A new method to enclose the pseudospectrum via the numerical range
of the inverse of a matrix or linear operator is presented. The method is
applied to finite-dimensional discretizations of an operator on an infinite-
dimensional Hilbert space, and convergence results for different approxi-
mation schemes are obtained, including finite element methods. We show
that the pseudospectrum of the full operator is contained in an inter-
section of sets which are expressed in terms of the numerical ranges of
shifted inverses of the approximating matrices. The results are illustrated
by means of two examples: the advection-diffusion operator and the Hain-
Lüst operator.

arXiv: http://arxiv.org/abs/2004.12790

Doctoral students in applied mathematics started a SIAM Student Chapter at the University of Wuppertal. The aim of the SIAM Student Chapter Wuppertal is to unite both graduate and undergraduate students with an interest in computational and applied mathematics. The chapter organizes local meetings on subjects of interest, including seminars by students and faculty of the University of Wuppertal, as well as invited speakers from other institutions, excursions to industry sites, and workshops on different topics in applied mathematics and beyond. The Society for Industrial and Applied Mathematics (SIAM) provides funds to support activities of the student chapter.

Website of the SIAM Student Chapter Wuppertal: https://siamchapter.uni-wuppertal.de

The IMACM-Juniors seminar trip took place from 11th to 13th February in Schmallenberg. The aim of the seminar was to bring the PhD students of the different working groups together. 15 Participants (14 PhD students, 1 Post Doc) of four different working groups of IMACM presented their research in the beautifully located seminar house. Furthermore, there was time to discuss research topics and general questions regarding the dissertation. In the evenings there was time for socializing while cooking together and playing board games.

On the 12th of July 2019, around twenty participants of the IMACM-Juniors attended this seminar. Jonas Thies from the Deutsches Zentrum für Luft- und Raumfahrt (DLR) and Urs Zimmermann from APTIV showed different perspectives from a scientific and an industrial view on software development and gave some insight into "best practices". Afterwards there was a further discussion with the speakers about the topic over a cup of coffee and cookies.

On the 11th of April 2019 the second IMACM-Juniors Kick-off meeting took place. A three minutes short presentation of each participant opened the meeting to give the chance to new and old members to get to know each other and their research interests. Afterwards, three Juniors gave a presentation on their work in more detail:

• Johanna Schultes:
  Bikriterielle Formoptimierung mittels Gewichteter Summen Methode: Ausfallwahrscheinlichkeit vs. Kosten
• Arthur Strebel:
  Introduction to multigrid methods
• Sergiy Bogdanov:
  Parallele Zeitintegration

Neben Kick-Off-Meeting und Seminarfahrt im Frühjahr, kommen die IMACM-Juniors dreimal im Jahr zu einem Meeting am sogenannten Pizza-Friday zusammen. Diese Treffen werden reihum von Mitgliedern der verschiedenen beteiligten Arbeitsgruppen im IMACM organisiert (Applied Mathematics/Numerical Analysis, Funktionalanalysis, Wissenschaftliches Rechnen und Hochleistungsrechnen, Optimierung und Approximation, Angewandte Informatik, Stochastik). Das Meeting wird genutzt, um sich auszutauschen, Ideen für zukünftige Aktionen und Workshops zu sammeln und Freiwillige für deren Organisation zu finden .

Nach Beendigung des offiziellen Teils wird der Rest des Abends am Pizza-Friday zum „sozializing“ genutzt. In geselliger Runde wird gemeinsam Pizza bestellt und Brett- und Gesellschaftsspiele gespielt.

Am 4.7.18 führte Prof. Dr. Jörg Frochte von der Hochschule Bochum in seinem Vortrag interessierte Promovierende und Studierende in das Maschinelle Lernen ein. Ergänzt wurde dies durch einen Einblick in sein Forschungsgebiet Q-Learning aus dem Bereich des Reinforcement Learnings. Im Anschluss an den Vortrag wurde beim gemeinsamen Kaffeetrinken diskutiert, insbesondere über die Rolle des maschinellen Lernens im alltäglichen Leben sowie Karrierechancen für Absolventinnen und Absolventen der Fächer Mathematik und Informatik.