Raghuwansh Raj

🏛️ Hausdorff Trimester Program - Geometric Statistics 2026

Sat, 12 Dec 2026 00:00:00 +0000

I am honored to be invited to participate in the Dual Trimester Program on Geometric Statistics: theory, application, and computation at the Hausdorff Research Institute for Mathematics (HIM) in Bonn, Germany from September 14 to December 12, 2026.

This is an exceptional opportunity to engage with leading mathematicians and researchers working at the forefront of geometric and statistical methods in mathematics.

Program Overview

The trimester program spans three months and includes multiple schools, workshops, and conferences:

School on Geometric Statistics

September 14-18, 2026

Foundational lectures on geometric statistics
Theory and applications of statistics on manifolds
Computational methods for geometric data analysis

Workshop: Stochastic Analysis, Statistics, and Computation on Manifolds and Singular Spaces

October 12-16, 2026

Advanced topics in stochastic analysis
Statistical methods on curved and singular spaces
Computational algorithms and implementations

Workshop: Geometry, Topology, and Learning on Smooth and Singular Spaces

November 9-13, 2026

Learning theory perspectives on geometric problems
Topological data analysis methods
Applications to machine learning on manifolds

Conference: Interactions of Statistics and Geometry III (ISAG III)

December 7-11, 2026

Presentation of cutting-edge research
Dialogue between statisticians and geometers
Exploring new directions in geometric statistics

About Hausdorff Research Institute for Mathematics

The Hausdorff Research Institute for Mathematics (HIM) is an international center devoted to advancing research in mathematics and mathematical economics. HIM brings together:

A critical mass of expertise and scientists at one location
An inspiring mathematical atmosphere
Opportunity for mathematicians to work on challenging projects undisturbed
Direct discussion with leading experts in their field

This unique environment has consistently led to substantial output of research results of the highest quality, with many projects initiated, pursued, and sometimes completed during HIM programs.

Program Goals

By participating in this trimester program, I aim to:

Deepen knowledge in geometric statistics and their applications
Explore connections between geometry, topology, and machine learning
Engage with world-leading experts in the field
Collaborate on research projects addressing fundamental problems
Build connections with the international mathematics community

Research Interests Alignment

The program aligns perfectly with my research interests in:

Geometric and topological deep learning
Mathematical foundations of GNNs and topological methods
Applications of geometry to machine learning
Algebraic and differential geometric approaches

Learn More

For more information about HIM and the Geometric Statistics program:

Geometric Statistics Trimester Program

About HIM

Hausdorff Research Institute

📐 London Geometry and Machine Learning (LOGML) Summer School 2026

Fri, 17 Jul 2026 00:00:00 +0000

I had the privilege to attend the London Geometry and Machine Learning (LOGML) Summer School 2026 held at Imperial College London from July 13-17, 2026.

This was my first summer school during my PhD journey, and it was an incredible opportunity to engage with the vibrant community of doctoral students, researchers, and experts working at the intersection of mathematics, geometry, and machine learning.

Program Overview

The summer school featured intensive lectures and tutorials covering:

Graph Representation Learning - Understanding and learning from graph-structured data
Learning Graphs from Data - Discovering graph structures from raw data
Equivariant Machine Learning - Building models that respect symmetries and invariances
Algebraic Geometry in Deep Learning - Mathematical foundations for neural network design
Discrete Structures for 3D Geometric Learning - Geometric approaches to 3D data
Graph Foundation Models - Pre-trained models for graph-based tasks
Physics-Informed Graph Neural Networks - Incorporating physical priors into GNNs

Key Learnings

I was particularly inspired by lectures from world-leading experts including:

Xiaowen Dong - Graph signal processing and learning
Dorina Thanou - Geometric methods in machine learning
Stefanie Jegelka - Graph neural networks and expressiveness
Olga Fink - Physics-informed machine learning

Their discussions on mathematical and physical priors in building graphical models, and the integration of AI in physical and health sciences, were enlightening.

