Mohammad Bardestani

On the chromatic number of structured Cayley graphs

In this paper, we will study the chromatic number of Cayley graphs of algebraic groups that arise from algebraic constructions. Using Lang-Weil bound and representation theory of finite simple groups of Lie type, we will establish lower bounds on the chromatic number of these graphs. This provides a lower bound for the chromatic number of Cayley graphs of the regular graphs associated to the ring of

Minimal dimension of faithful representations for p-groups

n\times n

QUASI-RANDOM PROFINITE GROUPS

matrices over finite fields. Using Weils bound for Kloosterman sums we will also prove an analogous result for

Faithful representations of Chevalley groups over quotient rings of non-Archimedean local fields

\mathrm{SL}_2

Polynomial configurations in sets of positive upper density over local fields

over finite rings.

Kirillov's orbit method and polynomiality of the faithful dimension of

Abstract For a group G, we denote by m faithful ⁢ ( G )

p

{m_{\textup{faithful}}(G)}

-groups

, the smallest dimension of a faithful complex representation of G. Let F be a non-Archimedean local field with ring of integers 𝒪

On equality of ranks of local components of automorphic representations

{\mathcal{O}}

Chromatic number of singular and quadratic graphs

and maximal ideal 𝔭