I support a nice Joël’s answer.
I think that success depends on communication and social activity, but personally I prefer to do more explicit carrier steps than those giving you only a hope that “maybe somebody somewhere will remember me”. I consider that if after a few months after the conference your listener will remember from where you are and that you are dealing with exterior differential systems, it will be very good. We may check this if we ask ourselves what we remember about conference speakers which were far from our mathematical interests, and I think that most of the mathematicians are narrow specialists.
I think that Internet is a good way to general (and, in particular to working and carrier) acquaintances and communications. In particular, we can use LinkedIn or MathOverflow for this purposes. Personally I gathered a material for two joint articles after few months at Mathematics Stack Exchange. When I was a graduate student and my English was more weak, I even had a sample letter to ask other mathematicians for papers. And I solved some open problems.
I think that success depends on many factors. For instance, I rarely visited conferences outside my city but I have 17 coauthors and big mathematical correspondence. Also my friend told me that I must attend conferences and directly contact with people to be invited, but I was invited to China when I had reviewed an article written by a Chinese professor.
Concerning the mentioned differences between American and Russian scientific styles of work, I think that the style is strongly depending on a personal choice.
Andrew Wiles had rejected his partisipation in conferences and was proving Fermat’s Last Theorem on his own (see for the details Chapter 6 of Simon Singh’s “Fermat's Last Theorem”, which fragments are here and here).
Paul Erdős “spent most of his life as a vagabond, traveling between scientific conferences and the homes of colleagues all over the world. He would typically show up at a colleague's doorstep and announce “my brain is open”, staying long enough to collaborate on a few papers before moving on a few days later. In many cases, he would ask the current collaborator about whom to visit next”. He was generoulsy sharing his mathematicas ideas with community and was easily responding to others’s ideas. He died from a heart attack attending a conference in Warsaw and he had in his pocket a ticked to Vilnius, where should be his next conference.
Personally I was bred in L’viv topological school which is a branch of a topological school from Moscow State University. I was very disliking conferences and preferring not to leave my city. For instance, when I was in secondary school, I even skipped a participation in Soviet Union mathematical olympiad, because I was not interested in it, althouh I had a gold medal in Ukraine. :-) But now, living in a real world, which seems to be similar and to have similar problems both in America and Russia, I am forced to do scientific carrier in order to make a possibility to be a scientist. :-(
As a resume I recommend you to choose (or form your own) a scientific style that works better for you, gives you growth and is good for you.