Jinyoung Park is an Assistant Professor of Mathematics at the Courant Institute, NYU. Her research interests include extremal and probabilistic combinatorics. She earned her PhD in mathematics from Rutgers University in 2020, under the supervision of Jeff Kahn. Following her PhD, she was a postdoctoral researcher at the Institute for Advanced Study (IAS) and Stanford University before joining the faculty of the Courant Institute at NYU in 2023. She has received several honours and awards, including the AMS Conant Prize, the Dénes König Prize, and the Maryam Mirzakhani New Frontiers Prize.

In this series of lectures, we will explore the rich theory that surrounds a deceptively simple object: sums of independent random variables. We will start with the basics of central limit theorems and large deviation theory, before moving on to “universality” phenomena and Littlewood-Offord theory. This will then set us up nicely to touch on further topics such as random matrices, discrepancy theory and random polynomials.

These lectures will not assume any prior knowledge in the area, beyond familiarity with undergraduate probability and combinatorics.

Matthew Jenssen is a Reader in Probability in the Department of Mathematics at King’s College London and a UKRI Future Leaders Fellow. His research lies at the interface of combinatorics, statistical physics, and theoretical computer science, with particular interests in discrete probability, probabilistic and extremal combinatorics, algorithms, and random matrix theory. Much of his work aims to understand how large-scale structures emerge in systems governed only by local interactions.

He completed his PhD in Mathematics at the London School of Economics in 2017 under the supervision of Professor Jozef Skokan and Professor Julia Böttcher, where his doctoral work earned him the LSE PhD Prize for Outstanding Academic Performance. Following his PhD, Jenssen held a two-year postdoctoral position at the University of Oxford. In 2020, he joined the University of Birmingham as a Lecturer in Probability before moving to King’s College London as a Reader in January 2023.

Julian Sahasrabudhe is a Professor of Mathematics in the Department of Pure Mathematics and Mathematical Statistics (DPMMS) at the University of Cambridge. His research interests lie in extremal and probabilistic combinatorics, along with their intersections with probability, analysis, and combinatorial number theory, with a recent focus on Ramsey theory on graphs, random polynomials, and random matrices. He earned his PhD in mathematics from the University of Memphis in 2017 under the supervision of Béla Bollobás. Following his PhD, he was a post-doc at the Instituto de Matemática Pura e Aplicada (IMPA) in Rio de Janeiro, Brazil and Junior Research Fellow at Peterhouse, University of Cambridge.

He has received numerous prestigious honours and awards for his research, including the European Prize in Combinatorics (2021), the Salem Prize (2023), a European Research Council (ERC) Starting Grant (2024), the LMS Whitehead Prize (2024), the Mathematical Congress of the Americas (MCA) Prize (2025), and the Adams Prize (2026). He has been a speaker at the International Congress of Mathematicians (ICM) in Philadelphia.