# Two-part lecture series: Topology of a space from a random data sample | Extremal Morse critical points of a random distance function

By Sagnik Saha in Talk Series

September 26, 2021

It gives us immense pleasure to announce the next lecture in our ‘Two-part Lecture Series’, to be jointly hosted by CMIT and the School of Mathematics, IISER Thiruvananthapuram.

Kindly note that the two-part lectures will be delivered in a manner to cover the necessary basics in the first part of the talk, while the second part builds upon the same and continues.

This time, the two-part lecture will be delivered by Prof. D. Yogeshwaran, Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, Bangalore, on September 27 and September 29, 2021, at 2:40 PM. Please find the talk details below.

**Speaker**: Prof. D. Yogeshwaran, Indian Statistical Institute, Bangalore.

About the speaker: Prof. D. Yogeshwaran is an Associate Professor at Theoretical Statistics and Mathematics Unit, Indian Statistical Institute (Bangalore) working in probability(specifically, stochastic geometry) and interested in Random Topology. He completed his Ph.D. in Applied Probability from Universite’ Pierre et Marie Curie 2016 under Prof. Francois Baccelli and Prof. Bartek Blaszczyszyn. One of his latest publication was on “An analysis of probabilistic forwarding of coded packets on random geometric graphs.”

**Part I** (Organised and hosted by CMIT)

Title: Topology of a space from a random data sample.

Venue and time: Google Meet (online) | 02:40 PM (GMT +5:30), Monday, September 27, 2021.

Abstract: Given a data sample of $n$ I.I.D. random points on a metric space (say M), what can we infer about the topology of M? This is one of the basic questions in topological data analysis. In this talk, I will discuss what we mean by “inferring the topology” and some theoretical results towards the same. In particular, we will focus on the Morse-theoretic approach which has proved extremely promising. In the latter approach, topology can be “inferred” via study of critical points of the distance function to the data sample. We will see some basic results on critical points with the more finer results postponed to the second talk. I shall assume basic knowledge of probability, topology and multivariate calculus. The remaining topological notions shall be introduced heuristically in the talk.

Chair for the Session: G Ananthakrishna, BSMS 5th Year, School of Mathematics, IISER Thiruvananthapuram.

**Part II** (Organised and hosted by SoM, IISER Thiruvananthapuram)

Title: Extremal Morse critical points of a random distance function.

Venue and time: Google Meet (online) | 02:40 PM (GMT +5:30), Wednesday, September 29, 2021

Abstract: Given a random point-set (data sample) on a torus, we consider the distance function to this point-set and critical points of the distance function. The question is motivated by applications to topological data analysis described in the first talk. We shall see some recent results about the extremal Morse critical points of the distance function to Poisson points on a Torus. These results will be deduced from our abstract Poisson process approximation result that is of use in various other applications in stochastic geometry. This is a joint work with Omer Bobrowski (Technion, Israel) and Matthias Schulte (TU Hamburg, Germany).

Chair for the Session: Prof. Utpal Manna, School of Mathematics, IISER Thiruvananthapuram.

**Registration**: Students of IISER Thiruvananthapuram do not require registration for the talks. Participants from outside IISER Thiruvananthapuram can register here: link

All are cordially invited to attend the talks over Google Meet. Please join us in large numbers, we hope to see you all there! For any further queries, mail us at mathsclub@iisertvm.ac.in.

- Posted on:
- September 26, 2021

- Length:
- 3 minute read, 556 words

- Categories:
- Talk Series

- Series:
- Two-part talks

- See Also:
- Semi-direct product of categories and a Schur’s lemma for categorical representations (Part II)
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- Two-part lecture series: Development of the Theory of Equations | Polynomials, Matrices, and Linear Recurrences over Galois Fields