Shamil Asgarli

Let 𝔽_q be a finite field, and let ℙ²(𝔽_q) denote the projective plane over 𝔽_q. A subset B ⊆ ℙ²(𝔽_q) is called a blocking set if it intersects every line defined over 𝔽_q. Given an algebraic plane curve C in ℙ², under what...

The chromatic polynomial of a graph G counts the number of proper k-colorings of G. In 1995, Stanley extended this concept to define the chromatic symmetric function of a graph, which lives in the ring Sym of all symmetric functions. Building on this...

Consider the vector space (parameter space) of all homogeneous forms of degree $d$ in $n+1$ variables defined over some field $K$. Geometrically, the vanishing set of such a form corresponds to a hypersurface of degree $d$ in the projective space $P^...

Given a smooth plane curve C defined over an arbitrary field k, we say that C is transverse-free if it has no transverse lines defined over k. If k is an infinite field, then Bertini’s theorem guarantees the existence of a transverse line defined...