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Spring Semester 2020

Date / Time Speaker Title Location
24 March 2020
15:45-16:45 		Prof. Dr. Harry Baik
KAIST
Event Details

Online Geometry Seminar

Title Normal generators for mapping class groups are abundant in the fibered cone
Speaker, Affiliation Prof. Dr. Harry Baik, KAIST
Date, Time 24 March 2020, 15:45-16:45
Location
Abstract We show that for almost all primitive integral cohomology classes in the fibered cone of a closed fibered hyperbolic 3-manifold, the monodromy normally generates the mapping class group of the fiber. The key idea of the proof is to use Fried’s theory of suspension flow and dynamic blow-up of Mosher. If the time permits, we also discuss the non-existence of the analog of Fried’s continuous extension of the normalized entropy over the fibered face in the case of asymptotic translation lengths on the curve complex.
Normal generators for mapping class groups are abundant in the fibered cone read_more
7 April 2020
15:00-16:00 		Michael Chapman
Hebrew University of Jerusalem
Event Details

Online Geometry Seminar

Title Using the folded apartment to deduce cutoff
Speaker, Affiliation Michael Chapman, Hebrew University of Jerusalem
Date, Time 7 April 2020, 15:00-16:00
Location
Abstract In this talk, we will introduce the PGL Bruhat-Tits building and it's folded apartment. We will show how ideas from Peres-Lubetzky's work on cutoff of simple random walks on Ramanujan graphs can be interpreted by using the folded apartment. We will show a higher-dimensional analog of this idea that enabled Parzanchevski and me to prove cutoff of simple random walks on higher dimensional Ramanujan complexes, giving an example of a family of transitive graphs that exhibit cutoff at a non-optimal time point. All relevant definitions and background will be given in the talk.
Assets Michael Chapman Presentationfile_download
Recording on YouTubefile_download
Using the folded apartment to deduce cutoff read_more
14 April 2020
15:00-16:00 		Dr. Jenya Sapir
SUNY - Binghamton
Event Details

Online Geometry Seminar

Title Tessellations from long geodesics on surfaces
Speaker, Affiliation Dr. Jenya Sapir, SUNY - Binghamton
Date, Time 14 April 2020, 15:00-16:00
Location
Abstract I will talk about joint work of Athreya, Lalley, Wroten and myself. Given a hyperbolic surface S, a typical long geodesic arc will divide the surface into many polygons. We give statistics for the geometry of a typical tessellation. Along the way, we look at how very long geodesic arcs behave in very small balls on the surface.
Assets Jenya Sapir Slidesfile_download
Tessellations from long geodesics on surfacesread_more
22 April 2020
15:45-16:45 		Dr. Maria Dostert
EPFL
Event Details

Online Geometry Seminar

Title Kissing number in non-Euclidean spaces
Speaker, Affiliation Dr. Maria Dostert, EPFL
Date, Time 22 April 2020, 15:45-16:45
Location
Abstract The kissing number is the maximal number of unit spheres which can touch a central unit sphere in Euclidean space without pairwise intersecting in their interior. In this talk we consider an analogous problem in hyperbolic H^n and spherical S^n spaces, for n ≥ 2. We provide upper and lower bounds for the kissing number of congruent radius r > 0 spheres in H^n and S^n. For that purpose, the kissing number is replaced by the kissing function κ_H (n, r), resp. κ_S (n, r), which depends on the dimension n and the radius r. After we obtain some theoretical upper and lower bounds for κ_H (n, r), we study their asymptotic behavior and apply a suitable semidefinite program to obtain upper bounds. Furthermore, we locate the values of κ_S (n, r) over subintervals in [0, π] with relatively high accuracy. This is a joint work with Alexander Kolpakov.
Assets Maria Dostert Slidesfile_download
Kissing number in non-Euclidean spacesread_more
29 April 2020
15:45-16:45 		Dr. Anton Ayzenberg
Higher School of Economics, Russia
Event Details

Online Geometry Seminar

Title Multipolytopes, volume polynomials, duality algebras.
Speaker, Affiliation Dr. Anton Ayzenberg, Higher School of Economics, Russia
Date, Time 29 April 2020, 15:45-16:45
Location
Abstract (based on joint work w. Mikiya Masuda)We are interested in combinatorics of simplicial complexes. The famous g-theorem in this field gives necessary and sufficient conditions for the integral vector (f0, f1, f2,..., fn) to be the face vector of a convex simplicial sphere. The necessary condition in this theorem was proved by Richard Stanley by associating a certain algebra to a convex polytope (namely, the cohomology algebra of the corresponding projective toric variety) and exploiting its Lefschetz property. There are several elementary models of this polytope algebra, one of the simplest being the model constructed from the volume polynomial of a polytope.We study a wider class of combinatorial and geometrical objects: multipolytopes and multifans introduced by Hattori and Masuda. The notions of volume polynomial and its corresponding duality algebra can be extended to multipolytopes. This approach gives elementary explanations of some results on the combinatorics of triangulated manifolds.
Assets Anton Ayzenberg Slidesfile_download
Multipolytopes, volume polynomials, duality algebras. read_more
6 May 2020
15:45-16:45 		Kristóf Huszár
IST, Austria
Event Details

