SMS Fall Meeting: Swiss Geometry Day
Monday 3.11.2025, University of Neuchâtel
The fall meeting of the Swiss Mathematical Society takes place in the science building of the University of Neuchâtel in the form of a Geometry Day. Everyone is welcome to attend, but please register by October 27th.
Scientific Program
The four plenary speakers represent different geographical and mathematical research areas.
Ana Cannas da Silva (ETH Zürich, symplectic geometry)
Thomas Mettler (UniDistance Suisse, differential geometry)
Hugo Parlier (University of Fribourg, low-dimensional topology and geometry)
Immanuel van Santen (University of Bern, algebraic geometry)
Schedule
The talks and coffee breaks will take place in room F-100. For lunch we will convene in T103.
10:15-10:45: Coffee/Arrival
10:45-11:45: Thomas Mettler: Deformations of the Veronese embedding and Finsler 2-spheres of constant curvature
12:00-13:30: Lunch break (light lunch provided)
13:30-14:30: Ana Cannas da Silva: Toric Real Loci via Moment Polytopes
14:30-14:50: Coffee break
14:50-15:50: Immanuel van Santen: The Group of Birational Transformations Detects Rationality
15:50-16:00: Coffee break
16:00-17:00: Hugo Parlier: Using Hyperbolic Geometry in Combinatorics
Registration
Everyone is welcome to attend, but, for planning purposes, please register by October 27th via the registration form below. Please indicate interest in joining for the dinner after the event (cost not covered).
Contact
If you have questions about the event, don’t hesitate to contact Peter Feller.
Abstracts
Thomas Mettler
Title: Deformations of the Veronese embedding and Finsler 2-spheres of constant curvature
Abstract: A path geometry on a surface M prescribes a path for each direction in every tangent space. A path geometry may be encoded in terms of a line bundle P on the projectivised tangent bundle P(TM) of M. Besides P, the projectivised tangent bundle is also equipped with the vertical bundle L of the base-point projection P(TM) -> M. Interchanging the role of L and P leads to the notion of duality for path geometries. In my talk I will give an introduction to path geometries and proceed to talk about global aspects of the notion of duality for Finsler 2-spheres of constant curvature and with all geodesics closed. In particular, I will describe the construction of new examples of such Finsler 2-spheres from suitable deformations of the Veronese embedding.
Ana Cannas da Silva
Title: Toric Real Loci via Moment Polytopes
Abstract: Polytope combinatorics controls the topology of both toric symplectic manifolds and their toric real loci, as toric geometers have realized since the 1980s. Basic examples are complex projective space CPn and its real locus RPn both governed by the combinatorics of a standard n-dimensional simplex.
I will explain how a user-friendly polyhedral model for a toric real locus allows us to understand, in an elementary geometric way, its orientability and Euler characteristic. This computationally simple approach is illustrated by the counting, for each complex dimension up to 9, of the smooth toric Fano varieties that have an orientable real locus.
This talk is based on joint work with João Camarneiro.
I will explain how a user-friendly polyhedral model for a toric real locus allows us to understand, in an elementary geometric way, its orientability and Euler characteristic. This computationally simple approach is illustrated by the counting, for each complex dimension up to 9, of the smooth toric Fano varieties that have an orientable real locus.
This talk is based on joint work with João Camarneiro.
Immanuel van Santen
Title: The Group of Birational Transformations Detects Rationality
Abstract: In this talk, we investigate to what extent the automorphism group of an object determines the object itself. Our main focus will be on the group of birational transformations Bir(X) of an irreducible variety X, and on the question whether Bir(X) detects rationality. Specifically, if Bir(X) is isomorphic to Bir(Pn), does it follow that X and Pn are birationally equivalent? For varieties X of dimension at most n, this question was answered affirmatively by Serge Cantat in 2014. I will present an overview of such group-theoretical characterization problems and discuss recent progress in this direction.
This is joint work with Andriy Regeta (University of Padova), Christian Urech (ETH Zürich), Louis Esser (Princeton University), and Nathan Chen (Harvard University).
This is joint work with Andriy Regeta (University of Padova), Christian Urech (ETH Zürich), Louis Esser (Princeton University), and Nathan Chen (Harvard University).
Hugo Parlier
Title: Using Hyperbolic Geometry in Combinatorics
Abstract: Crossing numbers measure the complexity of a graph by quantifying the minimum number of edge crossings required in any drawing of the graph on a given surface. There are many contexts in which this measure is meaningful — for instance, when considering drawings in the plane, simple graphs, non-homotopic edge drawings for non-simple graphs, or complete graphs.
The talk will explain how you can use hyperbolic geometry to approach some of these problems, namely in the case of representing a large complete graph on a surface of genus g.
This is joint work with Alfredo Hubard and Arnaud de Mesmay.
The talk will explain how you can use hyperbolic geometry to approach some of these problems, namely in the case of representing a large complete graph on a surface of genus g.
This is joint work with Alfredo Hubard and Arnaud de Mesmay.
