Filip Misev (Regensburg)
Braids on three strings of maximal four-genus abstract
Abstract:
When we look at surfaces embedded in four-dimensional space, regular-ity (smooth/topological) of the embedding matters: The minimal genusof surfaces in the four-dimensional ball with a prescribed knot as theirboundary does not only depend on the knot but also on the regularity ofthe surface’s embedding. Four decades after this discovery, which goesback to Rudolph and to the celebrated work of Freedman, the discrep-ancy between smooth and topological remains difficult to characterizeand to quantify; for example the topological four-genus of torus knots islargely unknown to date.I would like to present a classification of knots obtained as the closuresof braids on three strings whose topological four-genus is maximal (thatis, equal to their classical genus). For the remaining braids on threestrings, we have bounds and some precise calculations.This reports on a project with S. Baader, L. Lewark, and P. Truöl.
10:20 • Université de Fribourg, room Phys 2.52
Stefano Rizzelli (Universit of Padova)
Inference on marginal expected shortfall under multivariate regular variation abstract
Abstract:
The marginal expected shortfall is arguably one of the most popular measures of systemic risk. The study of its extreme behaviour is particularly relevant for protecting against the risk of severe downturns in global financial markets. In this context, statistical inference is typically based on bivariate extreme-value models for a given financial variable of interest and another that incorporates systemic risk information. However, this disregards the more complex extremal dependence structure among a large number of financial institutions, of which the market is composed. To explicitly account for it, we propose an inferential procedure based on the theory of multivariate regular variation. We derive an approximation formula for the extreme marginal expected shortfall and derive an estimator, of which we also propose a bias-corrected version. We prove their asymptotic normality, which in turn allows the derivation of confidence intervals. A simulation study shows that the new estimators significantly improve the performance of the existing ones and the confidence intervals are very accurate. We showcase the usefulness of the proposed inferential procedure by analysing returns on stocks for financial institutions classified as "Global Systemically Important Banks" or "Domestic Systemically Important Banks" from US and Canada. The statistical results are extended to a general beta-mixing context that accommodates popular time series models with heavy-tailed innovations. This is a joint work with Simone Padoan (Bocconi University) and Matteo Schiavone (University of Padova).
13:30 • EPF Lausanne, Anthropole 3034
Prof. Dr. Krzysztof Krupinski (Uniwersytetu Wroclawskiego)
On some applications of model theory and topological dynamics abstract
Abstract:
Model theory is a fast growing branch of mathematical logic with deep interactions with algebra, algebraic geometry, combinatorics, and, more recently, topological dynamics. I will focus on a few interactions with topological dynamics and applications to additive combinatorics. I will discus type-definable components of definable groups, which lead to model-theoretic descriptions of Bohr compactificatios of groups and rings, and also to so-called locally compact models of approximate subgroups and subrings which in turn are crucial to get structural or even classification results about approximate subgroups and subrings. I will discuss my result that each approximate subring has a locally compact model, and mention some structural applications. In contrast to approximate subrings, not every approximate subgroup has a locally compact model. However, Ehud Hrushovski showed that instead it has such a model in a certain generalized sense (with morphisms replaced by quasi-homomorphisms). In order to do that, he introduced and developed local logics and definability patterns. In my recent paper with Anand Pillay, we gave a shorter and simpler construction of a generalized locally compact model, based on topological dynamics methods in a model-theoretic context. I will briefly discuss it, if time permits.
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1
Mathew Satriano
Beyond twisted maps: crepant resolutions of log terminal singularities and a motivic McKay correspondence. abstract
Abstract:
Crepant resolutions have inspired connections between birational geometry, derived categories, representation theory, and motivic integration. In this talk, we prove that every variety with log-terminal singularities admits a crepant resolution by a smooth stack. We additionally prove a motivic McKay correspondence for stack-theoretic resolutions. Finally, we show how our work naturally leads to a generalization of twisted mapping spaces. This is joint work with Jeremy Usatine.
14:15 • EPF Lausanne
Daniella Bar-Lev (Technion)
The DNA Storage Channel: From Theory to Practice abstract
Abstract:
In recent years, DNA-based storage systems have emerged as promising solutions for long-term data archival due to their high data density and durability. This talk explores the intricacies of DNA storage, highlighting its advantages and challenges. DNA-based storage possesses distinct characteristics that distinguish it from conventional storage mediums. Synthesized DNA strands contain inherent redundancy due to replication during synthesis and sequencing processes, yet their unordered arrangement introduces complexity to data retrieval. Additionally, synthesis and sequencing introduce errors such as insertions, deletions, and substitutions, posing significant challenges to data integrity. This talk will begin with an examination of the background of DNA storage and the challenges posed by the DNA storage channel. Throughout the presentation, we will emphasize several open problems related to the channel, underscoring the need for innovative solutions to advance DNA storage technology. To bridge theory with application, we will discuss two recent research projects. The first focuses on the DNA coverage depth problem, which aims to reduce both, cost and latency in DNA storage. We will investigate how error-correcting codes and retrieval algorithms impact the sequencing coverage depth and explore how this coverage can be optimized. Additionally, we will explore a scalable end-to-end DNA storage pipeline, integrating deep neural networks and tensor-product based error-correcting codes, significantly improving speed, accuracy, and code rate. These insights contribute to advancing the efficiency and feasibility of DNA storage solutions, setting the stage for future advancements.
15:15 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 25
Dr. Miguel Orbegozo Rodriguez (ETH Zürich, Switzerland)
Right-veering diffeomorphisms and contact geometry abstract
Abstract:
Although contact geometry has its origins in the 19th century, it wasn\'t until the 1970s that it began to be studied via topological methods. More recently, in 2002, the Giroux correspondence theorem established, in dimension 3, a close relationship between contact manifolds and open book decompositions (i.e fibered links). This means that properties of contact 3-manifolds can be studied by studying properties of mapping classes of surfaces. In this talk I will start by providing an overview to contact geometry in dimension 3, and introducing one of the most relevant properties, the dichotomy between tight and overtwisted contact structures. This can be studied, by a result of Honda-Kazez-Matic, via right-veering diffeomorphisms of surfaces. I will show that this property is not easy to detect in general before presenting a combinatorial way of detecting it.
15:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Vivien Caroline Bammert
Security of Algebraic Geometry Codes in Code-Based Cryptography abstract
Abstract:
Code-based cryptosystems are promising candidates for post-quantum cryptography, such as the McEliece and Niederreiter cryptosystems. Their security is based on the difficulty of decoding a general linear code. In this thesis, we study the security of algebraic geometry codes in code-based cryptography. These codes include very well-known families like generalized Reed-Solomon, BCH and Goppa codes. Furthermore, they can be described using certain tools, e.g. the theory of algebraic function fields, which we will focus on.
16:15 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 25
Prof. em. Dr. Giovanni Felder (ETH Zürich, Switzerland)
17:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG , Room F 30