September 2025
September 2025
Speaker: Pierre-Louis Blayac (Institut de Recherche Mathématique Avancée, Université de Strasbourg)
Title: Real hyperbolic spaces and their isometry groups
Description: We watched the videos of Pierre-Louis' first two talks for the SLMath workshop "Geometry and Dynamics in Higher Rank Lie Groups"
Talk 1: https://www.slmath.org/workshops/1104/schedules/38020
Talk 2: https://www.slmath.org/workshops/1104/schedules/38022
During coffe hour, we worked on the corresponding exercises, which can be found here: Exercises
Speaker: Gye-Seon Lee (Seoul National University)
Title: Convex cocompactness for Coxeter groups
Abstract: There are several notions of convex cocompactness for discrete subgroups of PGL(V) acting on the projective space P(V), where V is a finite-dimensional real vector space. This generalizes both the classical theory of convex cocompactness in real hyperbolic geometry, and the theory of divisible convex sets. In this talk, I will explain these notions in the context of Vinberg's theory of discrete reflection groups. Joint work with Jeffrey Danciger, François Guéritaud, Fanny Kassel and Ludovic Marquis
Talk: https://www.youtube.com/watch?v=RxbJajh_fAg
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Speaker: Anja Randecker (Heidelberg University)
Title: Counting geodesics on translation surfaces of large genus
Abstract: Translation surfaces are Riemann surfaces with a flat metric outside of finitely many points, called singularities. It is known that the number of geodesic segments from a singularity to another or the same singularity, up to a given length, grows quadratically in the length. The coefficient in the growth rate is called the Siegel-Veech constant.
In this talk, we see what Siegel-Veech constants express and how they can be calculated. The focus is on how Siegel-Veech constants behave when the genus is going to infinity.
Speaker: Diana Davis (Phillips Exeter Academy)
Title: Three nice proofs about periodic billiards on the regular pentagon
Abstract: Instead of giving a typical seminar talk (of which I already have many available online), today we present three little snacks. In joint work with Samuel Lelièvre (Université Paris-Saclay) I have been studying periodic billiard trajectories on the regular pentagon, which are beautiful, and have lots of interesting properties. Today I explain three short, elegant proofs of interesting properties of these trajectories.
Talk: https://www.youtube.com/watch?v=ikPlv3JsgqY
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Speaker: Nicholas Vlamis (CUNY, Graduate Center and Queens College)
Title: Large-scale geometry of abstract groups
Abstract: Up to quasi-isometry, finitely generated groups admit a canonical left-invariant metric, making large-scale geometric invariants into group-theoretic invariants. Are there other, non-finitely generated abstract groups with this property? In this talk, we exhibit such examples by "going against nature"—stripping the topology from several large, rich families of topological transformation groups (e.g., homeomorphism groups of manifolds) and showing that they nevertheless admit canonical large-scale geometries as abstract groups.
Speaker: Edgar A. Bering IV (San José State University)
Title: The solenoid approach to abstract commensurators
Abstract: Consider a group G and its automorphism group Aut(G). An Eilenberg–MacLane space K(G,1) for G provides a topological model of the group, and Whitehead’s theorem realizes Aut(G) as the pointed homotopy equivalences of a K(G,1). This perspective, and its geometric specializations, are an enduring theme in geometric group theory, particularly in the settings of linear groups, mapping class groups of surfaces, and automorphisms of free groups.
The abstract commensurator of a group G, denoted Comm(G), is the collection of isomorphisms φ: H → K between finite-index subgroups H, K ≤ G, modulo agreement on a common finite-index domain. When G is infinite, this is a natural relaxation of Aut(G), and it arises naturally in the study of lattices in Lie groups.While the algebraic definition of the commensurator is straightforward, it is difficult to immediately obtain a useful topological characterization. However, if a group G has a finite CW complex X as a K(G,1), the inverse limit of all finite-sheeted covers of X, called the full solenoid Ẋ over X, furnishes the desired model: Comm(G) is isomorphic to the pointed homotopy equivalences of Ẋ.
In this talk I will present these full solenoids using familiar examples. This is joint work with D. Studenmund.
