Baby geometri

Geometry and Topology Seminars

University of Pisa - Scuola Normale Superiore

Extremely rough outline of Embedding Calculus


Hyeonhee Jin

(MPIM Bonn)

  • March 14th
  • 16.00
  • Aula Riunioni - Dipartimento di Matematica + Teams
Goodwillie-Weiss embedding calculus can be used to study diffeomorphism grous, finite type invariants, and isotopy classes of surfaces in 4-manifolds. We aim to give a rough outline of the theory.

Coming soon

Title
Speaker
Language
March 21st
TBA
Viola Giovannini
(University of Luxembourg and University of Pisa)
ITA
TBA

Seminars will be in-person.

Minicourses


Lukas Lewark

University of Regensburg

An introduction to Khovanov homology and its applications

The Jones polynomial introduced in 1984 was the first so-called quantum invariant in knot theory. It associates to every knot a polynomial, which is not defined in a geometric but rather in a diagrammatic way. Fifteen years later, Khovanov homology was introduced as a so-called categorification of the Jones polynomial. In spite of its combinatoric origins, Khovanov homology has an ever-growing number of geometric applications in knot theory. In this mini-course, we will first work through the detailed construction of Khovanov homology, following a modern version of Bar-Natan’s tangle setup. Then, we will see some of the applications, such as Rasmussen’s proof of the Milnor conjecture (regarding the unknotting number of torus knots). Previous knowledge of knot theory and homological algebra is helpful, but will not be required.

Schedule

February 27th
11.00
Aula Riunioni - Dipartimento di Matematica
February 28th
11.00
Aula Riunioni - Dipartimento di Matematica
March 1st
11.00
Aula Riunioni - Dipartimento di Matematica
March 3rd
9.00
Aula Riunioni - Dipartimento di Matematica


Alessandro Sisto

Heriot-Watt University

Mapping Class Groups and relatives: hierarchically hyperbolic spaces

Hyperbolic spaces and groups were introduced by Gromov and have been studied extensively over the past few decades from a huge variety of points of view, and with applications to various fields such as the study of hyperbolic 3-manifolds. Many groups of interest in geometry and topology, most notably mapping class groups, are however not hyperbolic, and it is therefore natural to try to generalise the notion of the hyperbolic group to encompass as many of these examples as possible. The notion of hierarchical hyperbolicity, inspired by the deep work of Masur and Minsky, achieves just that. Roughly speaking, a hierarchically hyperbolic structure on a metric space or group is a coordinate system where the coordinates take values in hyperbolic spaces. I will give an introduction to hierarchically hyperbolic spaces, thereby describing the (coarse) geometry of mapping class groups, and explain what this kind of structure is good for and how to show that a given space or group is hyerarchical hyperbolic.

Schedule

March 1st
14.00
Aula Riunioni - Dipartimento di Matematica
March 2nd
11.00
Aula Riunioni - Dipartimento di Matematica
March 3rd
14.00
Aula Riunioni - Dipartimento di Matematica

Archive


Here you can find abstracts of the past seminars. You can also search for the ones from the previous editions!

The BabyGs:


The Baby Geometri (or BabyGs to their friends) are a group of PhD students from the University of Pisa (UNIPI) and the Scuola Normale Superiore (SNS). This site is intended to keep track of the seminars they organize. These are informal seminars mainly addressed to master or PhD students, about classical or research topics. Since the audience is really diversified, these seminars often start with a basic introduction to the area that can be appreciated by early-Master students. In 2021 we started keeping the seminars online as well, because of the pandemic. For the 2021/22 season, the BabyGs' organizers are...
Giuseppe

I study simplicial volume of compact and non-compact manifolds and bounded cohomology. I like interactions between algebra and topology.

Contact me!
Diego

I study low dimensional topology and in particular I am getting interested in the L-space conjecture.

Contact me!
Alice

I am mostly interested in low dimensional topology, especially knot theory.

Contact me!
Giovanni

I'm interested in Hyperbolic Geometry, with a particular stress to manifolds built by gluing polytopes.

Contact me!
Filippo

I am mainly interested in smooth 4-manifolds and related topics.

Contact me!

Be our guest


If you want to hold a seminar, or if you just want to chat, contact us!
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babygeometri@cs.dm.unipi.it

Credits


We thank the "Team per la Trasformazione Digitale" and all the people of Bootstrap Italia for the code. In particular we want to thank Riccardo for the help!