There's a story called The Gentle Seduction by Marc Stiegler that shares a lot of similarities with your description, though it differs in too many ways for it to be your story. Still, I'll mention it in case you've misremembered some details or you've conflated two different stories.
In this story the protagonist is a college professor as you say (we never learn her name) and her husband Jack is killed in an avalanche:
She married a forest ranger, a bright, quiet man with dark eyes and a rugged face. They had three small children and two large dogs, friendly dogs with thick soft fur. She loved all the members of her family, almost all the time; it was the theme that never changed though she thought about different things at different times.
Her children grew up and moved away.
Erich, the beautiful red chou, went to sleep one night and never awakened.
A terrible avalanche, from a seemingly safe slope, fell down the Mountain and buried a climbing team, her husband among them.
Haikku, her mighty and faithful akita, whimpered in his old age. He crooned his apology for leaving her alone, and that night he joined Erich and her husband.
She was 82. She had lived a long and happy life. She was not afraid to die. But she stood outside in the snow and faced a terrible decision.
The terrible decision is whether to take a pill containing nanomachines that will rebuild her aging body. She does take the pill and goes on to become a leading researcher in the nanotechnology field. However her work does not involve building simulations that her students find to be dangerous.
The story goes on to describe humanity reaching then surviving the singularity due to the nanotechnology the protagonist works with.
At the end of the story the protagonist does build a simulation of her husband, but she does not enter it to die:
It hurt her to think of him lost forever, and she had not felt hurt for a very long time. Feverish, she worked to rebuild him. The Earth-bound computers gave her all the help they had to give, every memory of every moment of Jack they had ever recorded. She traced her own memories, perfect now, of every word he spoke, every phrase he uttered, every look he gave her in their long walks. She built a simulation of him, the best and most perfect simulation she could build with all her resources, resources far beyond those of a million biological human minds. It was illegal to build a simulation such as this, one of the few laws recognized by the community, but this did not deter her.
The simulation looked like Jack; it talked like Jack; it even laughed like Jack. But it was not Jack. She then understood why it was illegal to build such a simulation; she also understood why it was not a law that needed to be enforced: such simulations always failed.
Jack was gone.
What could she do?
What she does is decide to live on. The story ends:
She dipped much longer still and asked one more time. This time she understood. The answer was so simple, so glorious, so joyful, that she did not ask the question again for a billion years.
And by then, it just didn’t seem to matter.
I read this in Stiegler's anthology The Gentle Seduction, which was published in 1990 so you could have read it in 2003.
I wouldn't normally suggest a story when it clearly differs from the description but in this case a lot of things match exactly, though of course others are a complete mismatch.
