# 18th Internet Seminar on Evolution Equations

The 18th Internet Seminar on Evolution Equations is devoted to the treatment of evolution equations with the aid of forms. The theory of symmetric and sectorial forms on Hilbert spaces is a powerful tool to treat a variety of parabolic equations. Part of these equations arise in the context of stochastic processes. The objective of the Internet Seminar is to present the abstract theory of forms and operators in Hilbert spaces, the connection to $ C_0 $-semigroups, and the relations to positivity and applications to parabolic differential equations. For these applications we will also provide the background on distributions and Sobolev spaces. We intend to cover recent developments concerning non-closable forms as well as non-autonomous equations.

We expect from the participants basic knowledge in functional analysis (bounded operators, uniform boundedness principle, closed graph theorem, Hahn-Banach theorem), foundations of Hilbert spaces, some familiarity with partial differential equations as well as foundations in complex analysis of one variable.

The annual Internet Seminars introduce master, Ph.D. and postdoc students to varying subjects related to evolution equations. The course consists of three phases.

- Phase 1 (October-February): A weekly lecture will be provided via the ISEM website. These lectures will be self-contained, and references for additional reading will be provided. The weekly lecture will be accompanied by exercises, and the participants are supposed to solve these problems.
- Phase 2 (March-May): The participants will form small international groups to work on diverse projects which supplement the theory of Phase 1 and provide some applications.
- Phase 3 (May 31 to June 6, 2015): Final one-week workshop at the Heinrich-Fabri Institut in Blaubeuren (Germany). There the teams will present their projects and additional lectures will be delivered by leading experts.

**ISEM team 2014/15 :**

- Virtual lecturers
- Wolfgang Arendt (Ulm)
- Jürgen Voigt (Dresden)
- Organizers
- Wolfgang Arendt (Ulm)
- Ralph Chill (Dresden)
- Christian Seifert (Hamburg)
- Hendrik Vogt (Bremen)
- Jürgen Voigt (Dresden)
- Website
- http://www.mat.tuhh.de/isem18

The poster and the announcement for the Internet Seminar can be downloaded here: Poster.pdf Announcement.pdf