The combination of uncontrolled diabetes and a black, dead-tissue eschar on the nose or palate is pathognomonic for mucormycosis (zygomycosis), an aggressive angioinvasive fungal infection. The responsible fungi belong to the Mucorales, and the single most common genus is Rhizopus.
Why this fungus and this host: in diabetic ketoacidosis the low pH plus high glucose, together with iron liberated from carrier proteins, create an ideal growth environment, and Rhizopus expresses ketone reductase to exploit it. The hyphae invade blood vessels, thrombose them, and the resulting infarction produces the black eschar.
$\text{DKA} + \text{black eschar} \Rightarrow \text{Mucorales (broad aseptate, 90}^{\circ}\text{ branching)}$
Aspergillus (septate, acute-angle hyphae) is a neutropenic-host pathogen, Candida produces budding yeast with pseudohyphae and mucosal disease, and Cryptococcus causes meningitis - none fit the diabetic eschar scenario.
\[\boxed{\textit{Rhizopus} \text{ (mucormycosis)}}\]