### Mathematisches Forschungskolloquium 2019

**Dr. Annalisa Iuorio**(Technische Universität Wien)**"Interplay of water and toxicity in vegetation pattern formation"**

Abstract: Vegetation patterns are largely present in nature. Their formation, however, is still far from being fully understood. A prevailing view is to treat water availability as the main causal factor for the emergence of vegetation patterns, as they are mostly observed in arid and semiarid regions. While successful, this hypothesis fails to explain the presence of vegetation patterns in humid environments. We present here a novel toxicity-mediated model for vegetation pattern formation and investigate its rich structure. This model consists of three PDEs accounting for a dynamic balance between biomass, water, and toxic compounds. Different (ecologically feasible) regions of the model’s parameter space give rise to stable spatial vegetation patterns in Turing and non-Turing regimes. Strong negative feedback gives rise to dynamic spatial patterns that continuously move in space while retaining their stable topology.**12.07.2019, 13:15 Uhr, Raum 427 (Ulmenstr. 69, Haus 3)**

Kolloquiumsleiter: Prof. Dr. Jens Starke

**Dr. Leo Perrin**(INRIA-Paris)**"How to Analyse an S-box, and, in the Process, Prove the Russian Standardizing Agency is Wrong"**

Abstract: S-boxes are functions mapping {0,1}^n to {0,1}^m (for m, n small, typically 4 or 8) that are the only source of non-linearity in many symmetric cryptographic primitives. In this tutorial, I will explain what the key properties of these objects are in terms of security and how to analyse these properties in practice using SAGE.

Then, I will describe the state of the art on how to recover the algorithm used to generate an S-box using only its truth table (a process called "S-box reverse-engineering"). In particular, I will walk you through a line of research that allowed me and my co-authors to eventually uncover the structure hidden inside the S-box used by the latest Russian standards, namely the hash function Streebog and the block cipher Kuznyechik. As I will show, the presence of this structure is incompatible with the explanations provided by its designers.

The corresponding techniques have applications far beyond the investigation of this specific S-box. They are in fact closely related to the method used by Dillon et al. to investigate the big APN problem, and more generally to the understanding of CCZ-equivalence.**26.06.2019, 13:30 Uhr, HS 228 (Ulmenstr. 69, Haus 3)**

Kolloquiumsleiter: Prof. Dr. Gohar Kyureghyan

**Dr. Shuxing Li**(Otto-von-Guericke Universität Magdeburg)**"Intersection distribution and its application"**

Abstract: For a point set of the classical projective plane PG(2,q), we introduce the concept of intersection distribution, which reflects how this point set interacts the lines of PG(2,q). For point set with q+1 points, which usually has a compact polynomial representation, the intersection dsitribution turns out to be very informative. Indeed, the intersection distribution measures how close a (q+1)-set to an oval or equivalently, how close the corresponding polynomial to an o-polynomial (when q is even) or to x^2 (when q is odd). These two closely related aspects, the geometric one and the polynomial one, of the intersection distribution, offer an advantage viewpoint to appreciate the connection between (q+1)-sets of PG(2,q) and their polynomials.

By characterizing the point sets with certain special intersection distributions, we show that the information of intersection distribution is crucial. While the computation of intersection distribution is in general difficult, via the polynomial viewpoint, we succeed in computing the intersection distribution for several classes of monomials. In fact, the intersection distribution provides a new angle to distinguish polynomials, especially monomials.

Finally, we display a natural application of intersection distribution to the Kakeya set on classical affine planes. While determining the size of a Kakeya set is hard, we can achieve this by considering several infinite families of Kakeya sets with simple polynomial representations, in which their sizes follow immediately from the intersection distributions.**19.06.2019, 15:15 Uhr, HS 228 (Ulmenstr. 69, Haus 3)**

Kolloquiumsleiter: Prof. Dr. Gohar Kyureghyan

**Dipl. Math. Alexandr Polujan**(Otto-von-Guericke Universität Magdeburg)**"Homogeneous Cubic Bent Functions: From Known Examples to New Constructions"**

