How will advancements in technology shape the way architects design buildings in the future?

I think this is a question where the answer depends on which advances on technology actually happen. The two areas it encompasses are materials science, and design technology.

3D printing - probably the biggest opportunity, this one is a combination of materials science and design technology. It's already being used on a very limited scale. In future it will enable the mass-production of housing stock as well as being suited for more "sculptural" monumental buildings. It has also been used in a simulated lunar environment with the idea of "printing" a moonbase which only has to be fitted with airlocks and filled with air ready to be used. With buildings being designed in CAD and converted directly to files for 3D extruders, curvature and a fractal look is likely to become popular instead of the more linear appearance we currently use. However, 3D printing has some significant limitations in structural strength which need to be overcome to allow mass adoption.
New forms of concrete. This one is actually a throwback. A couple of months ago, materials scientists announced they had finally worked out the secret of Roman concrete (it's in the chemical bonding process at a molecular level the ingredients undergo in the presence of moisture or something - a bit too technical for me !) This material is far stronger and more durable than any concrete we've been able to produce up until now, and understanding it's behaviour at a molecular level may enable us to "design" new types of concrete for specific purposes or environments.
AI design. It is inevitable that artificial intelligence will be used to aid the design process. For example, in modelling flows of movement in and around large structures, or fitting habitation units into the most compact space. However, I do hope that there's a level of sense-checking by humans, as AI technology can sometimes do things that look right at a glance but are terribly wrong when looked at n detail (just count the number of fingers and toes on many AI-generated images of humans...)