Termine

Barnet-Lab, Gee, Geraghty and Taylor have shown that essentially self dual Galois representations of a totally real field on Q_p-vector spaces that are unramified almost everywhere and de Rham at p are automorphic if they are ?potentially diagonalizable?. In this talk I will explain the objects in this theorem and explain how to reprove this theorem using p-adic automorphic forms of finite slope. Unlike the previous work mentioned above, this new method generalizes to the case of CM fields.

Real rank was introduced by Brown and Pedersen in 1991 as a variant of stable rank, generalizing a characterization of covering dimension in terms of the instability of tuples of continuous functions. Nuclear dimension, introduced by Winter and Zacharias in 2010, generalizes a different characterization of covering dimension, based on the colorability of refinements of open covers. The two notions agree for commutative C*-algebras, where they coincide with the covering dimension of the spectrum, but differ already for homogeneous C*-algebras. In this talk, I will recall both notions of dimension, discuss examples illustrating their differences, and sketch the proof of the main result: the real rank of a C*-algebra is bounded above by its nuclear dimension.

A day for MM postdocs to prepare for the next step, exchange and connect with other postdocs on career-and maths-related matters.

(1) Research Statements and Proposals (with Eugen Hellmann and Angela Stevens) - A session on preparing a research statement for applications or proposals for grant applications or permanent positions: What is important, tips+tricks, which level of specificity is needed, ...
Eugen Hellmann and Angela Stevens will also both share their advice and experience on shaping the academic profile and thus bridge to the second part of the day.

(2) Scientific Profile (with Shirly Geffen and Hendrik Weber) - A session on what is important in the postdoc profiling phase.

More information and registration in September....

In order to properly define, determine and examine the topological structure of a dynamical system at the heart of the brain, there is a need to find the correct model and reconcile it with statistical data revealing latent effective relations between hidden states. Often the statistical data for that task is highly limited, and the reconciliation procedure sways with anomalies, when the chosen model allows such discrepancies. Recent works propose dynamical causal modeling in order to enforce causal and observational limitation for the inference process. Our work proposes two new addition to the literature; the more general framework of Dynamic Multiscale Networks (DMNs) coupled with the needed integration of structural information of a given brains anatomy, and the numerical analysis of the effectiveness of such a model. The unique properties of these models might naturally favor small worldness and thus they might be primary candidates for any "economic" networks such as the mammal brain. In particular, the general posing of DMNs allows for reconciliation of sparse functional relations and dense structural information.

Further information

How many connected graphs have a prescribed degree sequence? This classical combinatorial question turns out to admit a surprisingly natural probabilistic interpretation. In joint work with Sasha Bell and Remco van der Hofstad, we derive asymptotic formulas for the number of connected graphs with a given degree sequence in the sparse regime. Our approach is based on the probabilistic method: rather than counting graphs directly, we study a random graph model in which the desired structures appear with a certain probability. A major challenge is that connectivity is exponentially unlikely in a random graph when many vertices have degree 1. We overcome this by using a probabilistic "change of perspective" that turns the rare event into a typical one. Pre-talk: Local convergence of random graphs The Benjamini-Schramm topology is a useful tool for understanding local functionals of large random graphs, such as degrees, triangle counts and clustering coefficients, but also more surprising properties such as the cover number, the size of the largest component and the spectral distribution. In the pre-talk I will give a gentle, high-level introduction to this notion of convergence, which will be useful (but not essential) for following the main talk.