Colin Guillarmou (CNRS and Université Paris-Saclay)
On the marked length spectrum of surfaces with Anosov geodesic flow. abstract
Abstract:
<p><span style="caret-color: #ffffff; font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; display: inline !important; float: none;">We show that the marked length spectrum determines the isometry class for surfaces with Anosov geodesic flows. This extends a result of Otal and Croke, known previously in negative curvature. This is joint work with Lefeuvre and Paternain.</span></p>
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 19.1
Beatrice Bernasconi (ETH Zürich)
Dynamical Sarkisov length in the plane Cremona group abstract
Abstract:
We will give an overview of the Sarkisov program in higher dimension and then describe it in the case of rational surfaces. We will define the Cremona group over the projective plane and some dynamical invariants for its elements. Finally, we will look at a very special dynamical invariant, namely the Sarkisov length.
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Prof. Dr. Francisco Javier Lobillo Borrero (Universidad de Granada)
A Hybrid Approach to Post-quantum Cryptography: Integrating Mceliece Structures Into Knapsack Criptosystems abstract
Abstract:
<p>This talk introduces a novel IND-CCA2 Key EncapsulationMechanism (KEM) based on the weighted subset sum problem. The cryptosystem uses a decoding algorithm inspired by Goppa codes, adapted for the ring of integers. Decryption is efficiently handled through a truncated version of the extended Euclidean algorithm. By allowin non-binary alphabets, the design aims to mitigate traditional lattice-reduction attacks that have historically compromised knapsack schemes.</p> <p>Additionally, to protect the system against lattice-reduction attacks to the private key, two possible masking mechanisms of the public key are proposed. Since the system is based on basic integer arithmetic, it offers high computational performance and it is potentially secure against quantum attacks.</p>
15:15 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 28
Marc Abboud (Université de Neuchâtel)
A uniform bound on common periodic points in families of regular plane polynomial automorphisms abstract
Abstract:
A regular plane polynomial automorphism is a subclass of polynomial diffeomorphism f: C^2 - > C^2 of the complex affine plane with positive topological entropy. Every polynomial diffeomorphism of positive topological entropy is conjugated to a regular one. Dujardin and Favre showed that two such transformations cannot share infinitely many periodic points unless they share a common iterate. We show that this results holds uniformly in a family: Take two 1-parameter families of regular plane polynomial automorphisms (f_t) and (g_t), then there exists a constant D >0 such that for every parameter t except for a finite number of them f_t and g_t share at most D periodic points. This generalises a result of Mavraki and Schmidt who showed it for endomorphisms of the projective line. I will give a brief overview of the history of this problem and explain key tools of the proof which is based on the theory of adelic divisors and arithmetic equidistribution. This is joint work with Yugang Zhang.
15:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Dr. Catherine Wolfram (ETH Zurich)
Abstract:
A dimer tiling (or perfect matching) of Z^d is a collection of edges which covers each vertex exactly once. The dimer model is the study of random dimer tilings. I will focus on questions about what random dimer tilings look like in the scaling limit, that is, on larger and larger subgraphs of Z^d. In two dimensions, the dimer model is exactly solvable, and many things are known about this (large deviations, limit shapes with an explicit description, Gaussian fluctuations…). The dimer model does not seem to be exactly solvable in higher dimensions (as is the case for many statistical mechanics models), and we know much less. In this talk, I’ll explain what the dimer model is, give some intuition for why two and three dimensions are different to study, explain the main large deviation result we prove for random dimer tilings of Z^3, and show simulations of random tilings. This is based on joint work with Nishant Chandgotia and Scott Sheffield.
16:15 • Universität Bern, Hörsaal B78, ExWi, Sidlerstrasse 5, 3012 Bern
Andrea Di Giusto (Eindhoven University of Technology)
The Service Rate Problem in Distributed Storage and Non-systematic Recovery Systems abstract
Abstract:
<p>Data centres are one of the backbones of modern-day digital infrastructure, with the amount of processed and stored data growing year by year. In this context, coding techniques are employed to ensure the availability and reliability of the stored data. One question that has recently emerged, is how to optimally store a certain number of data objects on a certain number of servers in a way that allows the system to serve certain amounts of requests for the objects. This problem is naturally phrased as a coding question, as it concerns the design of a redundancy strategy for the storage system. In this talk, we will introduce and formalize the service problem and the Service Rate Region as a measure of system flexibility. Connection to other well-established research topics will be outlined, such as PIR/batch codes and Majority Logic Decoding. The difference between systematic and non-systematic systems will be considered, and we will show how the latter can give a better performance when designed carefully.</p>
16:30 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 28
Prof. Dr. Loïc Béthancourt (Université Sorbonne Paris Nord)
Fractional diffusion limit in convex domain and reflected isotropic stable processes abstract
Abstract:
In this talk, I will present some recent results obtained with Nicolas Fournier. We are interested in a simple model describing the (random) motion of a particle in a gaz, namely the kinetic scattering equation. When the particle lives in $\\mathbb{R}^d$, and when the equilibrium (for the velocities) is heavy-tailed, it is easy to see that the position process, correctly rescaled, converges weakly to an $\\alpha$-stable process. We are interested in the case where the particle is confined into a convex smooth domain, by a certain reflection mechanism that I will describe. We show that, according to the boundary condition, two different types of reflected stable process may arise at the limit. After introducing the model and the results, I will mostly explain how we construct the limiting processes by piecing together their excursions inside the domain. If time permits, I will say a few words about the convergence.
17:15 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H12