Collaborative Project

During the summer school, I had the opportunity to work on a group project exploring:

Canonicalization of 3D Molecular Point Clouds - Collaborating with mentor Snir Hordan, we investigated how symmetry-aware preprocessing can help conventional neural architectures learn from molecular geometry more efficiently.

This work bridges the gap between geometric deep learning theory and practical molecular applications.

Key Takeaways

Deepened understanding of geometric and topological approaches in deep learning
Networked with talented researchers from institutions worldwide
Gained hands-on experience with cutting-edge techniques in equivariant learning
Explored applications in molecular geometry and 3D learning
Built connections with mentors and peers in the GDL community

Gratitude

I’m grateful to the LOGML Organizers, especially Dr. Lennart Bastian, the speakers, mentors, and fellow participants for creating such an intellectually stimulating and collaborative environment.

Learn More

For more information about LOGML:

Visit LOGML Official Website

Imperial College London

🧭 Spherical Harmonics and the Spherical Coordinate System

Mon, 16 Mar 2026 00:00:00 +0000

Spherical harmonics are one of the most important mathematical tools for analyzing functions defined on the surface of a sphere. They appear in many areas including quantum mechanics, geophysics, computer graphics, and modern geometric deep learning.

This post introduces the spherical coordinate system and explains how spherical harmonics arise naturally when studying functions on the sphere.

The Spherical Coordinate System

In three-dimensional space, we often represent points using Cartesian coordinates

\[ (x, y, z) \]

However, when working with spherical objects or rotationally symmetric problems, it is more natural to use spherical coordinates:

\[ (r, \theta, \phi) \]

where:

$r$ is the distance from the origin
$\theta$ is the polar angle (measured from the z-axis)
$\phi$ is the azimuthal angle (measured in the xy-plane)

The relationship between Cartesian and spherical coordinates is:

\[ x = r \sin\theta \cos\phi \]\[ y = r \sin\theta \sin\phi \]\[ z = r \cos\theta \]

This coordinate system is particularly useful when studying functions defined on the surface of a sphere, where $r$ is constant.

What Are Spherical Harmonics?

Spherical harmonics are a set of special functions defined on the sphere that form an orthogonal basis for functions on the sphere.

They are analogous to Fourier series, but instead of decomposing functions on a circle, they decompose functions on a sphere.

A spherical harmonic is usually written as

\[ Y_l^m(\theta, \phi) \]

where:

$l$ is the degree
$m$ is the order
$-l \le m \le l$

These functions arise as solutions to Laplace’s equation in spherical coordinates.

Why Spherical Harmonics Matter

Spherical harmonics appear in many scientific fields:

Physics

They are used to solve:

Schrödinger equation
gravitational potentials
electromagnetic fields

Computer Graphics

They are used for:

lighting models
environment maps
rendering reflections

Geometric Deep Learning

Modern AI models that operate on spheres, rotations, or 3D structures often rely on spherical harmonics for:

equivariant neural networks
molecular modeling
3D vision

Visualizing the Harmonics

Each spherical harmonic corresponds to a particular frequency pattern on the sphere.

Low-degree harmonics represent smooth variations, while higher-degree harmonics represent finer oscillations.

Conceptually:

🌐 Attending AWS Summit Paris 2024

Wed, 10 Apr 2024 00:00:00 +0000

Recently, I had the opportunity to attend AWS Summit Paris on behalf of my team at Stellantis France.

It was my first time participating in an event of this scale, and it was an incredible experience to be immersed in the tech ecosystem of France and Europe.

The summit was a full-day event with more than 50 companies showcasing their technologies and solutions through talks, presentations, and booths.

I had the chance to meet and listen to professionals working across many domains including:

Cloud infrastructure
Encryption and cybersecurity
Automotive technologies
SaaS and PaaS platforms
Supply chain systems
Artificial intelligence and machine learning

A major theme of this year’s summit was Large Language Models (LLMs) and the Retrieval Augmented Generation (RAG) approach used to address some of their practical challenges.

It was fascinating to see how organizations are integrating AI-driven solutions with AWS cloud infrastructure to build scalable and intelligent systems.

