Following the intensive sessions on cryptography and cybersecurity, Summer School 2026 continued with a series of online lectures focusing on fundamental topics in mathematics, particularly measure theory, functional analysis, probability theory, and stochastic processes. The sessions brought together mathematicians and researchers to introduce participants to important analytical and probabilistic frameworks.
Monday, July 27, 2026:
The program began with Prof. Dr. Christiana Rini Indrati, who presented “Introduction to Measure Theory” . The session introduced participants to the fundamental concepts of measure theory, providing a foundation for further study in modern analysis and probability.
At 09:00–12:00, Dr. Reetabratahar also delivered a session on Machine Learning. The session was conducted in a hybrid format at Meeting Room 1, 3rd Floor, Department of Mathematics, Universitas Gadjah Mada, allowing both onsite and online participants to take part.
Tuesday, July 28, 2026:
On Tuesday, Dr. Eder Kikianty presented “Introduction to Functional Analysis” . The lecture introduced the field of functional analysis and its role in studying mathematical structures arising in analysis.
Wednesday, July 29, 2026:
The following day featured Dr. Wolfgang Bock, who presented “Introduction to Probability Theory” . The session provided an introduction to probability theory, an essential framework for understanding uncertainty and random phenomena.
Thursday, July 30, 2026:
On Thursday, Prof. Dr. Jose Luis Da Silva presented “Introduction to Stochastic Processes” . The session extended the probabilistic themes of the previous day toward the study of processes that evolve randomly over time.
Friday, July 31, 2026:
The program also featured a Machine Learning session led by Dr. Reetabratahar. The session was conducted in a hybrid format, with participants attending both online and onsite at Meeting Room 1, 3rd Floor, Department of Mathematics, Universitas Gadjah Mada. It introduced participants to machine learning and its relevance to the broader themes of mathematics, computing, and digital technologies.
The final session of this part of the Summer School was delivered online by Prof. Dr. Nicolas Privault. He presented “Introduction to Stochastic Calculus,” introducing participants to the fundamental concepts and ideas of stochastic calculus and its role in the study of processes involving randomness. The session brought the week’s program to a close with a topic connecting probability theory with the analysis of stochastic processes.
Overall, this part of Summer School 2026 broadened the program beyond cryptography and cybersecurity by introducing participants to several core areas of modern mathematics. The sequence from measure theory and functional analysis to probability and stochastic processes provided a progression through important mathematical foundations used across analysis, probability, statistics, and related fields.