While most rail commuters are reading newspapers during their morning ride to work, William Minicozzi is hard at work.
"I love my job," said the mathematician, who doesn't need any fancy computers or calculators to do his research.
As daunting as it might seem, he does all of his math in his head, scribbling his inscrutable findings in note pads and on blackboards. So the 55-minute commute to Baltimore from his home in suburban Virginia is actually the perfect laboratory.
Minicozzi and neuroscientist Alfredo Kirkwood are among 100 outstanding young scientists across the nation who have been awarded Sloan Research Fellowships this year.
Kirkwood, an assistant professor in the Zanvyl Krieger Mind/Brain Institute, studies how the neural connections in the brain change with experience and learning, a phenomenon called neural plasticity, which is a popular field within neuroscience.
"My research is a little bit different from the rest of Mind/Brain in the sense that most people here are more focused on how the brain circuits use information to make choices and how they are involved in perception, and those kinds of questions," said Kirkwood, who came to Hopkins in June 1997. "I am more interested in how these brain circuits can change so that you can learn to use information and to perceive."
Kirkwood, a native of Chile who earned a doctorate in neuroscience from Brandeis University, specializes in a portion of the brain called the visual cortex, a section of gray matter that is known to be especially plastic and is where the sense of sight is headquartered.
Scientists made a startling discovery more than 30 years ago: Mammals, including people, go through a "critical period" in youth during which the neural connections are formed and strengthened between the eyes and the visual cortex.
If a blindfold is placed over the eye of an animal immediately after it is born and kept in place for the full length of the critical period, the connections are never made and the animal is blind in that eye.
"Those were very dramatic findings," Kirkwood said. "The cortex and the eye get disconnected forever."
Generally, the larger the animal, the longer the critical period. In rats, the period is about a month, whereas in humans it lasts about a decade.
"If you have a cataract, which is basically like a covering, you have to be operated on early in life, say at 5 years old, to get a full recovery of the eye. But if you wait until the child is 12 years old, that eye becomes blind forever," Kirkwood said.
"Whether the cortex can talk to the eye in a functional way will depend on what the animal sees and how it views the information. So then the cortex becomes a real model of how the brain learns how to be a brain, basically."
Kirkwood primarily studies the visual cortex in rats, comparing the neural connections in brains of rats that have been raised in the dark to those in animals that have been raised under normal lighting conditions.
Minicozzi came to Hopkins in 1995 after earning a doctorate from Stanford University and serving one year as a postdoctoral fellow at New York University's Courant Institute.
He specializes in geometric analysis, using mathematics to study geometry and shapes known as manifolds, which are spaces that on a small scale may look flat but are actually more complex. Examples of manifolds include spheres and doughnuts.
"When we stand on the Earth and look around, it appears that we are just standing on a flat space," said Minicozzi, an assistant professor in the Department of Mathematics. "But actually the whole space is curved."
To understand more about the nature of these shapes, mathematicians use differential geometry, the same language used in many physics applications.
In 1996, Minicozzi, working with mathematician Tobias Colding at New York University, solved a problem that had been puzzling experts in the field since the mid-1970s.
Their breakthrough dealt with the difficult feat of measuring the curvatures of complex geometric shapes, or spaces. When space bends back onto itself, like a sphere, it's called positively curved. Mathematicians had theorized that the well-understood methods used to analyze flat space would also work in analyses of positively curved space.
He and Colding proved that the theory was true, explained Minicozzi as his phone rang in the background. He didn't bother answering; it was almost certainly Colding, calling to share yet another mathematical insight. Such is the life of a mathematician: trading numerous ideas in e-mail messages, phone conversations and professional gatherings held in far-flung international locations.
Sloan Fellowships, awarded by the Alfred P. Sloan Foundation, are for university researchers in the fields of physics, chemistry, computer science, mathematics, neuroscience and economics. The average age of this year's fellows is 33. They will receive a $35,000, two-year grant to support their work.