Aktuelles

Donnerstag, 23.11.2023: Infinitesimale Variationen der Hodge Struktur anhand von Flächen in torischen 3-folds

Julius Giesler (Universität Tübingen)

Wir behandeln Griffiths Konstruktion der infinitesimalen Variation von Hodge Strukturen explizit für den Fall von Flächen in torischen 3-folds. Dabei verlassen wir die ”Kategorie der Laurentpolynomen“ nicht. Wir testen das infinitesimale Torelli Theorem für K3 ähnlichen Flächen vom allgemeinem Typ und zeigen, dass das Theorem für diese Flächen falsch sein kann. Weitere Gegenbeispiele erhalten wir aus elliptischen Flächen in torischen 3-folds. Unter Einbeziehung der minimalen Picardzahl erhalten wir für all diese Flächen eine Formel, die mehrere Invarianten durcheinander ausdrückt.

Uhrzeit:	14:00
Ort:	Seminarraum S07 (C5H10)
Gruppe:	Oberseminar Algebraische Geometrie
Einladender:	V. Batyrev, J. Hausen, Th. Markwig

Donnerstag, 23.11.2023: Black hole horizons in a binary black hole merger

Dr. Daniel Pook-Kolb (Max Planck Institute for Gravitational Physics)

Apparent horizons are routinely used in numerical relativity to describe black holes in simulations of dynamical systems. Advances in numerical methods allowed us to follow these objects into the interior of merging black holes, revealing how the two original horizons connect with the remnant horizon. In this talk, I will present results on head-on mergers, showing that the evolution of apparent horizons is much more intricate than previously thought: In the interior of the newly formed common horizon, the original horizons are individually annihilated by unstable horizon-like structures. An important role for understanding this behaviour is played by the MOTS stability operator. This completes our picture of how two black holes become one and provides the analogue of the famous pair-of-pants diagram of the event horizon now for the apparent horizon.

Uhrzeit:	14:00
Ort:	Hörsaal 2.22 (Haus 9, Potsdam), per Zoomübertragung in N15 (C-Bau Tübingen) and virtual via zoom, for zoom link please contact Martina Neu
Gruppe:	Oberseminar Geometrische Analysis, Differentialgeometrie und Relativitätstheorie
Einladender:	Carla Cederbaum, Gerhard Huisken, zusammen mit Jan Metzger (Potsdam)

Donnerstag, 23.11.2023: Mode optimized hybrid CPU-GPU density matrix renormalization group method

Prof. Örs Legeza (Wigner Research Centre for Physics, Budapest)

We present a hybrid numerical approach to simulate quantum many body problems on two spatial dimensional quantum lattice models, for quantum chemical system and for nuclear structure theory via the non-Abelian ab initio version of the density matrix renormalization group method on state-of-the-art high performance computing infrastructures. We demonstrate for selected strongly correlated systems that altogether several orders of magnitude in computational time can be saved by performing calculations on an optimized basis and by utilizing hybrid CPU-multiGPU parallelization. At least an order of magnitude reduction in computational complexity results from mode optimization, while a further order of reduction in wall time is achieved by massive parallelization. Our results are measured directly in FLOP and seconds. A detailed scaling analysis of the obtained computational complexity and performance as a function of matrix ranks and as a function of system size is discussed. Finally, connection to the restricted active space density matrix renormalization group is also introduced together with a rigorous scaling law.

Uhrzeit:	14:15
Ort:	S6 (C5H05)
Gruppe:	Oberseminar Numerik
Einladender:	Lubich, Prohl

Donnerstag, 23.11.2023: Propagation bounds for lattice bosons

Carla Rubiliani (Tübingen)

Lieb-Robinson bounds characterise the speed of information propagation for spin systems. In recent years, much effort has been dedicated to extending them to more general settings. To generalise them to bosonic systems, the first step is to obtain bounds on the propagation of bosons through the lattice. In this talk, we will present a propagation bound that works for long-range interacting bosons but is not stable in the thermodynamic limit, and we will see how we have adapted the proof to obtain two new results that are now thermodynamically stable. While the first bound only holds for finite-range interactions, the second also works for long-range ones. The main tool for the proofs are the so-called ASTLO (adiabatic space-time localisation observables). They allow us to smoothly track particles in the regions of interest and proved to be a very useful tool since we are able to control their time evolution.

Uhrzeit:	14:30
Ort:	C3N14
Gruppe:	Oberseminar Mathematical Physics
Einladender:	Capel, Keppeler, Lemm, Pickl, Teufel, Tumulka

Freitag, 24.11.2023: Amenable group actions on spaces and operator algebras

Prof. Dr. Siegfried Echterhoff (Universität Münster)

16:00-16:45 Uhr Vor-Kolloquium im N14 für Studierende und Promovierende, moderiert von Dr. Rodrigo Avalos, Vortragender Prof. Dr. Siegfried Echterhoff The Banach-Tarski paradox and amenable groups The Banach-Tarski paradox states that the unit ball in three dimensional space can be partitioned into finitely many pieces in such way that we can resemble two full balls from these pieces. Hence we may double the unit ball. That this is possible is due to axiom of choice and the fact that the free group in two generators is not amenable. On the other hand, amenability of the circle group implies that similar partitions do not exist for the unit disc in the plane! We shall explain these facts. Kolloquium 17:15 Uhr Amenable group actions on spaces and operator algebras Motivated by the study of paradoxical decompositions (as in the Banach-Tarski paradoxon), the notion of an amenable group has been introduced by von Neumann in the 1920’s. In the 1980’s Zimmer introduced the concept of amenable group actions on measure spaces in order to study rigidity properties of lattices in Lie groups. In the meantime, various notions of amenability were introduced for actions on topological spaces and on operator algebras, where the latter can be viewed as non-commutative analogues of measure or topological spaces. They have important applications in the interplay between group theory and operator algebras. After a gentle introduction to various notions of amenable actions we want to give an overview over some exciting recent results.

Uhrzeit:	16:00
Ort:	N14
Gruppe:	Kolloquium
Einladender:	Carla Cederbaum