Online Geometry Seminar

Title Combinatorial width parameters for 3-manifolds
Speaker, Affiliation Kristóf Huszár, IST, Austria
Date, Time 6 May 2020, 15:45-16:45
Location
Abstract Algorithms in computational 3-manifold topology typically take a triangulation as an input and return topological information about the underlying 3-manifold. However, extracting the desired information from a triangulation (e.g., evaluating an invariant) is often computationally very expensive. In recent years this complexity barrier has been successfully tackled in some cases by importing ideas from the theory of parameterized algorithms into the realm of 3-manifolds. In this talk we focus on the key combinatorial parameter in this context (i.e., the treewidth of a compact, orientable 3-manifold), and relate it with classical topological invariants (e.g., Heegaard genus) in a quantitative way. Joint work with Jonathan Spreer and Uli Wagner.
Assets Kristof Huszar Slidesfile_download
Kristof Huszar Video (mp4, 62 MB)file_download
Combinatorial width parameters for 3-manifoldsread_more
13 May 2020
13:00-14:00 		Prof. Dr. Clara Löh
Universität Regensburg
Event Details

Online Geometry Seminar

Title p-Adic simplicial volumes
Speaker, Affiliation Prof. Dr. Clara Löh , Universität Regensburg
Date, Time 13 May 2020, 13:00-14:00
Location ONLINE Seminar
Abstract The simplicial volume of an oriented manifold is the l^1-semi-norm of the fundamental class with coefficients in a normed ring. The case of \R-coefficients is Gromov's classicial simplicial volume, which is related to Riemannian geometry. In this talk, we will focus on p-adic versions, i.e., on \Z_p- and \Q_p-coefficients. These p-adic versions are related to p-power torsion in homology. The big picture is still somewhat unclear, but at least we can handle the surface case and there are some nice open problems. This is joint work with Steffen Kionke.
Assets Clara Löh Notesfile_download
p-Adic simplicial volumesread_more
ONLINE Seminar
20 May 2020
15:45-16:45 		Dr. Bram Petri
Sorbonne Université
Event Details

Online Geometry Seminar

Title Statistics of finite degree covers of torus knot complements
Speaker, Affiliation Dr. Bram Petri, Sorbonne Université
Date, Time 20 May 2020, 15:45-16:45
Location ONLINE Seminar
Abstract Abstract: a classical theorem due to Hempel states that the fundamental group of a compact three manifold is residually finite. In other words, the manifold has many finite degree covers. This leads to the question how many such covers there are of a given degree, what their typical properties are and what data of the manifold is encoded in these statistics. In this talk, I will speak about joint work with Elizabeth Baker in which we studied these questions for torus knot complements.
Statistics of finite degree covers of torus knot complementsread_more
ONLINE Seminar
27 May 2020
15:45-16:45 		Dr. Oren Becker
Cambridge University
Event Details

Online Geometry Seminar

Title Stability of approximate group actions
Speaker, Affiliation Dr. Oren Becker, Cambridge University
Date, Time 27 May 2020, 15:45-16:45
Location ONLINE Seminar
Abstract An approximate unitary representation of a group G is a function f from G to U(n) such that f(g_1g_2) is close to f(g_1)f(g_2) for all g_1,g_2. Is every approximate unitary representation just a slight deformation of a unitary representation? The answer depends on G and on the norm on U(n). If G is amenable, the answer is positive for the operator norm on U(n) (Kazhdan '82). The answer remains positive if we use the normalized Hilbert-Schmidt norm and allow a slight change in the dimension n (Gowers-Hatami '15, De Chiffre-Ozawa-Thom '17). For both norms, the answer is negative if G is a nonabelian free group (or a nonelementary word-hyperbolic group). In this talk we shall discuss a similar notion where U(n) is replaced by Sym(n) with the normalized Hamming metric. We study the cases where G is either free, amenable or equal to SL_r(Z), r>=3. When G is finite, a slight variation of our main theorem provides an efficient probabilistic algorithm to determine whether a function f:G->Sym(n) is close to a homomorphism when |G| and n are both large. Based on a joint work with Michael Chapman.
Assets Oren Becker Slidesfile_download
Stability of approximate group actionsread_more
ONLINE Seminar
3 June 2020
15:45-16:45 		Dr. Doron Puder
Tel-Aviv University
Event Details

