In Summer 2025, the Math Apprenticeship Programme continued to grow in scope, welcoming students from across institutions to explore advanced mathematical ideas through independent study. Each student worked under the guidance of a faculty mentor to write an expository article or create a research-style poster on a topic they were excited to learn about, often extending far beyond their formal coursework.
Many of these projects were inspired by the Apprenticeship Lectures offered throughout the programme-deep, week-long mini-courses on topics such as group representations, polynomial dynamics, stochastic processes, and formal verification.
The resulting articles reflect the curiosity, creativity, and initiative of the students, as well as the generosity and mentorship of faculty. These works are intended for an undergraduate audience, and aim to balance motivation, intuition, and mathematical depth.
We hope this collection serves both as a record of the students’ efforts and as an invitation to explore beautiful ideas in mathematics.
Autoregressive Models, Aarav Bhatt (IIT Delhi) under the supervision of Sarvesh Iyer
Winding Numbers And The Fundamental Theorem Of Algebra, Abhimanyu Pant (Ashoka University) under the supervision of Sameer Kulkarni
The Ising Spin Model Of Financial Markets, Abhinav Baskar (Ashoka University) under the supervision of Sarvesh Iyer
Spectral Analysis of Markov Chains, Abhiroop Sarkar (Ashoka University) under the supervision of Sarvesh Iyer
Representation Theory And Mackey’s Irreducibility Criterion, Ankitbhai Gojiya (IIT Roorkee) under the supervision of Sagar Shrivastava
Local Dynamics Around Attracting Fixed Points Of Meromorphic Maps, Anwesha Ghosh (Ashoka University) under the supervision of Niladri Patra
Flat Origami And Folded States, Arjun Singh (Ashoka University) under the supervision of Sagar Shrivastava
From Balls and Urns to Jobs and Firms: Modeling Labor Markets as Stochastic Processes, Ayushman Sinha (Ashoka University) under the supervision of Sarvesh Iyer
Bond Pricing And Interest Rates, Diksha (Delhi University) under the supervision of Sarvesh Iyer
Local Fields, Gayatri Subhash (Ashoka University) under the supervision of Saniya Wagh
Understanding Noether’s Theorem In Lagrangian And Hamiltonian Formulation, Harsimar Kaur (Ashoka University) under the supervision of Sagar Shrivastava
Sign, Refresh, Repeat: Strengthening Threshold Cryptography With Accountability, Himaanshi Bansal (Ashoka University) under the supervision of Ratna Dutta
To Counter A Dictator: Anamorphic Encryption, Ishaan Varior (Ashoka University) under the supervision of Ratna Dutta
Formal Verification using Dafny, Jagrit Goel (IIT Delhi) under the supervision of Aalok Thakkar
Burnside’s Theorem, Jyoti (IIT Roorkee) under the supervision of Sagar Shrivastava
Equivalence Of Simplicial And Singular Homology In ∆-Complexes, Kanchan Bharti (IIT Kanpur) under the supervision of Mohit Upmanyu
Building Trustworthy Software, A Dafny-Driven Approach To Approved User Interactions, Kudakwashe Mavis Chakanyuka (Ashoka University) under the supervision of Aalok Thakkar
Evaluating The Impact Of Design Measures On Carbon Emissions In Residential Buildings Across Climate Zones Using Machine Learning, Mannat Kaur (Stanford University) under the supervision of Debayan Gupta
Exploring Spectral Graph theory, Maya Prashanth Seshadri (Ashoka University) under the supervision of Sagar Shrivastava
Distribution of Odd Denominator Farey Fractions, Naityik Singh (IISER Pune) under the supervision of Sneha Choubey
Mini Case-Studies In Algorithm Verification With Dafny, Nimay Gupta (University of Oxford) under the supervision of Aalok Thakkar
The Three Gap theorem, Om Chaudhari(CMI) under the supervision of Sneha Choubey
Visibility Of Lattice Points, Piyush Kumar Jha (CMI) under the supervision of Sneha Choubey and Shanta Laishram
Proof of the Riemann mapping theorem, Rituja Gayen (Ashoka University) under the supervision of Niladri Patra
Chaos: Existence and Construction, Riya Arora (Ashoka University) under the supervision of Sameer Kulkarni
Extremal Set Theory, Rohan Roy (CMI) under the supervision of Amitabh Tripathi
Arboreal Representation For The Generic Monic, Ryan Azim Shaikh (IIT Delhi) under the supervision of Niladri Patra
An Exposition On Van Der Waerden Numbers, Saksham Sahai Srivastava (IISER Pune) under the supervision of Amitabh Tripathi
An Exploration Of Riemann Surfaces, Shreyansh Kumar (Ashoka University) under the supervision of Niladri Patra
Number Theory, Sonali Anant (IISER Berhampur) under the supervision of Amitabh Tripathi
Exploring p-Adic Numbers, Sreejit Dey (Ashoka University) under the supervision of Saniya Wagh
Irreducible Polynomials & Newton Polygons, Sufiyan Ashraf Tejani (IIT Kharagpur) under the supervision of Shanta Laishram
Irreducible Polynomials & Newton Polygons, Suraj Kumar Maharana (IIT Kharagpur) under the supervision of Shanta Laishram
Inscribed Rectangle Problem, Upanshu Lakhani (Ashoka University) under the supervision of Mohit Upmanyu
Exploring Stochastic And Bayesian Elements In War Of Attrition, Vedika Navani (Ashoka University) under the supervision of Sarvesh Iyer
An Introduction To Turing Instability, Vedant Rana (Ashoka University) under the supervision of Ashish Pandey
Local Dynamics Around Attracting Fixed Points Of Meromorphic Maps, Vishnu Varadarajan (Ashoka University) under the supervision of Niladri Patra
Introduction To Random Noise Generation, Yashdeep Singh (IIT Delhi) under the supervision of Sarvesh Iyer
Theory Of Congruences And Quadratic Reciprocity Law, Yuvraj Verma (Ashoka University) under the supervision of Niladri Patra
Here is the link to the Archives of Math Apprenticeship Programme of the past years.