There looks like there’s a slider in the header that’s not being used, but is still taking up some significant space. There are also some margins & padding that can be eliminated. Since Zinnia does not have a Custom CSS option, I would install a CSS plugin like Custom CSS Manager and add the following rules:
.header {
padding-bottom: 0;
}
.section-wide {
margin-top: 0;
}
.responsiveslides {
display: none;
}
.post-header {
display: none;
}
I would also think about eliminating the menu, since it looks like your site consists of just one page and the menu really doesn’t have a function other than taking up space. You can hide the menus (both the mobile and desktop versions) with this CSS rule:
.nav {
display: none;
}
Your slider images look very nice, by the way. They’re making me hungry!