Online Geometry Seminar

Title Random Covers of Surfaces and Their Asymptotic Statistics
Speaker, Affiliation Dr. Doron Puder, Tel-Aviv University
Date, Time 3 June 2020, 15:45-16:45
Location ONLINE Seminar
Abstract Let \Gamma_g be the fundamental group of the closed orientable surface of genus g, namely \Gamma_g = < a_1,b_1,...,a_g,b_g | [a_1,b_1]...[a_g,b_g]>. Fix an element \gamma in \Gamma_g and let \phi:\Gamma_g \to S_N be a uniformly random homomorphism to the symmetric group S_N. Together with Michael Magee, we develop new techniques to study the random permutation \phi(\gamma), and derive several results which are analogous to well-known results when \Gamma_g is replaced with a free group. My talk will focus on this work - I'll state the results and try to convey some ideas from the proof. This work is also the basis to a second work, with Magee and Naud, in which we study random covers of a fixed hyperbolic surface. There, we show that with high probability, the smallest new eigenvalue of such random cover is at least 3/16-\varepsilon.
Assets Doron Puder notesfile_download
Doron Puder figures to the notesfile_download
Random Covers of Surfaces and Their Asymptotic Statisticsread_more
ONLINE Seminar
11 June 2020
13:00-14:00 		Amitay Kamber
Hebrew University of Jerusalem
Event Details

Online Geometry Seminar

Title Density Theorems and the Ramanujan Property
Speaker, Affiliation Amitay Kamber, Hebrew University of Jerusalem
Date, Time 11 June 2020, 13:00-14:00
Location ONLINE Seminar
Abstract Ramanujan graphs were introduced by Lubotzky, Phillips, and Sarnak, and are graphs whose spectrum is optimal. Recently, a number of results showed that they are optimal in other senses. For example, Peres and Lubetzky proved that random walks on Ramanujan graphs exhibit cutoff.
The Ramanujan property has analogs in other situations - for example, in hyperbolic surfaces or locally symmetric spaces in general. However, the question of whether some natural families of graphs are Ramanujan is extremely difficult, and, moreover, some natural generalizations of it are actually false in some situations. Density estimates of eigenvalues are weaker conditions, which are based on the work of Sarnak and Xue from the 90s. They are meant to replace the Ramanujan property in applications and are far easier to prove. I will survey the definition of this property, explain how it can be proved, and present some open questions.
Assets Amitay Kamber Notesfile_download
Density Theorems and the Ramanujan Propertyread_more
ONLINE Seminar
17 June 2020
15:45-16:45 		Dr. Alena Erchenko
Stony Brook
Event Details

Online Geometry Seminar

Title Flexibility and obstructions in a fixed conformal class
Speaker, Affiliation Dr. Alena Erchenko, Stony Brook
Date, Time 17 June 2020, 15:45-16:45
Location ONLINE Seminar
Abstract In this talk, we discuss the flexibility of metric entropy and restrictions on topological entropy of geodesic flow on closed surfaces of negative Euler characteristic with smooth non-positively curved Riemannian metrics with fixed total area in a fixed conformal class. These results are closely related to the geometry in the considered class of metrics. In particular, we obtain a collar lemma, a thick-thin decomposition, and precompactness in this class. We also discuss some open questions and the extension of some of the results to metrics of fixed total area in a fixed conformal class with no focal points and with certain integral bounds on the positive part of the Gaussian curvature.
Flexibility and obstructions in a fixed conformal classread_more
ONLINE Seminar
24 June 2020
15:45-16:45 		Dr. Emily Stark
University of Utah
Event Details

