Test
Friday, 7.4.17, 12:00-13:00, Hörsaal II, Albertstr. 23b
Bla bla
Test
Wednesday, 12.4.17, 12:00-13:00, Hörsaal II, Albertstr. 23b
Applications of ultraproducts of finite structures to Combinatorics
Wednesday, 19.4.17, 16:00-17:00, Raum 404, Eckerstr. 1
The fundamental theorem of ultraproducts (Łos' Theorem) provides a transference principle between the finite structures and their limits. Roughy speaking, it states that a formula is true in the ultraproduct M of an infinite class of structures if and only if it is true for "almost every" structure in the class.\n\nWhen applied to ultraproducts of finite structures, Łos' theorem presents an interesting duality between finite structures and their infinite ultraproducts. This kind of finite/infinite connection can sometimes be used to prove qualitative properties of large finite structures using the powerful known methods and results coming from infinite model theory, and in the other direction, quantitative properties in the finite structures often induce desirable model-theoretic properties in their ultraproducts.\n\nThese ideas were used by Hrushovski to apply ideas from geometric model theory to additive combinatorics, locally compact groups and linear approximate subgroups. More examples of this fruitful interaction were given by Goldbring and Towsner to provide proofs of the Szemerédi's regularity lemma and Szemerédi's theorem: every subset of the integers with positive density contains arbitrarily large arithmetic progressions. \n\nThe purpose of the talk will be to present these ideas and outline some of the applications to asymptotic combinatorics. If time permits, I will give a brief overview of the Erdos-Hajnal conjecture and present a proof (due to A. Chernikov and S. Starchenko) of the Erdos-Hajnal property for graphs without the order property using ultraproducts, pseudofinite dimensions and basic properties of stable formulas.\n\n
Thursday, 27.4.17, 17:00-18:00, Hörsaal II, Albertstr. 23b
Holography and the representation theory of residue families
Friday, 28.4.17, 10:15-11:15, Raum 404, Eckerstr. 1
We shall introduce the concept of holography principle in\nconformal differential geometry. A prominent role in the \nanalysis is played by the residue family operators, and their\nrepresentation theoretical interpretation will be explained.
Short-time near-the-money skew in rough fractional stochastic volatility models
Friday, 28.4.17, 11:00-12:00, Raum 232, Eckerstr. 1
We consider rough stochastic volatility models where the driving noise of volatility\nhas fractional scaling, in the rough regime of Hurst parameter H < 1/2. This regime\nrecently attracted a lot of attention both from the statistical and option pricing\npoint of view. With focus on the latter, we sharpen the large deviation results of\nForde-Zhang (2017) in a way that allows us to zoom-in around the money while\nmaintaining full analytical tractability. More precisely, this amounts to proving\nhigher order moderate deviation estimates, only recently introduced in the option\npricing context. This in turn allows us to push the applicability range of known at-\nthe-money skew approximation formulae from CLT type log-moneyness deviations\nof order t1/2 (recent works of Alo‘s, Le ?on Vives and Fukasawa) to the wider\nmoderate deviations regime.\nThis is work in collaboration with C. Bayer, P. Friz, A. Gulsashvili and B. Stemper
A General Framework for Uncovering Dependence Networks
Friday, 28.4.17, 12:00-13:00, Raum 404, Eckerstr. 1
Dependencies in multivariate observations are a unique gateway to uncovering relationships among processes. An approach that has proved particularly successful in modeling and visualizing such dependence structures is the use of graphical models. However, whereas graphical models have been formulated for finite count data and Gaussian-type data, many other data types prevalent in the sciences have not been accounted for. For example, it is believed that insights into microbial interactions in human habitats, such as the gut or the oral cavity, can be deduced\nfrom analyzing the dependencies in microbial abundance data, a data type that is not amenable to standard classes of graphical models. We present a novel framework that unifies existing classes of graphical models and provides other classes that extend the concept of graphical models to a broad variety of discrete and continuous data, both in low- and high-dimensional settings. Moreover, we present a corresponding set of statistical methods and theoretical guarantees that allows for efficient estimation and inference in the framework.