one way is to test the url in-line
<ul class="nav navbar-right nav-pills speakernav">
<li><a href="/talks" @if(request()->segment(1)=='talks') class="active" @endif >Browse Talks</a></li>
<li><a href="/newtalk" @if(request()->segment(1)=='newtalk') class="active" @endif >Post a Talk</a></li>
<li><a href="/register" @if(request()->segment(1)=='register') class="active" @endif >
@if(Auth::check()){{ Auth::user()->name }} @else Login @endif</a></li>
</ul>
The segment(1) part returns the first part of the path and ignores any parameters, eg /talks/edit
So the test if the link should be active is in-line in the menu partial or master layout.
You can do similar with named routes.
There are also a lot of packages available that can do some of the work for you; https://packagist.org/search/?q=laravel%20active%20menu