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Spring Semester 2025

Date / Time Speaker Title Location
19 March 2025
15:30-16:30 		Raphael Appenzeller
Universität Heidelberg
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Geometry Seminar

Title Characterizing hyperbolicity via game theory
Speaker, Affiliation Raphael Appenzeller, Universität Heidelberg
Date, Time 19 March 2025, 15:30-16:30
Location HG G 43
Abstract The cop numbers are two new integer-valued invariants of finitely generated groups defined in terms of a two player pursuit game played on Cayley graphs. We use the cop numbers to give a new characterization of hyperbolic groups and virtually free groups. We discuss potential applications and recent progress on remaining open questions. This is joint work with Kevin Klinge.
Characterizing hyperbolicity via game theoryread_more
HG G 43
26 March 2025
15:30-16:30 		Yash Lodha
University of Hawaii at Manoa
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Geometry Seminar

Title Two new constructions of finitely presented infinite simple groups
Speaker, Affiliation Yash Lodha, University of Hawaii at Manoa
Date, Time 26 March 2025, 15:30-16:30
Location HG G 43
Abstract I will describe two new constructions of finitely presented infinite simple groups. First, I will present a construction of finitely presented (and type F∞) simple groups that act by orientation preserving homeomorphisms on the real line. These are the first such examples. Next, I will present a construction of a family of finitely presented infinite uniformly simple groups, where the Ulam width can get arbitrarily large. Among the class of finitely generated (but not finitely presentable) groups, the existence of such examples was demonstrated in the work of Ivanov from 1989. Our construction provides the first such family of examples in the class of infinite finitely presented groups. This is joint work with James Hyde.
Two new constructions of finitely presented infinite simple groupsread_more
HG G 43
2 April 2025
15:30-16:30 		Leonid Monin
EPFL
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Geometry Seminar

Title Geometry of matrix inversion
Speaker, Affiliation Leonid Monin, EPFL
Date, Time 2 April 2025, 15:30-16:30
Location HG G 43
Abstract In this talk I will explain how to invert matrices using an action of algebraic torus on certain algebraic varieties. Along the way, I will recall the construction of permutohedral toric variety and the space of complete quadrics, and explore the connection between them. As an application, I will present a recent polynomiality result for characteristic numbers of quadrics which was conjectured by Sturmfels and Uhler. Only very basic knowledge of algebraic geometry is needed.
Geometry of matrix inversionread_more
HG G 43
9 April 2025
15:30-16:30 		Anthony Genevois
Institut Montpellierain Alexander Grothendieck
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Geometry Seminar

Title Quasi-median graphs, right-angled Artin groups, and homotopy
Speaker, Affiliation Anthony Genevois, Institut Montpellierain Alexander Grothendieck
Date, Time 9 April 2025, 15:30-16:30
Location HG G 43
Abstract After a general introduction to applications of metric graph theory in geometric group theory, focused on quasi-median graphs, I will explain how one can deduce from such a perspective new quasi-isometric invariants for right-angled Artin groups. This is joint work with Carolyn Abbott and Eduardo Martinez-Pedrosa.
Quasi-median graphs, right-angled Artin groups, and homotopyread_more
HG G 43
16 April 2025
15:30-16:30 		Jeremy Tyson
University of Illinois Urbana-Champaign
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Geometry Seminar

Title Dimension interpolation and conformal dimension
Speaker, Affiliation Jeremy Tyson, University of Illinois Urbana-Champaign
Date, Time 16 April 2025, 15:30-16:30
Location HG G 43
Abstract The conformal dimension of a metric space $(X,d)$ measures its optimal shape from the perspective of quasiconformal geometry. It is defined by infimizing dimension over metrics in the quasisymmetric equivalence class of $d$. Introduced by Pierre Pansu in 1989, conformal Hausdorff dimension played an important early role in the development of analysis on metric spaces. Subsequently a variant notion, conformal Assouad dimension, gained prominence. Assouad dimension—which bounds Hausdorff dimension from above—is a scale-invariant, quantitative measurement of optimal coverings of a space. Dimension interpolation is an emerging program of research in fractal geometry which identifies geometrically natural one-parameter dimension functions interpolating between existing concepts. Two exemplars are the Assouad spectrum (Fraser-Yu, 2015), which interpolates between box-counting and Assouad dimension, and the intermediate dimensions (Falconer-Fraser-Kempton, 2020), which interpolate between Hausdorff and box-counting dimension. In this talk, I’ll discuss the mapping-theoretic properties of intermediate dimensions and the Assouad spectrum, with applications to the quasiconformal classification of sets and to the range of conformal Assouad spectrum. The latter results are based on a recent joint project with Efstathios Chrontsios Garitsis (Univ of Tennessee) and an ongoing collaboration with Jonathan Fraser (Univ of St. Andrews).
Dimension interpolation and conformal dimensionread_more
HG G 43
23 April 2025
15:30-16:30
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Geometry Seminar

