Siddharth Setlur

About

I'm a first year PhD student at the Hodge Insitute, University of Edinburgh supervised by Darrick Lee and Sjoerd Beentjes. I am part of the EPSRC funded Centre for Doctoral Training (CDT) in Algebra, Geometry and Quantum Fields (AGQ).

Previously, I was at ETH Zürich where I obtained my BSc and MSc in Mathematics.

My MSc thesis entitled Optimizing Functions Based on Signed Barcodes was supervised by Sara Kališnik and Steve Oudot, whom I visited as an intern at INRIA Saclay during Fall 2022.

My bachelor's thesis entitled Examining Persistent Homology from Three Different Theoretical Perspectives was supervised by Sara Kališnik.

Research Interests

I'm drawn to areas of mathematics that lie at the intersection of pure and applied mathematics. In particular, I've spent a lot of time working in topological data analysis (TDA), which aims to leverage tools from algebraic topology to analyze data. Currently, I'm interested in appying tools from category theory to causal inference. More recently, I'v taken an interest in interpretability of AI models, in particular the mathematical foundations of mechanistic interpretability.

In Fall 2025, I'm co-organizing the Applied Geometry, Algebra, and Topology in Edinburgh (AGATE) seminar with Djordje Mihajlovic and Darrick Lee.

Publications

Differentiability and Optimization of Multiparameter Persistent Homology

The International Conference on Machine Learning (ICML) 2024. [Video] [Code]
Luis Scoccola^†, Siddharth Setlur^†, David Loiseaux, Mathieu Carrière, and Steve Oudot.

^† denotes first or joint first authorship.

Talks

Talks/presentations that I've given:

I created a tutorial on Persistence Based Losses in Machine Learning as part of the Spring 2025 AATRN+WinCompTop Tutorial-a-thon.
In August 2023 I contributed a talk on Signed Barcodes for Multidimensional Persistence at the BIREP Summer School on persistence modules—The Interplay of Representation Theory and Topological Data Analysis.
As part of a reading course, I gave a talk on the method of interlacing polynomials and their application to building bipartite Ramanujan graphs of all degrees to Afonso Bandeira's research group . It was based on a paper by Marcus, Spielman and Srivatsava.
I gave a talk at ZUCMAP 2022, where I used examples and a recent application to introduce persistent homology in an intuitive manner to undergraduate students. Toward the end I also (briefly) spoke on persistence modules, graded \(F[t]-\) modules and the existence of persistence barcodes. Here are my (handwritten) slides and a recording.

Teaching

Spring 2025, University of Edinburgh. TA for Advanced Research Computing.
Fall 2023, ETH Zürich. TA for Analysis 1 (in German).

Notes

A collection of expository notes I've written:

During a reading course on expander graphs supervised by Afonso Bandeira, I wrote an exposition about the Alon-Bopanna bound . The bound motivates the definition of Ramanujan graphs and is critical to the theory of expander graphs.
My final project for Algebraic Geometery 2 introduces Whitney stratifications with a view toward intersection homology . It draws from various sources and describes why algebraic varieties admit Whitney stratifications and the role these stratifications play in the definition of intersection homology.

Other Activities

In Spring 2022, I helped organize the Zurich Undergraduate Colloquium in Mathematics and Physics.