Moving Announcement
This page will not be updated any more since I'm moving away.
My new homepage
is under construction --- it doesn't look good now but you are
welcome to pay a visit.
The contact information
listed on this page will be out-dated before the end of July, 2007, though my email will last a little bit longer.
Contact
Department of Mathematics
Brandeis University, MS 050
Waltham, MA 02454-9110
Office:
Goldsmith 102
Email: liji at brandeis.edu
Phone: (Office) (781) 736-3087
Fax: (781) 736-3085
Files
-
Preprints
(with Ira Gessel) On Point-Determining Graphs, pdf, 22 pages, 16 figures, arXiv: 0705.0042, 2007.
Prime Graphs and Exponential Composition of Species, pdf, 27 pages, 6 figures, arXiv: 0705.0038, 2007. -
Presentation Slides
Counting Point-Determining Graphs and Prime Graphs, pdf, 50 pages, thesis defense, Brandeis University, May 2007.
A Bijection for Counting Bi-Point-Determining Graphs, pdf, 23 pages, Brandeis Combinatorics Seminar, April 2007.
Arithmetic Product of Species and Cartesian Product of Graphs, pdf, 50 pages, MIT Combinatorics Seminar, March 2007.
Counting Point-Determining Graphs, pdf, 28 pages, Joint Meetings of AMS at New Orleans, January 2007.
Who am I
I am a fifth-year graduate student at Brandeis University, Department of Mathematics. My thesis advisor is Professor Ira Gessel, and my studying area is algebraic combinatorics. More precisely, I am working on finding applications and new aspects of Joyal's combinatorial theory of species in combinatorial enumerations on graphs.
In my thesis, Counting Point-Determining Graphs and Prime Graphs, I counted objects like point-determining graphs, connected point-determining graphs, phylogenetic trees, bi-point-determining graphs, bicolored point-determining graphs, and prime graphs. On the theoretical part, I discovered the notion of exponential composition of species, based on Maia and Mendez's arithmetic product of species, and gave enumerative formulas for the cycle index series of the exponential composition of an arbitrary species.
My undergraduate study was maintained in Nankai University, Tianjin, China.
Coffee Drinking Machine
Quotes by Erdös: A mathematician is a device for turning coffee into theorems.
Ji says: Coffee does not necessarily generate theorems, but without coffee there is simply no mathematics. So I must be heading towards something... a coffee drinking machine, or a mathematician?
Thus Spoke Ji: Mathematics is for those kind of people who appreciate beauties in their purest forms. Mathematics itself is not practical, even if it, like everything else, can be persued in a practical way. But in order to appreciate mathematics, you have to be impractical from time to time. You have to be able to enjoy the deduction of a theorem that is beautiful in its being perfectly deducted even though it is definitely and thoroughly useless in the real life. It is the beauty of such "useless" theorems that makes mathematics more a kind of art, as in "art for art's sake", than a scientific practice. --- In a way, mathematics could be treated as simple as pure logic: it comes from nowhere other than human minds, and it leads to nowhere other than human hearts.
December 8, 2006, Brandeis University
