As part of the Ashoka Math Apprenticeship Programme, students had the opportunity to attend Apprenticeship Lectures offered by faculty members each week. These lectures were designed to go beyond regular coursework and introduce students to advanced or interdisciplinary topics in mathematics.
Students selected one lecture per week to attend. The lectures featured a mix of theoretical foundations, computational techniques, and research-style open-ended questions. Some of the articles in this year’s collection were directly inspired by these lectures.
Polynomial Dynamics – Niladri Sekhar Patra
This course introduces students to the field of holomorphic (complex) dynamics, centered around the behavior of rational functions on the Riemann sphere under iteration. Beginning with a primer on complex analysis, students study dynamical systems generated by polynomial maps, with special focus on parameter spaces and their topological and geometric structure.
Group Representations and Applications – Saniya Wagh
An introduction to group theory and its linear representations. Students explore how group actions can be studied using matrices, with applications to number theory, topology, and Fourier analysis.
Characters and Fourier Analysis on Groups – Saniya Wagh
A follow-up to the first week’s lecture. This course delves into character theory of finite groups and the use of Fourier analysis in group representations. If time permits, it introduces extensions to infinite groups.
Algebraic Geometry – Sameer Kulkarni
Students are introduced to foundational ideas of algebraic geometry, starting with projective geometry and moving to varieties, key theorems, and their real-world applications. Emphasis is placed on how algebraic geometry developed as a subject.
Distribution of Sequences in Number Theory – Sneha Chaubey
This lecture explores global and local distribution properties of sequences arising in number theory and physics. Both deterministic and non-deterministic sequences are considered, with connections to analytic and probabilistic techniques.
Stochastic Process and Probability – Sarvesh Ravichandran Iyer
Focuses on discrete stochastic processes, covering filtering techniques, social balance models, epidemic models, and stochastic geometry. If time permits, point processes are also introduced.
Post-Quantum Cryptography – Ratna Dutta
Introduces students to the need for quantum-resistant cryptographic systems in light of future quantum computing capabilities. Covers both classical cryptographic foundations and emerging post-quantum techniques.
Formal Verification and Proof Assistants – Aalok Thakkar
Students learn to construct and verify mathematical proofs using the Coq proof assistant. Topics include formal logic, the Curry–Howard Isomorphism, and the process of using software to ensure proof correctness.