Let me be honest with you. When I applied to UCR for my PhD I didn't think I would end up studying here, I didn't know too much about this school, nor about its faculty members. However, the Department of Mathematics in Riverside has a lot of good and worldwide famous mathematicians. Among them, John Baez caught my attention when I applied to UCR, and he is, together with my PhD advisor Qi S. Zhang, the main reason I decided to come here.
John Baez is a very active professor, not only in the university, but also online: in his webpage (one of the first "blogs" in the world wide web) you can find, literally, all sorts of things; I love to get lost surfing through it! He is an awesome instructor, I had the opportunity to attend one of his classes, MATH209A, an introduction to measure theory, and after that I decided to do my best to attend as many of his classes as I could. That's the reason that I have been attending his seminars on Network Theory and on Category Theory!
John Baez is a very active professor, not only in the university, but also online: in his webpage (one of the first "blogs" in the world wide web) you can find, literally, all sorts of things; I love to get lost surfing through it! He is an awesome instructor, I had the opportunity to attend one of his classes, MATH209A, an introduction to measure theory, and after that I decided to do my best to attend as many of his classes as I could. That's the reason that I have been attending his seminars on Network Theory and on Category Theory!
Last year, his seminar was on Network Theory, one of the topics in which he and his students are working. The idea behind it is to apply Category Theory to everyday physics, such as electrical circuits or control theory, as well as to any other subject that uses diagrams or networks (such as biology, chemistry, or theoretical physics). The goal is to unify the language of all of this fields through Category Theory, in the same way that it has happened in different areas of Mathematics. The first four sessions can be found on youtube:
This year, however, the focus of his Seminar is on the applications of Category Theory within mathematics, so that the graduate students in the Math Department learn how can Category Theory help them in their own fields. So far, the seminar has been an absolute success, it is hard to find an empty seat, and all the sessions have been really exciting (and I must say that I am not particularly interested in Category Theory). He is talking about different topics that were suggested by the students over the summer, and relating them to Category Theory.
Among the topics he has covered so far, I particularly liked Lecture 2, where he explained the duality between commutative C*-algebras and Compact Hausdorff topological spaces, which are opposite of each other in the categorical sense, even if that sounds crazy. I also loved his categorical approach to Galois Theory; I really think that any mathematician that has ever studied Galois Theory using the classical approach (studying fields through groups) should have a look at the general setting were Galois Theory is defined! You can find some notes on the Seminar in his website, taken by some of the students.
Next quarter, professor Baez is offering a class on Category Theory, with a more formal approach to the field. I am looking forward to it, attending John Baez classes is always worth it!
Among the topics he has covered so far, I particularly liked Lecture 2, where he explained the duality between commutative C*-algebras and Compact Hausdorff topological spaces, which are opposite of each other in the categorical sense, even if that sounds crazy. I also loved his categorical approach to Galois Theory; I really think that any mathematician that has ever studied Galois Theory using the classical approach (studying fields through groups) should have a look at the general setting were Galois Theory is defined! You can find some notes on the Seminar in his website, taken by some of the students.
Next quarter, professor Baez is offering a class on Category Theory, with a more formal approach to the field. I am looking forward to it, attending John Baez classes is always worth it!
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