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Autumn Semester 2019

Date / Time Speaker Title Location
19 September 2019
16:00-17:00 		Vasco Schiavo
EPF Lausanne, Switzerland
Event Details

Geometry Graduate Colloquium

Title What is superamenability?
Speaker, Affiliation Vasco Schiavo, EPF Lausanne, Switzerland
Date, Time 19 September 2019, 16:00-17:00
Location HG G 19.2
Abstract Almost every PhD student working in the field of geometric group theory has at least once heard the word amenability and knows that the notion of amenability was suggested by J.v. Neumann in his famous paper "Zur allgemeinen Theory des Masses" in 1929 as a solution for the Banach-Tarski paradox. But this is not completely true; in fact the notion that J.v. Neumann had in mind to give an explanation to the Banach-Tarski paradox was slightly different than the notion of amenability. The original idea of J.v. Neumann is called today superamenability and in this talk we will define it, give some characterizations and explain why it is the good notion to solve the Banach-Tarski paradox. PS: You don't need to know the definition of amenability!
What is superamenability?read_more
HG G 19.2
26 September 2019
16:00-17:00 		Anna Ribelles Pérez
University of Munich, Germany
Event Details

Geometry Graduate Colloquium

Title Handle pushing and distortion in the mapping class group
Speaker, Affiliation Anna Ribelles Pérez, University of Munich, Germany
Date, Time 26 September 2019, 16:00-17:00
Location HG G 19.2
Abstract Given a group G with finite generating set S, we define a norm of an element g of G by measuring its distance to the identity in the Cayley graph Cay(G,S). If G is a subgroup of another finitely generated group G', we can complete S to a finite generating set S' of the ambient group, and consider the norm of any g in Cay(G', S') instead. In the ambient graph we have more generators at our disposal, and can therefore potentially get to g from the identity element in fewer steps. The idea behind distortion is to compare the geometries of both Cayley graphs by quantitatively measuring the efficiency of these shortcuts. In this talk, we will describe some hands-on, geometric methods to certify distortion of certain subgroups of the mapping class group.
Handle pushing and distortion in the mapping class groupread_more
HG G 19.2
3 October 2019
16:00-17:00 		Dr. Matthew Cordes
ETH Zurich, Switzerland
Event Details

Geometry Graduate Colloquium

Title Infinite approximate groups
Speaker, Affiliation Dr. Matthew Cordes, ETH Zurich, Switzerland
Date, Time 3 October 2019, 16:00-17:00
Location HG G 19.2
Abstract An approximate group is a group that is "almost closed" under multiplication. Infinite approximate groups were studied implicitly long before the formal definition. Approximate subgroups of R^n that are Delone sets can be constructed using "cut-and-project" methods and are models for mathematical quasi-crystals. Indeed, Yves Meyer gave a classification of Delone approximate subgroups in R^n. Recently, Björklund and Hartnick have begun a program investigating infinite approximate lattices in locally compact second countable groups using geometric and measurable structures. In the talk I will introduce infinite approximate groups and their geometric aspects using their connection with non-periodic tilings. Time permitting, I will touch on some joint work with Hartnick and Tonic.
Infinite approximate groupsread_more
HG G 19.2
10 October 2019
16:00-17:00 		Emilio Corso
ETH Zurich, Switzerland
Event Details

