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Spring Semester 2024

Date / Time Speaker Title Location
28 February 2024
15:30-16:30 		Dr. Miguel Orbegozo Rodriguez
ETH Zurich, Switzerland
Details

Geometry Seminar

Title Right-veering diffeomorphisms and contact geometry
Speaker, Affiliation Dr. Miguel Orbegozo Rodriguez, ETH Zurich, Switzerland
Date, Time 28 February 2024, 15:30-16:30
Location HG G 43
Abstract Although contact geometry has its origins in the 19th century, it wasn't until the 1970s that it began to be studied via topological methods. More recently, in 2002, the Giroux correspondence theorem established, in dimension 3, a close relationship between contact manifolds and open book decompositions (i.e fibered links). This means that properties of contact 3-manifolds can be studied by studying properties of mapping classes of surfaces. In this talk I will start by providing an overview to contact geometry in dimension 3, and introducing one of the most relevant properties, the dichotomy between tight and overtwisted contact structures. This can be studied, by a result of Honda-Kazez-Matic, via right-veering diffeomorphisms of surfaces. I will show that this property is not easy to detect in general before presenting a combinatorial way of detecting it.
Right-veering diffeomorphisms and contact geometryread_more
HG G 43
13 March 2024
15:30-16:30 		Laura Marino
Institut de Mathématiques de Jussieu-Paris Rive Gauche
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Geometry Seminar

Title Gordian distance bounds from Khovanov homology
Speaker, Affiliation Laura Marino, Institut de Mathématiques de Jussieu-Paris Rive Gauche
Date, Time 13 March 2024, 15:30-16:30
Location HG G 43
Abstract The Gordian distance u(K,K') between two knots K and K' is defined as the minimal number of crossing changes needed to relate K and K'. The unknotting number of a knot K, a classical yet hard to compute knot invariant, arises as the Gordian distance between K and the trivial knot. Several lower bounds for both invariants exist. A well-known bound for the unknotting number is given by the Rasmussen invariant, which is extracted from Khovanov homology, a bigraded chain complex associated to a knot up to chain homotopy equivalence. In this talk, I will introduce a new lower bound for the Gordian distance, \lambda, coming from Khovanov homology. After introducing all the relevant ingredients I will present some results about \lambda. In particular, \lambda turns out to be sharper than the Rasmussen invariant as a lower bound for the unknotting number. This is based on joint work with Lukas Lewark and Claudius Zibrowius.
Gordian distance bounds from Khovanov homologyread_more
HG G 43
20 March 2024
15:30-16:30 		PD Dr. Menny Akka Ginosar
ETH Zurich, Switzerland
Details

Geometry Seminar

Title Seifert surfaces, planes in four space, and Gauss composition
Speaker, Affiliation PD Dr. Menny Akka Ginosar, ETH Zurich, Switzerland
Date, Time 20 March 2024, 15:30-16:30
Location HG G 43
Abstract In this talk I will present results from a recent joint work with Peter Feller, Alison Beth Miller and Andreas Wieser (https://arxiv.org/abs/2311.17746). I will first present a geometric approach to the classical Gauss composition of binary quadratic forms. The new method is based on a parameterisation of two-dimensional subspaces of the space of 2x2 matrices and provides an easy to remember way to compute the Gauss composition. This approach naturally leads to a robust construction of pairs of Seifert surfaces for the same knot that are non-isotopic in the 4-ball. It also provides a complete characterisation of the Seifert forms of such disjoint Seifert surfaces. These topological results will be discussed in the second part of the talk. No background in number theory or knot theory will be assumed.
Seifert surfaces, planes in four space, and Gauss compositionread_more
HG G 43
10 April 2024
 Shahar Mendelson
FIM (ANU)
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Geometry Seminar

Title Special lecture on the majorizing measures theorem on the occasion of the announcement of the awarding of the Abel prize to Michel Talagrand
Speaker, Affiliation Shahar Mendelson, FIM (ANU)
Date, Time 10 April 2024,
Location HG G 43
More information https://math.ethz.ch/news-and-events/events/research-seminars/daco-seminar.html
Special lecture on the majorizing measures theorem on the occasion of the announcement of the awarding of the Abel prize to Michel Talagrandread_more
HG G 43
17 April 2024
15:30-16:30 		Isacco Nonino
University of Glasgow
Details

Geometry Seminar

Title Smooth structures on non-compact 4-manifolds
Speaker, Affiliation Isacco Nonino, University of Glasgow
Date, Time 17 April 2024, 15:30-16:30
Location HG G 43
Abstract When studying smooth structures on a 4-dimensional topological manifold M, there are three main topics one has to cover: existence, uniqueness and behavior of their diffeotopy groups. I will explain the reasons why the 4 dimensional case is so interesting and wild, and remark the striking difference between the compact and non-compact settings. I will then give an overview on the recent work on diffeotopy groups of exotic smoothings of R4, and show how the results were generalized to a wider class of non-compact 4 manifolds.
Smooth structures on non-compact 4-manifoldsread_more
HG G 43
24 April 2024
15:30-16:30 		Tanushree Shah
University of Vienna
Details