Title Easter break
Speaker, Affiliation
Date, Time 23 April 2025, 15:30-16:30
Location
Easter break
30 April 2025
15:30-16:30 		Stephan Stadler
MPIM Bonn
Details

Geometry Seminar

Title Isoperimetric gaps in CAT(0) spaces
Speaker, Affiliation Stephan Stadler, MPIM Bonn
Date, Time 30 April 2025, 15:30-16:30
Location HG G 43
Abstract A metric space X satisfies a Euclidean isoperimetric inequality for n-spheres, if every n-sphere S ⊂ X bounds a ball B ⊂ X with voln+1(B)≤ C · voln(S)(n+1)/n. Every CAT(0) space X satisfies Euclidean isoperimetric inequalities for 1-spheres with the sharp constant C=1/4π. Moreover, if such inequalities hold with a constant strictly smaller than 1/4π, then X has to be Gromov hyperbolic. In particular, a sharp isoperimetric gap appears. In the talk I will focus on the case n=2, namely fillings of 2-spheres by 3-balls. This is based on joint work with Drutu, Lang and Papasoglu.
Isoperimetric gaps in CAT(0) spacesread_more
HG G 43
7 May 2025
15:30-16:30 		Hugo Parlier
Université de Fribourg
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Geometry Seminar

Title Criss-crossing curves
Speaker, Affiliation Hugo Parlier, Université de Fribourg
Date, Time 7 May 2025, 15:30-16:30
Location HG G 43
Abstract The crossing lemma for simple graphs gives a lower bound on the necessary number of crossings of any drawing of a graph in the plane in terms of its number of edges and vertices. Viewed through the lens of topology, this leads to other questions about arcs and curves on surfaces. In joint work with Alfredo Hubard, we provide estimates on the necessary number of intersections of any realization of m distinct homotopy classes of curves on a (fixed) surface. These estimates allow us to answer questions raised by Pach, Tardos, and Toth concerning a version of the crossing lemma for graph drawings with non-homotopic edges. Our approach uses the geometry of hyperbolic surfaces in an essential way.
Criss-crossing curvesread_more
HG G 43
14 May 2025
15:30-16:30 		Stefanie Zbinden
Heriot-Watt University
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Geometry Seminar

Title The contraction space and its applications
Speaker, Affiliation Stefanie Zbinden, Heriot-Watt University
Date, Time 14 May 2025, 15:30-16:30
Location HG G 43
Abstract In the realm of CAT(0) groups, there exists the following powerful dichotomy. Either the group has linear divergence, in which case all asymptotic cones are cut-point free, or the group has a Morse geodesic, in which case all asymptotic cones have cut-points and the group is acylindrically hyperbolic. This talk focuses on work in progress with Cornelia Drutu and Davide Spriano, where we show that the above dichotomy holds for a larger class of groups. In particular, that it holds for groups acting ''nicely'' on injective metric spaces and geodesic median spaces. The main tool of the proof is the contraction space construction, a construction which assigns a hyperbolic space to any given geodesic metric space. We will introduce and motivate this construction and outline how it can be used in the proof of the dichotomy.
The contraction space and its applicationsread_more
HG G 43
21 May 2025
15:30-16:30 		Paula Truöl
MPIM Bonn
Details

Geometry Seminar

Title Non-complex cobordisms between quasipositive knots
Speaker, Affiliation Paula Truöl, MPIM Bonn
Date, Time 21 May 2025, 15:30-16:30
Location HG G 43
Abstract Quasipositive knots occur in complex geometry as transverse intersections of smooth algebraic curves in the complex plane ℂ2 with the 3-sphere. A complex cobordism is a surface that arises as a transverse intersection of a smooth algebraic curve with the region bounded between two 4-balls of different radius with common center in ℂ2. The two knots bounded by a complex cobordism are necessarily quasipositive, and such a cobordism is necessarily optimal (defined in the talk). Feller asked whether these two necessary conditions for the existence of a complex cobordism between two knots are sufficient. In a joint work with Maciej Borodzik we answer this in the negative for cobordisms of any genus g ≥ 0. In the case of genus g = 0, we improve our result to strongly quasipositive knots. In the talk, we will define the relevant terms and provide some context for our results.
Non-complex cobordisms between quasipositive knotsread_more
HG G 43
28 May 2025
15:30-16:30 		Livio Liechti
Université de Fribourg
Details

Geometry Seminar

Title Pseudo-Anosov stretch factors of maximal algebraic degree
Speaker, Affiliation Livio Liechti, Université de Fribourg
Date, Time 28 May 2025, 15:30-16:30
Location HG G 43
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.
Pseudo-Anosov stretch factors of maximal algebraic degreeread_more
HG G 43

Organisers: Manfred Einsiedler, Urs Lang, Lukas Lewark, Christian Urech

Archive: SS 25 AS 24 SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 AS 20 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11 SS 11 AS 10 SS 10 AS 09 SS 09

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