematical theory of the three-dimensional Navier-Stokes equations. The lecture series will be based on the recent monograph by Robinson, Rodrigo and Sadowski: The Three-Dimensional Navier-Stokes Equations, Cambridge University Press, 2016, in particular Chapters 1-8. The book is available as an e-book at the library of the University of Würzburg.

Prerequisites: Basics of functional analysis and partial differential equations. I plan to only recall what is written in Sections 1.1-1.8. If you do not know Lebesgue and Sobolev spaces, it will be useful to study these before the term starts.

The lecture series will take place in room SE 40, Emil-Fischer-Str. 40, Tuesday 14-16 and Thursday 10-12. The excercise classes will take place Wednesdays 8-10, also in SE 40.

*Master/Research seminar Mathematics in the Sciences*Joint with Prof. B. Zwicknagl, Topic: Calculus of variations and applications, for further information click here.

*Oberseminar Mathematik in den Naturwissenschaften*(details and speakers here)

[Wintersemester 2016/17

*Research in Groups (Arbeitsgemeinschaft) on "Calculus of Variations: the vectorial case".*Topics include lower semicontinuity of integral functionals, relaxed variational problems, notions of polyconvexity, quasiconvexity and rank-one convexity, Gamma-convergence methods etc. The focus of this Research in Groups will be on analytical methods and concepts. Nevertheless, all these mathematical topics have interesting real-world applications in nonlinear elasticity, micromagnetic materials or so-called smart materials, which I will be happy to tell more about or which can be a topic of master theses. Of course, also the analytical topics discussed can form the basis of master (or bachelor) theses.

Prerequisites: Basics of measure theory and functional analysis, in particular weak convergence and Sobolev spaces.

A preliminary discussion has already taken place, in which we fixed the schedule and organizational details of this Research in Groups. There will be a lecture series in SE 30 on Thursdays 10-12. There will be a blockseminar for the student's talk.

Please contact me if you are interested in joining this Research in Groups but happen not to have attended the preliminary discussion. If you prefer to attend a

*Seminar*(Bachelor or Master) on this topic instead of the Research in Groups, please let me know so that we can discuss how this can be done.*Oberseminar Mathematik in den Naturwissenschaften*(details and speakers here)

#### Sommersemester 2016

- Nonlinear Analysis (Nichtlineare Analysis). An introduction to the calculus of variations.
- Bachelorseminar Partielle Differentialgleichungen
*Oberseminar Mathematik in den Naturwissenschaften*(details and speakers here)

#### Wintersemester 2015/16

- Einführung in die Funktionalanalysis
- Bachelorseminar Grundlagen der Navier-Stokes-Gleichungen bzw. der Analysis elastischer Festkörper und deren Mikrostrukturen
- Research in Groups/Seminar Mathematics in the Sciences
- Masterseminar Minimal Surfaces and Harmonic Maps (jointly with Prof. Roth and Prof. Waldmann),

first meeting in S1.101 on Monday, 12 October, 2:15 pm *Oberseminar Mathematik in den Naturwissenschaften*(details and speakers here)

#### Sommersemester 2015

- Seminar Mathematische Modellierung
- Seminar Nichtlineare partielle Differentialgleichungen (Mathematik in den Naturwissenschaften)
*Oberseminar Mathematik in den Naturwissenschaften*(details and speakers here)

#### Wintersemester 2014/2015 [Sabbatical / Forschungssemester]

#### Sommersemester 2014

*Vorlesung Analysis 2*, 4 St., Mi, Do 10-12 in Turing-HS*Seminar Mathematik in den Naturwissenschaften*, Vorbesprechung am Dienstag, 8.4.14 um 14:15 Uhr in SE 40*Oberseminar Mathematik in den Naturwissenschaften*(details and speakers here)

#### Wintersemester 2013/2014

- Winter school on Calculus of Variations in Physics and Materials Science (10.-14.02.2014)
- Vorlesung Analysis I
- Arbeitsgemeinschaft Mathematik in den Naturwissenschaften
- Seminar Mathematik in den Naturwissenschaften (in die Arbeitsgemeinschaft integriert)
- Oberseminar Mathematik in den Naturwissenschaften (details and speakers here)

#### Sommersemester 2013

- Vorlesung Mathematische Kontinuumsmechanik mit Übung
- Oberseminar Mathematik in den Naturwissenschaften (details and speakers here)

#### Sommersemester 2012

- Mathematik für Studierende der Physik und Informatik 2
- Bachelor-Seminar Variationsrechnung
- Oberseminar Mathematik in den Naturwissenschaften (details and speakers here)

#### Wintersemester 2011/12

- Winter school on Calculus of Variations in Physics and Materials Science (08.-13.01.2012)
- Mathematik für Studierende der Physik und Informatik 1
- Arbeitsgemeinschaft Mathematik in den Naturwissenschaften
- Oberseminar Mathematik in den Naturwissenschaften (details and speakers here)

#### Sommersemester 2011

- Einführung in die Variationsrechnung
- Seminar Mathematische Modellierung
- Oberseminar Mathematik in den Naturwissenschaften (details and speakers here)

## Winter semester 2016/17

*Research in Groups (Arbeitsgemeinschaft) on "Calculus of Variations: the vectorial case".*Topics include lower semicontinuity of integral functionals, relaxed variational problems, notions of polyconvexity, quasiconvexity and rank-one convexity, Gamma-convergence methods etc. The focus of this Research in Groups will be on analytical methods and concepts. Nevertheless, all these mathematical topics have interesting real-world applications in nonlinear elasticity, micromagnetic materials or so-called smart materials, which I will be happy to tell more about or which can be a topic of master theses. Of course, also the analytical topics discussed can form the basis of master (or bachelor) theses.

Prerequisites: Basics of measure theory and functional analysis, in particular weak convergence and Sobolev spaces.

A preliminary discussion has already taken place, in which we fixed the schedule and organizational details of this Research in Groups. There will be a lecture series in SE 30 on Thursdays 10-12. There will be a blockseminar for the student's talk.

Please contact me if you are interested in joing this Research in Groups but happen not to have attended the preliminary discussion. If you prefer to attend a

*Seminar*(Bachelor or Master) on this topic instead of the Research in Groups, please let me know so that we can discuss how this can be done.*Oberseminar Mathematik in den Naturwissenschaften*(details and speakers here)

## Sommersemester 2016

- Nonlinear Analysis (Nichtlineare Analysis). An introduction to the calculus of variations.
- Bachelorseminar Partielle Differentialgleichungen
*Oberseminar Mathematik in den Naturwissenschaften*(details and speakers here)

## Winter term 2015/16

- Einführung in die Funktionalanalysis
- Bachelorseminar Grundlagen der Navier-Stokes-Gleichungen bzw. der Analysis elastischer Festkörper und deren Mikrostrukturen
- Research in Groups/Seminar Mathematics in the Sciences
- Masterseminar Minimal Surfaces and Harmonic Maps (jointly with Prof. Roth and Prof. Waldmann),

first meeting in S1.101 on Monday, 12 October, 2:15 pm *Oberseminar Mathematik in den Naturwissenschaften*(details and speakers here)

## Sommersemester 2015

- Seminar Mathematische Modellierung
- Seminar Nichtlineare partielle Differentialgleichungen (Mathematik in den Naturwissenschaften)
*Oberseminar Mathematik in den Naturwissenschaften*(details and speakers here)