Adam Kanigowski (University of Maryland)
Sparse Equidistribution Problems in Dynamics
10:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Paolo Tomasini
Equivariant elliptic cohomology from mapping stacks abstract
Abstract:
Equivariant elliptic cohomology is an equivariant cohomology theory associated to an elliptic curve. In this talk we will present a novel construction of complexified equivariant elliptic cohomology in an algebraic setting, in terms of functions over a stack of quasi-constant maps from an elliptic curve into a quotient stack. Based on joint work with Nicolò Sibilla.
13:15 • EPF Lausanne, CE 1 100
René Pfitscher (Université Sorbonne Paris Nord)
Siegel transforms and counting rational approximations on flag varieties abstract
Abstract:
In the divergence case of Khintchine\'s theorem, Schmidt established an asymptotic formula for the number of rational approximations of bounded height to almost every real number. Using tools from homogeneous dynamics and the geometry of numbers, we prove a version of this theorem for intrinsic Diophantine approximation on projective quadrics, Grassmannians, and other examples of flag varieties.
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room F 5
Lycka Drakengren (ETH Zürich)
The Chow ring of A_4 is... abstract
Abstract:
We outline a strategy for showing that the Chow ring of A_4 is tautological. The geometric setup involves a parametrization of the complement of the Jacobian locus by a moduli space of 6-nodal quartics in P^3. An ongoing collaboration with Sam Canning and Aitor Iribar-López.
13:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Prof. Dr. Gianira Nicoletta Alfarano (Université de Rennes)
The Geometry of One-Weight Linear Codes abstract
Abstract:
A one-weight code, or constant-weight code, is an error-correcting code in which all codewords share the same weight. In 1984, Bonisoli provided a classification of one-weight linear codes by leveraging the connection between codes equipped with the Hamming metric and projective systems. More recently, similar geometric techniques have been applied to the study of linear codes in the rank metric. In this talk, we discuss one-weight linear rank-metric codes, by exploiting a new geometric framework. This is a joint work with Martino Borello and Alessandro Neri.
15:15 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 28
Livio Liechti (Université de Fribourg)
Pseudo-Anosov stretch factors of maximal algebraic degree abstract
Abstract:
In his seminal 1988 Bulletin article, Thurston showed that the stretch factor of a pseudo-Anosov map of a closed orientable surface is an algebraic integer of degree bounded from above by the dimension of the Teichmüller space of the surface. Thurston further claimed, without proof, that a construction of examples presented later in the article shows that this bound is sharp—a construction which nowadays is known as Thurston’s construction or Thurston—Veech construction. Margalit remarked in 2011 what Strenner wrote down in his 2017 article on algebraic degrees of stretch factors, namely that no proof of Thurston\'s claim has ever been published. In this talk, we present almost explicit examples of pseudo-Anosov maps obtained via the Thurston—Veech construction with stretch factors of maximal algebraic degree, finally substantiating Thurston\'s claim. This is joint work with Erwan Lanneau.
15:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Sasha Glazmann
On percolation on planar graphs
16:00 • EPF Lausanne, CM1 517
Fernando Figueroa (Northwestern University)
Abstract:
Log Calabi-Yau Pairs are a generalization of Calabi-Yau varieties, naturally occurring when considering families or branched covers. The Complexity of a Calabi-Yau pair measures how far it is from being a toric pair. More concretely, Brown, McKernan, Svaldi and Zong proved that any Calabi-Yau pair of index one and complexity 0 is a toric pair. Recent work of Mauri and Moraga has studied its crepant birational analogue, the "birational complexity", which measures how far the pair is from admitting a birational toric model. In this talk we will extend some of the previously known results for Calabi-Yau pairs of index one to arbitrary index. In particular we completely characterize Calabi-Yau pairs of complexity zero and arbitrary index. This is based on joint work with Joshua Enwright.
16:00 • Universität Basel, Seminarraum 00.003, Spiegelgasse 1
Prof. Dr. Alessandro Neri (University of Naples Federico II)
Ferrers Diagram Rank-Metric Codes abstract
Abstract:
Ferrers diagram rank-metric codes were first studied in 2009 by Etzion and Silberstein, motivated by their application in network coding. Concretely, they arise from subspace codes entirely contained in a unique Schubert cell. In their work, the authors proposed a conjecture on the largest dimension of a linear space of matrices over a finite field whose nonzero elements are supported on a given Ferrers diagram and have all rank lower bounded by a fixed positive integer r. Since then, their conjecture has been proved only in some few cases, and as of today it still remains widely open. In this talk, I will give an overview of the main combinatorial and algebraic properties of Ferrers diagram rank-metric codes and on the state of art on the Etzion-Silberstein conjecture, starting from the first findings, until some very recent results.
16:15 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 28
Fael Rebei (ENS de Lyon)
Exploration processes of the Brownian half-plane abstract
Abstract:
This project is an ongoing work with Armand Riera. The Brownian half-plane is a random surface that arises as the universal scaling limit in the Gromov-Hausdorff sense of large graphs embedded in the closed half-plane. We will present two exploration processes of this surface; the horohulls and the hulls, which correspond roughly to exploring it from a point at infinity, and from its root. We characterize the law of the horohulls, which in turn provides information on the local topology of the half-plane. We describe the joint law of the horohulls and the hulls, and support the idea that they are dual processes. Then, we exhibit a simple martingale which is a function of the hulls, which allows to define another surface whose law is absolutely continuous to whose of the Brownian half-plane. We show that this surface exhibits hyperbolic features, with some links to 3D non random geometry. We end with a few conjectures/open questions.
17:15 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H12