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X-WR-CALNAME:Discrete Mathematics Group
X-ORIGINAL-URL:https://dimag.ibs.re.kr
X-WR-CALDESC:Events for Discrete Mathematics Group
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TZID:Asia/Seoul
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TZOFFSETFROM:+0900
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DTSTART:20250101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20260113T163000
DTEND;TZID=Asia/Seoul:20260113T173000
DTSTAMP:20260415T173831
CREATED:20251201T074437Z
LAST-MODIFIED:20251208T125825Z
UID:11942-1768321800-1768325400@dimag.ibs.re.kr
SUMMARY:Ferdinand Ihringer\, Boolean Functions Analysis in the Grassmann Graph
DESCRIPTION:Boolean function analysis for the hypercube $\{ 0\, 1 \}^n$ is a well-developed field and has many famous results such as the FKN Theorem or Nisan-Szegedy Theorem. One easy example is the classification of Boolean degree $1$ functions: If $f$ is a real\, $n$-variate affine function which is Boolean on the $n$-dimensional hypercube (that is\, $f(x) \in \{ 0\, 1 \}$ for $x \in \{ 0\, 1 \}^n$)\, then $f(x) = 0$\, $f(x) = 1$\, $f(x) = x_i$ or $f(x) = 1 – x_i$. The same classification (essentially) holds if we restrict $\{ 0\, 1\}^n$ to elements with Hamming weight $k$ if $n-k\, k \geq 2$. If we replace $k$-sets of $\{ 1\, \ldots\, n \}$ by $k$-spaces in $V(n\, q)$\, the $n$-dimensional vector space over the field with $q$ elements\, then suddenly even the simple question of classifying Boolean degree $1$ functions\, here traditionally known as Cameron-Liebler classes\, becomes seemingly hard to solve. \nWe will discuss some results on low-degree Boolean functions in the vector space setting. Most notably\, we will discuss how vector space Ramsey numbers\, so extremal combinatorics\, can be utilized in this finite geometrical setting.
URL:https://dimag.ibs.re.kr/event/2026-01-13/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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