Termine

Abstract: It is now well-known that two birationally equivalent hyperkähler manifolds must belong to the same deformation family, as complex manifolds. This property is known to fail for other classes of varieties with trivial first Chern class, such as Calabi?Yau threefolds. In this talk, I will report on joint work in progress with Isabel Stenger and Long Wang, where we investigate a rather dramatic failure of that property. I?ll introduce a specific Calabi?Yau threefold introduced by Schoen and studied by Namikawa and Grassi?Morrison in the early 90s. I will then recount how this threefold has many non-isomorphic birational models with interesting geometric features. At last, my goal is to explain how these birational geometric features can be used to distinguish between many deformation types.

Abstract: Embedding group rings into division rings provides methods for tackling problems which superficially seem unrelated. One way of constructing such embeddings (in characteristic 0) is by proving that they satisfy the Atiyah Conjecture. I will give a survey of the status of the Atiyah Conjecture, as well as applications to other problems, and discuss joint work with Sam Fisher on proving the conjecture for congruence subgroups of mapping class groups and outer automorphism groups of RAAGs.

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.