Abstract:
Incidence geometries are a powerful and general framework to axiomatically describe classical geometric objects, in terms of relations between objects of different types. Important cases of incidence geometries are induced by point -- line geometries, i.e. geometries determined by two sets \${\\cal P}\\neq\\emptyset\$ and \$\\cal L\$ (called respectively points and lines) and an incidence relation such that and for any two given distinct points there is at most a line which is incident with them both. In a point-line geometry, we say that two points \$p\$ and \$q\$ are collinear (written \$p\\perp q\$) if there is a line \$\\ell\\in{\\cal L}\$ such that both \$p\$ and \$q\$ are incident with \$\\ell\$. In this talk we shall focus mostly on \$\\Gamma\$-geometries i.e. point--line geometries where given \$(p,\\ell)\\in{\\cal P}\\times{\\cal L}\$ we have either \$\\forall q\\in\\ell: p\\perp q\$ or \$|\\{ q\\in\\ell: p\\perp q\\}|\\leq 1\$. Projective spaces, polar spaces as well as their grassmannians are all \$\\Gamma\$ geometries. Next, we shall discuss the notion of projective embeddings as providing useful "concrete" models for geometries, by representing their points as varieties embedded in a suitable projective space. By regarding embedded geometries as projective systems it is possible to construct codes which usually admit large automorphism groups and sport a rich "local" structure which can be used in order to perform efficient decoding. In this talk, I will report on the general constructions and then focus on the case of polar Grassmannians and of the representation of flag geometries of a given geometry. All of these results are joint work with Ilaria Cardinali from University of Siena. References [1] Ilaria Cardinali and Luca Giuzzi, Codes and caps from orthogonal Grassmannians, Finite Fields and their Applications 24 (2013) 148–169.
[2] ________, Enumerative Coding for Line Polar Grassmannians with Applications to Codes, Finite Fields and their Applications 46 (2017) 107–138.
[3] ________, Linear codes arising from the point-hyperplane geometry – part I: the Segre embedding, Finite Fields and their Applications 111 (2026) 102766.
[4] ________, Linear codes arising from the point-hyperplane geometry – part II: the twisted embedding, arXiv:2507.16694 (2025).
[5] ________, On minimal codes arising from projective embeddings of point–line geometries, arXiv:2511.22747 (2025).

15:15 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 28

ETH Zürich

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Singular chains as Coalgebras abstract

15:30 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43

Universität Bern

Colloquia on Probability and Statistics

Dr. Nathan Kirk (University of St. Andrews)

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16:15 • Universität Bern, Hörsaal B77, ExWi, Sidlerstrasse 5, 3012 Bern

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16:30 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H 28

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17:15 • UZH Irchel, Winterthurerstrasse 190, Zürich, Building Y27, Room H12

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EPFL Lausanne

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10:00 • EPFL Lausanne

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Nachdiplomvorlesung

Sylvain Crovisier (Université Paris-Saclay)

Ergodic theory of surface diffeomorphisms

10:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43

Université de Genève

Séminaire de Topologie et Géométrie

Ilaria Colazzo (University of Leeds)

A Hopf Algebra Perspective on Set-Theoretic Pentagon Solutions abstract

14:15 • Université de Genève, Conseil Général 7-9, Room 1-15

ETH Zürich

ETH-FDS seminar

Sven Wang (EPFL, Lausanne)

On global polynomial-time computable estimators in statistical nonlinear inverse problems abstract

16:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room E 5

ETH Zürich

Talks in Financial and Insurance Mathematics

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17:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43

ETH Zürich

Inaugural Lectures

PD Dr. Lukas Lewark (ETH Zürich, Switzerland)

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18:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG , Room G 19.1

Friday, March 6

ETH Zürich

Nachdiplomvorlesung

Tom Hutchcroft (California Institute of Technology (Caltech))

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10:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43

EPF Lausanne

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Thomas Koerber (University of Vienna)

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14:15 • EPF Lausanne, MA A1 12

EPF Lausanne

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Daniela Witten (University of Washington)

Testing hypotheses via orthogonalization abstract

15:15 • EPF Lausanne, CM 1 517

address: Alessandra Naldi Windler, Departement Mathematik, HG G 51.4, ETH Zurich, Raemistrasse 101, CH-8092 Zurich
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