Geometry Graduate Colloquium

Title Thin groups and Super Approximation: local-global principles in circle packings and continued fractions.
Speaker, Affiliation Emilio Corso, ETH Zurich, Switzerland
Date, Time 10 October 2019, 16:00-17:00
Location HG G 19.2
Abstract The notion of 'thin matrix group' has risen to prominence rather recently, despite ubiquity of examples arising in the study of Fuchsian and Kleinian groups. Previously discarded as irrelevant to arithmetic problems, due to the pathological behaviour of L-functions associated to their automorphic representations, they appear quite naturally in several number-theoretical questions, many of which are geometric in spirit. The purpose of this talk is to illustrate the widespread usage of such groups through the discussion of two long-standing conjectures, the first formulated in the context of Apollonian circle packings, the second emerging from the theory of continued fractions, and historically motivated by Diophantine applications to multidimensional numerical integration. In both examples, the extension of classical results in strong approximation theory to thin groups, under a unifying local-global paradigm borrowed from the language of Hilbert's eleventh problem, allows for substantial, though still incomplete, progress towards the full conjecture.
Thin groups and Super Approximation: local-global principles in circle packings and continued fractions. read_more
HG G 19.2
17 October 2019
16:00-17:00 		Robert Alexander Crowell
ETH Zurich, Switzerland
Event Details

Geometry Graduate Colloquium

Title The Tropical Division Problem and the Minkowski Factorization of Generalized Permutahedra
Speaker, Affiliation Robert Alexander Crowell, ETH Zurich, Switzerland
Date, Time 17 October 2019, 16:00-17:00
Location HG G 19.2
Abstract Generalized permutahedra are a family of polytopes with rich combinatorial structure. They can be defined for any finite reflection group and allow to generalize the notion of matroids to Coxeter matroids. Generalized permutahedra are known to factorize uniquely as signed and weighted Minkowski sums of certain polytopes that act as a basis. We will discuss how the factorization of tropical polynomials can be used to study the factorization of such polytopes. With this perspective we can give a complete description of generalized permutahedra. We conclude the discussion with an open question.
The Tropical Division Problem and the Minkowski Factorization of Generalized Permutahedraread_more
HG G 19.2
24 October 2019
16:00-17:00 		Esmee Te Winkel
University of Warwick, UK
Event Details

Geometry Graduate Colloquium

Title Gromov boundaries of curve graphs
Speaker, Affiliation Esmee Te Winkel, University of Warwick, UK
Date, Time 24 October 2019, 16:00-17:00
Location HG G 19.2
Abstract Let S be a hyperbolic surface. The curve graph of S is a graph whose vertices are curves on S. Edges in the curve graph correspond to disjointness of the associated curves. This combinatorial object has proven to be extremely useful for studying the mapping class group of S. Masur and Minsky showed that the curve graph is hyperbolic. Its Gromov boundary has a description as a space of laminations, due to Klarreich. In the first part of this talk I will introduce curve graphs and laminations. I will explain how ending laminations relate to the boundary of the curve graph. Secondly, I will define the pants graph, a different graph of curves on S. This graph represents more of the structure of the mapping class group, however it is no longer hyperbolic. Time permitting, we might discuss what laminations show up in the 'boundary' of the pants graph.
Gromov boundaries of curve graphsread_more
HG G 19.2
31 October 2019
16:00-17:00 		Davide Spriano
ETH Zurich, Switzerland
Event Details

Geometry Graduate Colloquium

Title An overview of classical Geometric Group Theory
Speaker, Affiliation Davide Spriano, ETH Zurich, Switzerland
Date, Time 31 October 2019, 16:00-17:00
Location HG G 19.2
Abstract In 1911, Dehn postulated the study of groups via algorithmic properties, and observed that they are, at least for surface groups, intimately related with geometry. More than 100 years later, the study of groups via geometric properties is a thriving subject of study. In this colloquium, we will provide an overview of some of the classical techniques used in geometric group theory, starting from Dehn approach to arrive to more modern methods.
An overview of classical Geometric Group Theoryread_more
HG G 19.2
7 November 2019
16:00-17:00 		Giuliano Basso
ETH Zurich, Switzerland
Event Details