Geometry Seminar

Title Contact structures on 3-manifolds
Speaker, Affiliation Tanushree Shah, University of Vienna
Date, Time 24 April 2024, 15:30-16:30
Location HG G 43
Abstract We will start with friendly introduction to contact structures. They come in two flavors: tight and overtwisted. Classification of overtwisted contact structures is well understood as opposed to tight contact structures. We will look into recent techniques developed to study these by understanding special knots(legendrian knots) in overtwisted 3 manifolds. We will look at what more classification results can we hope to get using the current techniques and what is far-fetched.
Contact structures on 3-manifoldsread_more
HG G 43
1 May 2024
Details

Geometry Seminar

Title Cantonal Holiday (Tag der Arbeit)
Speaker, Affiliation
Date, Time 1 May 2024,
Location HG G 43
Cantonal Holiday (Tag der Arbeit)
HG G 43
8 May 2024
17:15-18:30 		PD Dr. Menny Akka Ginosar
ETH Zurich, Switzerland
Details

Geometry Seminar

Title Inagural lecture of Menny Akka
Speaker, Affiliation PD Dr. Menny Akka Ginosar, ETH Zurich, Switzerland
Date, Time 8 May 2024, 17:15-18:30
Location HG G 19.1
More information https://ethz.ch/en/news-and-events/events/details.homogeneous-spaces-a-playground-for-arithmetic-dynamics-groups-and-geometry.70141.html
Inagural lecture of Menny Akkaread_more
HG G 19.1
15 May 2024
15:30-16:30 		Alexandra Kjuchukova
University of Notre Dame
Details

Geometry Seminar

Title Slice and ribbon obstructions from irregular branched covers of knots
Speaker, Affiliation Alexandra Kjuchukova, University of Notre Dame
Date, Time 15 May 2024, 15:30-16:30
Location HG G 43
Abstract I will give an introduction on how to obtain invariants of a knot $K$ from irregular covers of $S^3$ branched along $K$. In an extended example, I will show how examining a particular unknot in a Seifert surface for a twist knot $K_n$ can in one infinitude of cases detect that $K_n$ is not ribbon and, in another, that it is not slice. The talk will draw on old, recent and ongoing works with Cahn, Orr and Shaneson.
Slice and ribbon obstructions from irregular branched covers of knotsread_more
HG G 43
22 May 2024
15:30-16:30 		Harald Helfgott
CNRS
Details

Geometry Seminar

Title Expansion, divisibility and parity
Speaker, Affiliation Harald Helfgott, CNRS
Date, Time 22 May 2024, 15:30-16:30
Location HG G 43
Abstract We will discuss a graph that encodes the divisibility properties of integers by primes. We will prove that this graph has a strong local expander property almost everywhere. We then obtain several consequences in number theory, beyond the traditional parity barrier, by combining the main result with Matomaki-Radziwill. (This is joint work with M. Radziwill.) For instance: for lambda the Liouville function (that is, the completely multiplicative function with lambda(p) = -1 for every prime), (1/\log x) \sum_{n\leq x} lambda(n) \lambda(n+1)/n = O(1/sqrt(log log x)), which is stronger than well-known results by Tao and Tao-Teravainen. We also manage to prove, for example, that lambda(n+1) averages to 0 at almost all scales when n restricted to have a specific number of prime divisors Omega(n)=k, for any "popular" value of k (that is, k = log log N + O(sqrt(log log N)) for n<=N). We shall also discuss a recent generalization by C. Pilatte, who has succeeded in proving that a graph with edges that are rough integers, rather than primes, also has a strong local expander property almost everywhere, following the same strategy. As a result, he has obtained a bound with O(1/(log x)^c) instead of O(1/sqrt(log log x)) in the above, as well as other improvements in consequences across the board.
Expansion, divisibility and parityread_more
HG G 43
29 May 2024
15:30-16:30 		Dr. Christian Urech
ETH Zurich, Switzerland
Details

Geometry Seminar

Title Cremona groups and CAT(0) cube complexes
Speaker, Affiliation Dr. Christian Urech, ETH Zurich, Switzerland
Date, Time 29 May 2024, 15:30-16:30
Location HG G 43
Abstract The Cremona group of rank n is the group of birational transformations of the projective n-space. Cremona groups have been studied for around 150 years and attracted a lot of attention in the last decades due to their rich group theoretical and dynamical properties. In this talk, I will first give a short introduction to Cremona groups (no prior knowledge of algebraic geometry assumed). Then I will present natural constructions of CAT(0) cube complexes on which Cremona groups act by isometries, and explain how we can deduce old and new results from this action. This is joint work with Anne Lonjou.
Cremona groups and CAT(0) cube complexesread_more
HG G 43

Organisers: Marc Burger, Manfred Einsiedler, Peter Feller, Alessandra Iozzi, Urs Lang

Archive: 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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