NEU: Frankfurter Seminar - Kolloquium des Instituts für Mathematik

Die Idee: 4 Schwerpunkte = 1 Kolloquium

Zum Wintersemester 2017/18 startet das "Frankfurter Seminar" in seine erste Runde. Das Institut für Mathematik freut sich, Ihnen dieses neue Format anbieten zu können, an dem sich alle vier Schwerpunkte des Instituts beteiligen.

Der nächste Vortrag findet am 24. Januar 2018 um 16:45 Uhr statt.

Im Hilbertraum, Robert-Mayer-Straße 8, 3. OG.

Kaffee und Tee gibt es ab 16:15 Uhr.



Vorkolloquium für Doktoranden, Post-Docs und interessierte Studierende

Vor jedem Vortrag findet für Doktoranden, Post-Docs und interessierte Studierende ein Vorkolloquium statt, um die Vorträge "aus der anderen Ecke des Instituts" für alle Interessierten zugänglicher zu machen.

Das Vorkolloquium findet immer von 15.00 (c.t.) - 16.00 Uhr im Hilbertraum vor dem jeweiligen Vortrag statt.

                                          Im nächsten Ginkgo-Seminar spricht Herr Tim Jahn zum Thema "Die Methode der finiten Elemente".

Veranstaltungen WiSe 2017/ 2018








15. November 2017

Hendrik Lenstra (Universität Leiden)

"Solving equations in orders"

An "order" is a commutative ring of which the additive group is, for some non-negative integer n, the group of vectors with n integral coordinates. The lecture is devoted to the algorithmic problem of solving polynomial equations in one variable in orders.









13. Dezember 2017

Camillo De Lellis (Universität Zürich)

"The Onsager's Theorem and beyond"

In 1949 the famous physicist Lars Onsager made a quite striking statement about solutions of the incompressible Euler equations: if they are Hölder continuous for an exponent larger than ⅓, then they preserve the kinetic energy, whereas for exponents smaller than ⅓ there are solutions which do not preserve the energy. The first part of the statement has been rigorously proved by Peter Constantin, Weinan E and Endriss S. Titi in the nineties. In a series of works László Székelyhidi and myself have introduced ideas from differential geometry and differential inclusions to construct nonconservative solutions and started a program to attack the other portion of the conjecture. After a series of partial results, due to a few authors, Phil Isett fully resolved the problem one year ago. However this has not stopped the growing of the subject, which affects several other equations of fluid dynamics and, perhaps most surprising, the incompressible Navier-Stokes.









24. Januar 2018

Barbara Wohlmuth (Technische Universität München)

"A priori and a posteriori modifications in finite element flow simulations"

We discuss two types of local and computationally inexpensive modifications resulting in finite element approximations of higher accuracy. In case one, a local recovery of the discrete flux is performed such that mass conservation on a dual mesh can be guaranteed. The corrected flux enters then into the advective part of the energy equation. In case two, the flowability in the discrete scheme is locally enhanced such that energy can be preserved. A variational crime analysis then guarantees improved convergence rates. All theoretical results are illustrated by a series of simulations including large scale runs where a all-in-once multigrid solver is used for the flow part.









31. Januar 2018

Günter Ziegler (Freie Universität Berlin)

"Semi-algebraic sets of integer points"

We look at sets of integer points in the plane, and discuss possible definitions of when such a set is “complicated” — this might be the case if it is not the set of integer solutions to some system of polynomial equations and inequalities. Let’s together work out lots of examples, and on the way let’s try to develop criteria and proof techniques …

The examples that motivated our study come from polytope theory: Many question of the type “What is the possible pairs of (number of vertices, number of facets) for 4-dimensional polytopes?” have been asked, many of them with simple and complete answers, but in other cases the answer looks complicated. Our main result says: In some cases it IS complicated! (Joint work with Hannah Sjöberg.)