## Math Calendar

In their classical formulation, systolic inequalities aim to study Riemannian metrics on a given compact surface by looking at the length of the shortest non-constant periodic geodesic, also known as the systole. One of the fundamental questions in the field is to find an upper bound, independent of the metric, for the systolic length when the metric has unit area.

After briefly discussing this question in general, we will concentrate on the case of the two-sphere. Here an interesting class of metrics pops up: Those for which all geodesics are systoles. Abbondandolo, Bramham, Hryniewicz and Salomao showed recently that these so-called Zoll metrics locally maximize the systolic length in the space of Riemannian metrics on the two-sphere.

Their proof uses symplectic techniques and will lead us, in the second talk, to consider an analogue of systoles and of Zoll metrics for contact hypersurfaces inside symplectic manifolds. In the contact world, global upper bounds for the systole do not hold but Zoll hypersurfaces still remain local maximizers for the systolic length.

These phenomena are related to the famous Viterbo conjecture in symplectic geometry about the capacity of convex domains in euclidean space, which will finally bring us to the frontier of current research.

Zoom details can be found in the website of the seminar: https://www.few.vu.nl/~trt800/ddtg.html

The Workshop will consist of 3 minicourses ("Infinite dimensional geometry", "C^0 Symplectic Topology", "the Pontryagin maximum principle"), as well as ten talks given by junior participants.

Further details of the event can be found in http://utrechtgeometrycentre.nl/15iyrw/

The Zoom link will be sent to staff and students a few days before the event.

The Workshop will consist of 3 minicourses ("Infinite dimensional geometry", "C^0 Symplectic Topology", "the Pontryagin maximum principle"), as well as ten talks given by junior participants.

Further details of the event can be found in http://utrechtgeometrycentre.nl/15iyrw/

The Zoom link will be sent to staff and students a few days before the event.

The Workshop will consist of 3 minicourses ("Infinite dimensional geometry", "C^0 Symplectic Topology", "the Pontryagin maximum principle"), as well as ten talks given by junior participants.

Further details of the event can be found in http://utrechtgeometrycentre.nl/15iyrw/

The Zoom link will be sent to staff and students a few days before the event.

The Workshop will consist of 3 minicourses ("Infinite dimensional geometry", "C^0 Symplectic Topology", "the Pontryagin maximum principle"), as well as ten talks given by junior participants.

Further details of the event can be found in http://utrechtgeometrycentre.nl/15iyrw/

The Zoom link will be sent to staff and students a few days before the event.

The Workshop will consist of 3 minicourses ("Infinite dimensional geometry", "C^0 Symplectic Topology", "the Pontryagin maximum principle"), as well as ten talks given by junior participants.

Further details of the event can be found in http://utrechtgeometrycentre.nl/15iyrw/

The Zoom link will be sent to staff and students a few days before the event.

Website of the seminar: http://utrechtgeometrycentre.nl/ugc-seminar/

Zoom details will be sent by email to the staff and student mailing lists a few days before the event.

In the past five years, deep learning methods have become state-of-the-art in solving various inverse problems. Before such approaches can find application in safety-critical fields, a verification of their reliability appears mandatory. Recent works have pointed out instabilities of deep neural networks for several image reconstruction tasks. In analogy to adversarial attacks in classification, it was shown that slight distortions in the input domain may cause severe artifacts.

In this talk, we will shed new light on this concern and deal with an extensive empirical study of the robustness of deep-learning-based algorithms for solving underdetermined inverse problems. This covers compressed sensing with Gaussian measurements as well as image recovery from Fourier and Radon measurements, including a real-world scenario for magnetic resonance imaging (using the NYU-fastMRI dataset). Our main focus is on computing adversarial perturbations of the measurements that maximize the reconstruction error. In contrast to previous findings, our results reveal that standard end-to-end network architectures are not only surprisingly resilient against statistical noise, but also against adversarial perturbations. Remarkably, all considered networks are trained by common deep learning techniques, without sophisticated defense strategies.

This is joint work with Jan Macdonald and Maximilian März (both TU Berlin).

Written under supervision by Prof. dr. G.L.M. Cornelissen with dr. V.Z.Karemaker as a second reader.

**Abstract:** A well-known theorem infinite automata theory is the following: a power series over a finite field isalgebraic if and only if its coefficient sequence is automatic. This result isknown as Christol's Theorem. In a recent paper, Bridy proved new bounds for thenumber of states for the automaton of an algebraic power series. Although thesebounds are sharp in some specific cases, there are many examples of algebraicpower series with automata which are far smaller than expected from the bounds.After introducing the theory of function fields and automata, we study Bridy'sbounds in more detail. We use an experimental approach to study the automata ofseveral families of algebraic power series. Lastly, we provide a MAGMAprocedure which for a given irreducible polynomial over a finite field computesall power series solutions and their automata.

My presentation will be held online via Microsoft Teams. You canjoin the team via the following link: https://teams.microsoft.com/l/team/19%3a411fef3f93f34df2b811f3c2986b464f%40thread.tacv2/conversations?groupId=1b15352a-1c37-4fdd-9529-80abaccd80c6&tenantId=d72758a0-a446-4e0f-a0aa-4bf95a4a10e7, or using the code **texxvti **. If any problems occur while trying tojoin, please notify me via e-mail: o.vanzomeren@students.uu.nl.

Zoom details are sent in the weekly announcements. To join the mailing list you can drop us an email to fridayfishseminar[at]gmail.com.

Website of the seminar: http://utrechtgeometrycentre.nl/friday-fish-seminar-online-edition/