The next meeting of the Algebra and Logic Seminar will take place on April 24, 2026 (Friday) at 1:00 pm (UTC+3) in Room 578 and online via Zoom.

A talk on:

Sets preserved by a large subgroup of the special linear group

will be delivered by

Kaloyan Slavov (Medical University, Sofia).

Abstract. The classical Kakeya problem in Euclidean space asks how “small” a set can be if it contains a unit line segment in every direction. More generally, packing sets contain all images of a given set under a collection of transformations. Finite field analogues offer a combinatorial and algebraic perspective and motivate our work.

We study sets \(E\) in the affine plane over a finite field that are invariant under a large subgroup \(R\) of \(SL_2\). We prove that if \(|R|>c|E|^{3/2}\), then \(E\) must be contained in a line. The exponent \(3/2\) is sharp. We conclude with a remark on a related phenomenon in the Euclidean setting. This is joint work with Thang Pham and Le Quang-Hung.

Everybody is invited.

Algebra and Logic Department, IMI – BAS
http://www.math.bas.bg/algebra/seminarAiL/
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