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  • Student in a lecture hall
  • [Translate to Englisch:] Studierende im Hörsaal während einer Vorlesung
Mathematics in the Sciences

Courses

Current Courses

Dozentin: Prof. Dr. Anja Schlömerkemper  

 

Assistent: Francesco De Anna

We will discuss examples as well as existence and uniqueness proofs for linear partial differential equations and nonlinear partial differential equations of first order. This lecture series will follow part I of L.C. Evans, Partial Differential Equations.

More details will be provided in WueCampus.

 

Lecturer: Prof. Dr. Anja Schlömerkemper

Fixed point theorems have various applications in mathematics. For instance, Banach's fixed point theorem is an essential ingredient to the proof of the implicit function theorem as discussed in Analysis 2. In this seminar we will discuss this and further fixec point theorems and their applications. The reading course will be based on chapter 1 of Eberhard Zeidler, Applied Functional Analysis, Vol. 108.

Basic knowledge of functional analysis is required. If you happen not to have passed an exam on functional analysis, but like to participate anyhow, please contact  Prof. Dr. Anja Schlömerkemper in advance.

A preliminary discussion will take place on  Wednesday, 15 April 2020 at 9.30 am on Zoom. If you like to participate, please contact Prof. Schlömerkemper for further information.

 

 

Look at events.

 

Past Courses

  • 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.

 

 

 

 

 

 

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

 

Wintersemester 2015/16

 

Sommersemester 2015

 

Wintersemester 2014/2015 [Sabbatical / Forschungssemester]

 

Sommersemester 2014

 

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

Winter term 2015/16

Sommersemester 2015