Talk: https://www.youtube.com/watch?v=3WiZHge01wE --------------------------------------------------------------------------------------------------------------------------------------------------
Speaker: Thomas W Mattman (California State University, Chico)
Title: Linking Numbers in Random Book Embeddings of Graphs
Abstract: (joint with Ichihara - paper available at arXiv.org)
For a hyperbolic knot in S³, Dehn surgery along slope r ∈ ℚ ∪ {1/0} is exceptional if it results in a non-hyperbolic manifold. We say meridional surgery r = 1/0 is trivial as it recovers the manifold S³. We provide evidence in support of two conjectures. The first (inspired by a question of Professor Motegi) states that there are boundary slopes b₁ < b₂ such that all non-trivial exceptional surgeries occur, as rational numbers, in the interval [b₁, b₂]. We say a boundary slope is NIT if it is non-integral or toroidal. Second, when there are non-trivial exceptional surgeries, we conjecture there are NIT boundary slopes b₁ ≤ b₂ so that the exceptional surgeries lie in [⌊b₁⌋, ⌈b₂⌉]. Moreover, if ⌈b₁⌉ ≤ ⌊b₂⌋, the integers in the interval [⌈b₁⌉, ⌊b₂⌋] are all exceptional surgeries.
Talk: https://media.csuchico.edu/media/Thomas+Mattmans+Personal+Meeting+Room/1_bzv4ujt6
Speaker: Slavyana Geninska (Université de Toulouse, Institut Mathématique de Toulouse)
Title: The limit sets of finitely generated subgroups of irreducible lattices in PSL(2,R)^n
Abstract: In this talk we will give a description of the limit sets of finitely generated subgroups of irreducible lattices in PSL(2,R)^n. We will give examples of thin groups with limit sets of non empty interior.
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Speaker: Harry Bray (George Mason University)
Title: A 0-1 law for horoball packings of coarsely hyperbolic metric spaces.
Abstract: On the cusp of the 100 year anniversary, Khinchin's theorem implies a strong 0-1 law for the real line; namely, the set of real numbers within distance q^{-2-\epsilon} of infinitely many rationals p/q is Lebesgue measure 0 for \epsilon>0, and full measure for \epsilon=0. In these lectures, I will present an analogous result for horoball packings in Gromov hyperbolic metric spaces. An application is a logarithm law describing asymptotics for the depth in the packing of a typical geodesic. This is joint work with Giulio Tiozzo.
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Speaker: Kenji Kozai (Lesley University)
Title: Linking Numbers in Random Book Embeddings of Graphs
Abstract: A book embedding of a graph consists of edges embedded on half-planes (“pages”) that are identified along a common line containing the vertices (“spine”) of the book. Using this idea, we can generate a random book embedding of a graph by shuffling the pages of the book. This talk discusses one such model for a random embedding of a graph based on book embeddings. The linking numbers of two component links consisting of “monotonic” cycles are shown to be distributed according to the Eulerian numbers. This is joint work with REU students Yasmin Aguillon, Eric Burkholder, Xingyu Cheng, Spencer Eddins, Emma Harrell, Elijah Leake, and Pedro Morales.
Talk: https://www.youtube.com/watch?v=sjcVybwfPzo&list=PLre7G0QXuTdAuuVIB2J5Id_y9z9knRPl2
Speaker: David Hume (University of Birmingham)
Title: Regular maps, and how to avoid them: growth and asymptotic dimension.
Talk: https://www.youtube.com/watch?v=Pu8pHLiiHyY&list=PLre7G0QXuTdD5XJfKQ16XHH3BMlggYgP4
Speaker: Chandrika Sadanand (Bowdoin College)
Title: Symmetries of flat surfaces of infinite type
Abstract: Flat surfaces have two types of symmetries: isometries and affine symmetries. In this talk we ask “what groups of symmetries are realized by flat structures on a fixed topological surface of infinite type?” Joint with Artigiani, Randecker, Valdez and Weitze-Schmithüsen, we approach these problems using ideas of Aougab, Patel and Vlamis (who answered the analogous question for hyperbolic metrics).
Talk: www.youtube.com/watch?v=gYx0eEXDG30&list=PLre7G0QXuTdDQpOv8Lg9wX4a7qQKWu0ef&index=1 -----------------------------------------------------------------------------------------------------------------------------------------------------
Speaker: Jean-Philippe Burelle (Université de Sherbrooke)
Title: Proper affine actions of surface groups
Abstract: After motivating the study of proper affine actions and giving some background, I will explain a recent result obtained in collaboration with Neza Zager Korenjak: every positive Anosov representation of a surface with non-empty boundary into SO(2n,2n-1) admits a proper affine deformation.
Talk: www.youtube.com/watch?v=6cLsmgMhF64&list=PLre7G0QXuTdDQpOv8Lg9wX4a7qQKWu0ef&index=2
Speaker: Arielle Leitner, (Afeka College of Engineering)
Title: What is a Coarse Space
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Speaker: Giuseppe Martone, (Sam Houston State University)
Title: What is a Train Track