The most likely type of avalanche activity we'll see this week is cornice falls. Large cornices that have been forming all winter are starting to weaken from the warm temperatures. They will be breaking off in random locations through the week. This is a simple problem to manage:

The next thing to keep in mind is wet snow avalanche activity. This threat increases during the heat of the day when the snow gets wet. Point release loose wet snow avalanches are what you might see. These can fan out and get wider as they descend slopes. Most of these will be natural but you can initiate them by disturbing the snow also. These need a very steep slope to be a threat. This problem is also simple to manage:

The last thing to keep in mind is the old persistent weak layers of sugary faceted snow that formed much earlier in the season. These layers caused the most dangerous avalanches in March. Since then, the snowpack has settled and gained strength. Generally, by this time of the winter it becomes very unlikely to see slab avalanches breaking into these old weak layers. However, it was a very unusual and prolonged season with these weak layers and I have a hard time trusting them still. In the unlikely event that a person triggers one of these, it would be on high elevation very steep slopes that face north, northeast and east.

One more note on these old weak layers. There is a good chance that these will become active again during the spring warm up. Eventually, water will start percolating through the snowpack down to those layers and they will weaken. At this point, natural avalanches could occur. I don't think things will get to that point this week, but maybe. Generally, this happens later in the spring and usually no one is out recreating in the mountains when these avalanches start to shed.