Geometry seminar

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Date / Time

Speaker

Title

Location

28 February 2024
15:30-16:30

Dr. Miguel Orbegozo Rodriguez
ETH Zurich, Switzerland

Event Details

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

13 March 2024
15:30-16:30

Laura Marino
Institut de Mathématiques de Jussieu-Paris Rive Gauche

Event Details

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

20 March 2024
15:30-16:30

PD Dr. Menny Akka Ginosar
ETH Zurich, Switzerland

Event Details

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

10 April 2024

Shahar Mendelson
FIM (ANU)

Event Details

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

17 April 2024
15:30-16:30

Isacco Nonino
University of Glasgow

Event Details

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.