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Location: Mondi 2 Seminar Room, Central Building, ISTA
Time: 22 April 2026, 13:30 — 16:00
Speakers: Luka Milićević, Oliver Roche-Newton
Schedule:
13:30 — 14:30
Luka Milićević (Mathematical Institute of the Serbian Academy of Sciences
and Arts): A quasipolynomial inverse theorem for uniformity norms in finite vector
spaces of high characteristicAbstract
The inverse theory for Gowers uniformity norms is one of the central
topics in additive combinatorics and one of the most important aspects of
the theory is the question of bounds. In this talk, I will discuss a work
in progress, which proves a quasipolynomial inverse theorem for Uk norm
in Fpn in the case of high characteristic (meaning p ≥ k). I will
discuss the key ingredients of the argument, in particular the abstract
Balog-Szemerédi-Gowers theorem and algebraic regularity method, as well as
highlight the differences from the previous work on the U4 norm.14:30 — 15:00
Tea break
15:00 — 16:00
Oliver Roche-Newton (JKU Linz): Elementary techniques for problems on convexity and sum sets
Abstract
A generalisation of the sum-product phenomenon is the notion that strictly convex functions disrupt additive structure. For instance, it is known that, for any set A of real numbers and any strictly convex or concave function, at least one of the sum sets A+A or f(A)+f(A) is large. By taking f to be the logarithmic function, this becomes a sum-product estimate. This talk will discuss some personal favourite variants of this problem, as well as some interesting constructions which show some restrictions on growth can occur in these problems. It will largely focus on what can be achieved with elementary techniques, particularly a “squeezing” technique which has broken new ground in recent years.
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.