On April 27-28, 2017 the workshop “Women in PDEs @ Karlsruhe” will take place. The aim of this workshop is to provide a platform to bring together students of mathematics (in Bachelor or Master programs), young researchers (PhD students and postdocs) and established female mathematicians from academia and industry working on partial differential equations (PDEs). Outstanding invited speakers will give talks on their current research topics. A panel discussion will give the possibility to discuss questions not only concerning research but also career choices/planning and practical questions of managing career and family.
In the following I would like to present the main ideas of bifurcation theory along with some basic examples that illustrate the theory. For the sake of shortness let me formulate the fundamental question of bifurcation theory in an abstract way. Suppose you are given an equation \(F(x,\lambda)=0\) with the property that \(x=0\) is always a solution, the so-called trivial solution. Is it possible to find some \(\lambda^*\) such that a sequence of nontrivial solutions converges to \((0,\lambda^*)\)? In other words: Do nontrivial solutions bifurcate from the trivial solutions? In the following I will present three equations from analysis, linear algebra and ordinary differential equations showing that bifurcation theory is a topic worth studying! The reading requires some amount of advanced mathematics — do not hesitate to contact me if you need some additional explanations. By the way: Next semester I will give a lecture on that topic which is suited for master students or advanced bachelor students with a background in analysis, differential equations and possibly boundary value problems, see below for more information. Continue Reading →
From October 12th till October 14th the CRC workshop on Time Integration of PDEs 2016 took place in the Kurhaus Trifels in Annweiler, close to the castle Trifels. The about 20 participants informed each other by giving talks on their latest results of their research. The main topics were Krylov methods, highly oscillatory problems, alternating direction implicit methods as well as locally explicit and implicit time integration. The breaks between the sessions were used for many fruitful discussions and exchanges of ideas and also for doing undisturbed research in pairs or small groups. The wheather was well-disposed to us, which we used for a beautiful hiking tour on Thursday afternoon. The productive workshop ended with a project discussion on Friday afternoon.
What happens if you take some of the most brilliant minds in mathematics and computer sciences (Fields, Abel, Turing, Nevanlinna Prize Laureates) and bring them together with 200 young scientists?
This is exactly what’s at the heart of the Heidelberg Laureate Forum (modelled after the similar annual Lindau Nobel meetings).
The result is a wonderful interaction between the young researchers and the laureates, creating some new scientific contacts and sparking ideas that might very well end up as the foundations of new research projects.
Last week I had the pleasure to participate in the “Nonlinear PDEs and Mathematical Physics workshop” at the Tsinghua Sanya International Mathematics Forum which took place in Sanya, the main city of China’s province Hainan.
It is an island at the most southern point of China and quite close to Macao, Hongkong or Vietnam. Hainan is a tourist region and all participants of the workshop could benefit (but sometimes also suffer) from the warm temperatures around 28 degree (Celsius). In summer it is even warmer so that we were very glad to have this conference at the beginning of December.
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