Top Flavours

University of Warwick (ONLINE)

17-18 June 2021

Welcome to TopFlavours 2021!

TopFlavours (Topology in Distinct Flavours) is a 2-day conference that will bring together early-career researchers in both pure and applied topology. It will take place online Thursday 17th - Friday 18th of June.

Registration is now open.

There will be two 1-hour lectures by the invited speakers.

Participants have the chance to give a 25-minute contributed talk or participate in the Gong Show.

invited speakers

Dr. Irakli Patchkoria

University of Aberdeen.

Title: Classification of module spectra and Franke’s algebraicity conjecture

Abstract: This is all joint work with Piotr Pstrągowski. Given an E_1-ring R such that the graded homotopy ring pi_*R is q-sparse and the global projective dimension d of pi_*R is less than q, we show that the homotopy (q-d)-category of Mod(R) is equivalent to the homotopy (q-d)-category of differential graded modules over pi_*R. Thus for such E_1-rings the homotopy theory of their modules is algebraic up to the level (q-d). Examples include appropriate Morava K-theories, Johnson-Wilson theories, truncated Brown-Peterson theories and some variations of topological K-theory spectra. We also show that the result is optimal in the sense that (q-d) is the best possible level in general where algebraicity happens. At the end of the talk we will outline how the results for modules can be generalized to the settings where we do not have compact projective generators. This proves Franke’s algebraicity conjecture which provides a general result when certain nice homology theories provide algebraic models for homotopy theories.

Dr. Gregory Henselman-Petrusek

University of Oxford

Title: Optimal cycle representatives in persistent homology

Abstract: Persistent homology has emerged as a powerful tool for understanding complex data.

However, interpretation and use of persistent shape statistics often hinges on a (theoretically) intractable inverse problem: selection of "good" cycle representatives in homology.

In this talk, we'll introduce/recall the basic notions of persistent homology, as well as some recent scientific applications. We'll discuss what makes cycle representatives "good" in this context, and explain recent empirical results that show good representatives can almost always be found by "guessing." We'll then explore some beautiful and interesting properties of optimal generators observed empirically, in real-world data.

About us

TopFlavours 2020 organizers:

There have been a number of UK based early-career topology meetings in the past. Some of the previous ones are listed below.

2019 Sheffield, ECTR (Early Career Topology Researchers)
2017 Sheffield, EL:ECTRIC (Ecstatic Lectures: Early Career Topology Researchers In Conference)
2016 ECSTATIC (Early Career Stage Topologists At Imperial College)

CONTACT

If you have any queries, please do not hesitate to get in contact:

TorrasCasasA (at) cardiff.ac.uk
Igor.Sikora (at) warwick.ac.uk