Sergi Elizalde

My main area of research is combinatorics. I like not only its beauty as a subject but also its wide applicability throughout mathematics and science. I have diverse mathematical interests, and combinatorics is the bridge that connects them. Even though I have a predilection for enumerative questions, I have also worked on algebraic combinatorics, computational biology, number theory, and combinatorial commutative algebra. In general, I am interested in the connections of combinatorics with other fields such as algebra, biology, geometry, probability, and computer science. I have acquired a broad background by working on different problems, and taking courses in different areas. I enjoy learning new problems and trying to solve them using combinatorial techniques. I finished my Ph.D. thesis at MIT in June of 2004, under the supervision of Professor Richard Stanley. After graduating I spent the year 2004-2005 as a postdoctoral fellow at MSRI, in Berkeley. In the fall I took part in the programs on Hyperplane Arrangements and Applications in the fall, and Probability, Algorithms and Statistical Physics in the spring. At the same time I worked with Professor Bernd Sturmfels on combinatorial problems arising from computational biology. During the months of May and June of 2005 I did a postdoctoral stay at the Institut MittagLeffler in Sweden, as part of the special program on Algebraic Combinatorics. As of July of 2005 I am a John Wesley Young Research Instructor at Dartmouth College. Here my research has been on enumerative problems concerning generalized triangulations and also pattern-avoiding permutations. I have benefited from being around Professor Peter Winkler, and I am currently also working with Professor Rosa Orellana on a problem in algebraic combinatorics. In the rest of this statement I will describe with more detail my research accomplishments in different areas, as well as future directions of my research (indicated by a vertical bar in the margin).