Online Geometry Seminar

Title Filtered ends and obstructing group actions
Speaker, Affiliation Dr. Emily Stark, University of Utah
Date, Time 24 June 2020, 15:45-16:45
Location ONLINE Seminar
Abstract Studying the topology of a space at infinity offers a powerful perspective in geometric group theory. Filtered ends capture a space at infinity relative to a subspace: one considers complements of increasing neighborhoods of a subcomplex in a simplicial complex. The i-th homology groups of the complements form an inverse system, and the i-th Cech homology group is the associated inverse limit. The goal is then to compute the Cech homology groups of the filtered end and to use homological arguments to study these pairs of spaces. In this talk, I will explain how both goals are possible in the setting of coarse embeddings into coarse PD(n) spaces. Indeed, Kapovich--Kleiner proved a coarse Alexander Duality theorem to compute these deep homology groups. We extend their construction to prove a relative duality theorem, thus developing the homology theory further. As applications, one can use the deep homology groups together with homological arguments to prove that certain groups cannot act properly on a given manifold. This is joint work with Chris Hruska and Hung Cong Tran.
Filtered ends and obstructing group actionsread_more
ONLINE Seminar
1 July 2020
15:45-16:45 		Dr. Federico Vigolo
Weizmann Institute of Science
Event Details

Online Geometry Seminar

Title Of measurable actions and finite graphs
Speaker, Affiliation Dr. Federico Vigolo, Weizmann Institute of Science
Date, Time 1 July 2020, 15:45-16:45
Location ONLINE Seminar
Abstract It is sometimes useful to think of finite graphs as if they were representing actions of finitely generated groups and, viceversa, to 'approximate' group actions by finite graphs. In this talk I will explain a few results - old and new - that were inspired by this philosophy. For the most part, these results concern notions of expansion and go from Margulis's construction of expander graphs to some recent results characterizing expansion in measure in terms of Markov spectral gap.
Of measurable actions and finite graphsread_more
ONLINE Seminar
8 July 2020
15:45-16:45 		Prof. Dr. Thomas Koberda
University of Virginia
Event Details

Online Geometry Seminar

Title Expanders and right-angled Artin groups
Speaker, Affiliation Prof. Dr. Thomas Koberda, University of Virginia
Date, Time 8 July 2020, 15:45-16:45
Location ONLINE Seminar
Abstract Right-angled Artin groups provide a fruitful correspondence between group theory and combinatorics. In this talk, I will discuss a characterization of expander graphs via the group theoretic properties of right-angled Artin groups. In the process, I will define a more general notion of vector space expanders, and connect all these concepts to related objects such as dimension expanders and higher dimensional expanders. This is joint work with R. Flores and D. Kahrobaei.
Assets Thomas Koberda Notesfile_download
Expanders and right-angled Artin groupsread_more
ONLINE Seminar
15 July 2020
15:45-16:45 		Prof. Dr. Fernando Oliveira
Event Details

Online Geometry Seminar

Title A Semidefinite Programming Bound for the Average Kissing Number
Speaker, Affiliation Prof. Dr. Fernando Oliveira,
Date, Time 15 July 2020, 15:45-16:45
Location ONLINE Seminar
Abstract Any packing of finitely many balls (of any sizes) in R^n has a contact graph, in which the vertices are the balls and two vertices are adjacent if the balls touch. Every such contact graph of a packing has an average degree. The average kissing number of R^n is the supremum of the average degrees of contact graphs of ball packings in R^n. I will describe a semidefinite programming approach which provides the best upper bounds for the average kissing number in dimensions 3, ..., 9. (Joint work with Maria Dostert and Alexander Kolpakov.)
A Semidefinite Programming Bound for the Average Kissing Numberread_more
ONLINE Seminar
22 July 2020
15:45-16:45 		Dr. Tyrone Ghaswala
Université du Québec à Montréal
Event Details

Online Geometry Seminar

Title Infinite-type surfaces and the omnipresent arcs
Speaker, Affiliation Dr. Tyrone Ghaswala, Université du Québec à Montréal
Date, Time 22 July 2020, 15:45-16:45
Location ONLINE Seminar
Abstract In the world of finite-type surfaces, one of the key tools to studying the mapping class group is to study its action on the curve graph. The curve graph is a combinatorial object intrinsic to the surface, and its appeal lies in the fact that it is infinite-diameter and δ-hyperbolic. For infinite-type surfaces, the curve graph disappointingly has diameter 2. However, all hope is not lost! In this talk I will introduce the omnipresent arc graph and we will see that for a large collection of infinite-type surfaces, the graph is infinite-diameter and δ-hyperbolic. The talk will feature a new characterization of infinite-type surfaces, which provided the impetus for this project. This is joint work with Federica Fanoni and Alan McLeay. *** After the talk, the speaker will be available to answe questions about his recent NCNGT talk "Promoting circular-orderability to left-orderability". The video is available at the links below.
Assets Promoting circular-orderability to left-orderability - Part 1file_download
Promoting circular-orderability to left-orderability - Part 2file_download
Infinite-type surfaces and the omnipresent arcsread_more
ONLINE Seminar

Organizers: Matthew Cordes, Francesco Fournier Facio, Konstantin Golubev

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