Discrete Analysis Days

  • Location: ISTA, Central Building, Mondi 2 

    Time: 22 October 2026, 13:30 — 16:00

    Speakers: Thomas Bloom, Mengdi Wang

    Schedule:

    13:30 — 14:30

    Thomas Bloom (University of Manchester):Counterexamples to Erdos

    Abstract

    The past year has seen an unprecedented wave of progress on Erdos problems, in large part due to the capabilities of AI models. This has been particularly striking for counterexamples; several famous questions of Erdos have been answered in a surprising direction. The study of these questions, and the counterexamples produced, allows for a fascinating exploration of where our intuition goes astray. I will explore this, and examine how both Erdos and the broader community missed these constructions, through three high-profile examples: the unit distance conjecture, the sum-product conjecture, and the size of dissociated sets.

    14:30 — 15:00

    Tea break

    15:00 — 16:00

    Mengdi Wang (EPFL): Linear exponential sums over primes in short intervals

    Abstract

    Let f denote either the Möbius function or the von Mangoldt function, and let α ∈ [0, 1]. I will discuss estimates for exponential sums of the form

    ∑x<n≤x+Hf(n)e(nα)\displaystyle \sum_{x<n\leq x+H} f(n)e(n\alpha)

    with particular emphasis on the short interval regime H<x and discuss how small H can be taken. Such estimates play a key role in studying Diophantine equations whose variables are restricted to primes in the interval [x, x + H], as well as in other arithmetic questions. This talk is based on several recent joint works with Kaisa Matomäki, Mayank Pandey, Javier Pliego, and Joni Teräväinen.

    The Discrete Analysis Days are a seminar series at the Institute of Science and Technology Austria, featuring talks at the intersection of combinatorics and number theory.