The event provided a great opportunity to learn about new developments in cloud computing, AI, and industry applications, while also connecting with professionals from across the European tech community.

Event Highlights

50+ companies presenting cutting-edge technologies
Focus on LLMs and RAG architectures
Discussions on cloud-native AI systems
Insights into automotive and industrial AI applications
Networking with professionals from across Europe

Learn More

You can find more details about the summit here:

Visit AWS Summit Paris

🌐 AWS Summit Paris 2024

Wed, 10 Apr 2024 00:00:00 +0000

Recently, I had the opportunity to attend AWS Summit Paris on behalf of my team at Stellantis France.

It was my first time participating in an event of this scale, and it was an incredible experience to be immersed in the tech ecosystem of France and Europe.

The summit was a full-day event with more than 50 companies showcasing their technologies and solutions through talks, presentations, and booths.

I had the chance to meet and listen to professionals working across many domains including:

Cloud infrastructure
Encryption and cybersecurity
Automotive technologies
SaaS and PaaS platforms
Supply chain systems
Artificial intelligence and machine learning

A major theme of this year’s summit was Large Language Models (LLMs) and the Retrieval Augmented Generation (RAG) approach used to address some of their practical challenges.

It was fascinating to see how organizations are integrating AI-driven solutions with AWS cloud infrastructure to build scalable and intelligent systems.

Event Highlights

50+ companies presenting cutting-edge technologies
Focus on LLMs and RAG architectures
Discussions on cloud-native AI systems
Insights into automotive and industrial AI applications
Networking with professionals across Europe

Learn More

Visit AWS Summit Paris

Example Talk: Recent Work

Mon, 01 Jan 2024 00:00:00 +0000

Example Talk

Dr. Alex Johnson · Meta AI

Research Overview

Multimodal LLMs
Efficient training
Responsible AI

Code & Math

def score(x: int) -> int:
 return x * x

$$ E = mc^2 $$

Dual Column Layout

Left Column

Point A
Point B
Point C

Right Column

Detail 1
Detail 2
Detail 3

Main Content (2/3 width)

This column takes up twice the space of the right column.

def example():
 return "code works too"

Note
Key points in smaller column

Image + Text Layout

Results

95% accuracy
10x faster inference
Lower memory usage

Breakthrough!

Speaker Notes

Press S to open presenter view with notes!

This slide has hidden speaker notes below.

Note:

This is a speaker note (only visible in presenter view)
Press S key to open presenter console
Perfect for remembering key talking points
Can include reminders, timing, references
Supports Markdown formatting too!

Progressive Reveals

Content appears step-by-step:

First point appears Then the second point Finally the conclusion This one can be highlighted!

Note: Use fragments to control pacing and maintain audience attention. Each fragment appears on click.

Diagrams with Mermaid

graph LR A[Research Question] --> B{Hypothesis} B -->|Valid| C[Experiment] B -->|Invalid| D[Revise] C --> E[Analyze Data] E --> F{Significant?} F -->|Yes| G[Publish] F -->|No| D

Perfect for: Workflows, architectures, processes

Note: Mermaid diagrams are created from simple text. They’re version-controllable and edit anywhere!

Research Results

Model	Accuracy	Speed	Memory
Baseline	87.3%	1.0x	2GB
Ours (v1)	92.1%	1.5x	1.8GB
Ours (v2)	95.8%	2.3x	1.2GB

Key Finding: 8.5% improvement over baseline with 40% memory reduction

Note: Tables are perfect for comparative results. Markdown tables are simple and version-control friendly.

Custom Backgrounds

This slide has a blue background!

You can customize:

Background colors
Background images
Gradients
Videos (yes, really!)

Use {{< slide background-color="#hex" >}}

There’s more content below! ⬇️

Press the Down Arrow to see substeps.

Note: This demonstrates Reveal.js’s vertical slide feature. Great for optional details or deep dives.

Substep 1: Details

This is additional content in a vertical stack.