Abstract**15.05.2019, 13:15 Uhr, HS 228 (Ulmenstr. 69, Haus 3)**

Kolloquiumsleiter: Prof. Dr. Gohar Kyureghyan

**PD Dr. Wolfram Just**(Queen Mary University of London)**"Transfer operator technique for analytic maps - Or: Chaos in the Hilbert space"**

11.04.2019, 16:00 Uhr, Raum 427 (Ulmenstr. 69, Haus 3)

Kolloquiumsleiter: Prof. Dr. Jens Starke

**Prof. Dr. Eduard Feireisl**(Akademie der Wiss., Prag)**"On weak--weak uniqueness for the isentropic Euler system"**

Abstract: We discuss uniqueness of certain weak solutions in the class of general (measure--valued) solutions for the isentropic Euler system. The weak solution is unique provided it belongs to a certain Besov class and its symmetric gradient satisfies a one--sided Lipschitz condition.**10.04.2019, 15:00 Uhr, HS 125 (Ulmenstr. 69, Haus 3)**Kolloquiumsleiter: Prof. Dr. Peter Takac, Ph. D.

**Prof. John Hogan**(University of Bristol, UK)**"The rough with the smooth; regularization of the Painlevé paradox"**

Abstract: When a piece of chalk is pushed across a blackboard, it can jump and judder, often accompanied by an unpleasant screeching noise. This unwanted phenomenon occurs in many engineering applications, including robotic manipulators. In 1905, Painlevé showed that the governing rigid body equations can produce a paradox: when the coefficient of friction exceeds a critical value, the rod appears to be driven the rigid surface. In an attempt to resolve this paradox, a jump in vertical velocity called impact without collision (IWC), has been proposed. But this approach can itself produce contradictions. A more consistent approach is to relax the rigid body assumption in the neighbourhood of the contact point, by assuming compliance there. This regularization produces a singularly perturbed problem. In this talk, I will show that the compliant problem has three major phases: the frictional torque compresses the compliant surface until the rod stops sliding, then the rod sticks, before finally leaving the surface. The rigid body problem has one non-hyperbolic point. Using blowup, I will show that the compliant problem has a canard at this point.

Joint work with Kristian Kristiansen (DTU).**21.03.2019, 13:00 Uhr, HS 326 (Ulmenstr. 69, Haus 3)**

Kolloquiumsleiter: Prof. Dr. Jens Starke

**Dr. Konstantinos Spiliotis**(National Technical University of Athens, Greece)**"Equation Free Computations on Neuronal Networks: From Neuronal Interactions To Emergent Brain Dynamics."**

Abstract**14.03.2019, 10:00 Uhr, Raum 427 (Ulmenstr. 69, Haus 3)**

Kolloquiumsleiter: Prof. Dr. Jens Starke

**Prof. Dr. Faruk Gologlu**(Charls University Prague)**"Families which are not equivalent to APN permutations"**

Abstract: Almost Perfect Nonlinear (APN) functions are important in cryptography. We will present theoretical results on inequivalence of APN functions to permutations including Gold and Kasami families. We also present results which explain why it wasn't possible to generalize the Kim function which is equivalent to the only known APN permutation on an even extension degree.**12.03.2019, 14:00 Uhr, HS 228 (Ulmenstr. 69, Haus 3)**

Kolloquiumsleiter: Prof. Dr. Gohar Kyureghyan

**Dr. Annalisa Iuorio**(TU Wien)**"Geometric Singular Perturbation Analysis of a Model for Micro-Electro Mechanical Systems (MEMS)"**

Abstract**07.03.2019, 14:00 Uhr, HS 326 (Ulmenstr. 69, Haus 3)**

Kolloquiumsleiter: Prof. Dr. Jens Starke

**Prof. Dr. Thomas Sunn Pedersen (Max-Planck-Institut für Plasmaphysik, IPP)**

"Neural Networks for the W7-X Experiment"

23.01.2019, 15:00 Uhr, HS 228 (Ulmenstr. 69, Haus 3)

Kolloquiumsleiter: Prof. Dr. Roger Labahn