Geometry Graduate Colloquium

Title Projection constants
Speaker, Affiliation Giuliano Basso, ETH Zurich, Switzerland
Date, Time 7 November 2019, 16:00-17:00
Location HG G 19.2
Abstract The linear projection constant of two Banach spaces is the smallest norm of a linear projection of the first onto the second. Linear projections constants have been the object of study of many researchers and the literature can be traced back to the classical book by Banach. In the talk, I will overview the rich history of linear projection constants and if times allows I will outline how they may be used to solve non-linear Lipschitz extension problems.
Projection constantsread_more
HG G 19.2
14 November 2019
16:00-17:00 		Gabriele Viaggi
University of Bonn, Germany
Event Details

Geometry Graduate Colloquium

Title An introduction to random surfaces and 3-manifolds
Speaker, Affiliation Gabriele Viaggi, University of Bonn, Germany
Date, Time 14 November 2019, 16:00-17:00
Location HG G 19.2
Abstract It is an interesting problem to study the topology and geometry of low dimensional manifolds from a probabilistic point of view investigating questions such as ``What is the shape of a random surface or 3-manifold?''. In order to make sense of this question, one has to provide a model for such random objects. A natural candidate comes from the fact that every surface and 3-manifold admits a triangulation: One could try to randomly pair the faces of a finite collection of simplices. Following Dunfield and Thurston we explain how this approach works in dimension 2 but fails in dimension 3.
An introduction to random surfaces and 3-manifoldsread_more
HG G 19.2
28 November 2019
16:00-17:00 		Alejandro Vargas
University of Bern, Switzerland
Event Details

Geometry Graduate Colloquium

Title Counting with tropical geometry
Speaker, Affiliation Alejandro Vargas, University of Bern, Switzerland
Date, Time 28 November 2019, 16:00-17:00
Location HG G 19.2
Abstract Tropical geometry is a young branch of algebraic geometry that rose to prominence by showing how to apply tools from polyhedral geometry to calculate invariants of algebraic varieties. In the first half of this talk I give a basic introduction of tropical geometry. In the second half I give three examples of counts in enumerative algebraic geometry that can be studied using tropical geometry: the number of plane curves of degree d and genus g passing through 3d - 1 + g points; the number of lines on a smooth cubic surface; and the number of degree d morphisms from a genus g curve to the projective line when d = g/2 + 1.
Counting with tropical geometryread_more
HG G 19.2
5 December 2019
16:00-17:00 		Levi Ryffel
University of Bern, Switzerland
Event Details

Geometry Graduate Colloquium

Title The Meridional Rank of Knots
Speaker, Affiliation Levi Ryffel, University of Bern, Switzerland
Date, Time 5 December 2019, 16:00-17:00
Location HG G 19.2
Abstract The meridional rank of a knot is the least number of meridians needed to generate the fundamental group of the knot complement. It is conjectured that the meridional rank is equal to the bridge index, a geometrically defined quantity. In this talk we give a technique involving Coxeter groups used to compute the meridional rank of some families of knots. No previous knowledge of knot theory is required.
The Meridional Rank of Knotsread_more
HG G 19.2
* 12 December 2019
16:00-17:00 		Samuel Colvin
University of Bristol, UK
Event Details

Geometry Graduate Colloquium

Title Boundaries of hyperbolic groups
Speaker, Affiliation Samuel Colvin, University of Bristol, UK
Date, Time 12 December 2019, 16:00-17:00
Location HG F 26.3
Abstract A core philosophy of Geometric Group Theory is building connections between disparate areas of mathematics to gain new insight. For instance, by turning a group into a graph, called a Cayley graph, one can study the large-scale geometry of this graph to say something about the algebraic properties of the original group. I will explain another of these connections which links the large-scale geometry of Gromov hyperbolic spaces and the analytical properties of bounded, complete metric spaces, and present some ways this link has been used to study groups.
Boundaries of hyperbolic groupsread_more
HG F 26.3

Note: events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location.

Organizers: Xenia Lorena Flamm, Merlin Incerti-Medici, Davide Spriano

Archive: SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 SS 21 AS 20 SS 20 AS 19 AS 18 SS 18

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