Navigate down for more, or right to skip to next topic →

Substep 2: More Details

Even more detailed information.

Press Up Arrow to go back, or Right Arrow to continue.

Citations & Quotes

“The best way to predict the future is to invent it.”

— Alan Kay

Or reference research:

Recent work by Smith et al. (2024) demonstrates that Markdown-based slides improve reproducibility by 78% compared to proprietary formats¹.

Media: YouTube Videos

Note: Embed YouTube videos with just the video ID. Perfect for demos, tutorials, or interviews.

Media: All Options

Embed various media types with simple shortcodes:

YouTube: {{< youtube VIDEO_ID >}}
Bilibili: {{< bilibili id="BV1..." >}}
Local videos: {{< video src="file.mp4" controls="yes" >}}
Audio: {{< audio src="file.mp3" >}}

Perfect for demos, interviews, tutorials, or podcasts!

Note: All media types work seamlessly in slides. Just use the appropriate shortcode.

Interactive Elements

Try these keyboard shortcuts:

→ ← : Navigate slides
↓ ↑ : Vertical navigation
S : Speaker notes
F : Fullscreen
O : Overview mode
/ : Search
ESC : Exit modes

Hidden Slide Demo (Inline Comment)

This slide is hidden using the  comment method.

Perfect for:

Speaker-only content
Backup slides
Work-in-progress content

Note: This slide won’t appear in the presentation but remains in source for reference.

Thanks

Questions?

🌐 Website:
🐦 X/Twitter:
💬 Discord:
⭐ GitHub:

All slides created with Markdown • No vendor lock-in • Edit anywhere

Note: Thank you for your attention! Feel free to reach out with questions or contributions.

🎨 Branding Your Slides

Add your identity to every slide with simple configuration!

What you can add:

Element	Position Options
Logo	top-left, top-right, bottom-left, bottom-right
Title	Same as above
Author	Same as above
Footer Text	Same + bottom-center

Edit the branding: section in your slide’s front matter (top of file).

📁 Adding Your Logo

Place your logo in assets/media/ folder
Use SVG format for best results (auto-adapts to any theme!)
Add to front matter:

branding:
 logo:
 filename: "your-logo.svg" # Must be in assets/media/
 position: "top-right"
 width: "60px"

Tip: SVGs with fill="currentColor" automatically match theme colors!

📝 Title & Author Overlays

Show presentation title and/or author on every slide:

branding:
 title:
 show: true
 position: "bottom-left"
 text: "Short Title" # Optional: override long page title

 author:
 show: true
 position: "bottom-right"

Author is auto-detected from page front matter (author: or authors:).

📄 Footer Text

Add copyright, conference name, or any persistent text:

branding:
 footer:
 text: "© 2024 Your Name · ICML 2024"
 position: "bottom-center"

Tip: Supports Markdown! Use [Link](url) for clickable links.

🔇 Hiding Branding Per-Slide

Sometimes you want a clean slide (title slides, full-screen images).

Add this comment at the start of your slide content:

<!-- no-branding -->
## My Clean Slide

Content here...

☝️ This slide uses  — notice no logo or overlays!

🔇 Selective Hiding

Hide just the header (logo + title):

<!-- no-header -->

Or just the footer (author + footer text):

<!-- no-footer -->

☝️ This slide uses  — footer still visible below!

✅ Quick Reference

Comment	Hides
`<!-- no-branding -->`	Everything (logo, title, author, footer)
`<!-- no-header -->`	Logo + Title overlay
`<!-- no-footer -->`	Author + Footer text

☝️ This slide uses  — logo still visible above!

🚀 Get Started

Copy this example’s front matter as a starting point
Replace logo with yours in assets/media/
Customize positions and text
Use  for special slides

Pro tip: Set site-wide defaults in config/_default/params.yaml under slides.branding!

Smith, J. et al. (2024). Open Science Presentations. Nature Methods. ↩︎

Experience

Tue, 24 Oct 2023 00:00:00 +0000

Link Prediction in Citation Networks

Tue, 01 Feb 2022 00:00:00 +0000

This project presents our solution for the CentraleSupélec Data Science Kaggle Competition, where we achieved 2nd Place for the task of link prediction in citation networks.

The goal of the project was to predict missing links between papers in a citation graph using machine learning and graph-based methods. The task required understanding the structure of citation networks and designing models that could effectively infer whether an edge should exist between two nodes.

Our approach focused on leveraging graph representations and learning meaningful relationships between papers based on the network structure. This project highlights the use of Graph Neural Networks (GNNs) and related techniques for relational learning on graph data.

You can view the full winning solution here:

View Kaggle Solution (PDF)

Twitter Sentiment Analysis on Stocks

Tue, 01 Jun 2021 00:00:00 +0000

This project analyzes Twitter sentiment related to stock market discussions to understand how social media opinions correlate with stock movements.

The goal of the project was to extract insights from large volumes of Twitter data and classify tweets based on their sentiment toward specific stocks. By applying Natural Language Processing (NLP) and machine learning techniques, the model identifies whether tweets express positive, negative, or neutral sentiment.

The workflow includes data preprocessing, feature extraction from text, sentiment classification, and analysis of sentiment trends related to financial markets. This project demonstrates how social media data can be leveraged for financial analytics and market sentiment understanding.

You can explore the project repository here:

View Project on GitHub

An example preprint / working paper

Sun, 07 Apr 2019 00:00:00 +0000

This work is driven by the results in my previous paper on LLMs.

Note

Create your slides in Markdown - click the Slides button to check out the example.

Add the publication’s full text or supplementary notes here. You can use rich formatting such as including code, math, and images.

An example conference paper

Mon, 01 Jul 2013 00:00:00 +0000

Note

Click the Cite button above to demo the feature to enable visitors to import publication metadata into their reference management software.

Note

Create your slides in Markdown - click the Slides button to check out the example.

Add the publication’s full text or supplementary notes here. You can use rich formatting such as including code, math, and images.

Raghuwansh Raj

🏛️ Hausdorff Trimester Program - Geometric Statistics 2026

Program Overview

School on Geometric Statistics

Workshop: Stochastic Analysis, Statistics, and Computation on Manifolds and Singular Spaces

Workshop: Geometry, Topology, and Learning on Smooth and Singular Spaces

Conference: Interactions of Statistics and Geometry III (ISAG III)

About Hausdorff Research Institute for Mathematics

Program Goals

Research Interests Alignment

Learn More

📐 London Geometry and Machine Learning (LOGML) Summer School 2026

Program Overview

Key Learnings

Collaborative Project

Key Takeaways

Gratitude

Learn More

🧭 Spherical Harmonics and the Spherical Coordinate System

The Spherical Coordinate System

What Are Spherical Harmonics?

Why Spherical Harmonics Matter

Physics

Computer Graphics

Geometric Deep Learning

Visualizing the Harmonics

🌐 Attending AWS Summit Paris 2024

Event Highlights

Learn More

🌐 AWS Summit Paris 2024

Event Highlights

Learn More

Example Talk: Recent Work

Example Talk

Dr. Alex Johnson · Meta AI

Research Overview

Code & Math

Dual Column Layout

Left Column

Right Column

Main Content (2/3 width)

Sidebar (1/3 width)

Image + Text Layout

Results

Speaker Notes

Progressive Reveals

Diagrams with Mermaid

Research Results

Custom Backgrounds

Vertical Navigation

Substep 1: Details

Substep 2: More Details

Citations & Quotes

Media: YouTube Videos

Media: All Options

Interactive Elements

Hidden Slide Demo (Inline Comment)

Thanks

Questions?

🎨 Branding Your Slides

📁 Adding Your Logo

📝 Title & Author Overlays

📄 Footer Text

🔇 Hiding Branding Per-Slide

🔇 Selective Hiding

✅ Quick Reference

🚀 Get Started

Experience

Link Prediction in Citation Networks

Twitter Sentiment Analysis on Stocks

An example preprint / working paper

An example conference paper