Counting quiver representations over finite fields

These are notes (taken by E. Vitale) of a summer school held at the University of Bologna in the week of 22-26 May, 2023 as part of the program Quiver Representations, Quiver Varieties and Combinatorics. This is the announcement for the course. Counting representations of quivers over finite fields In these lectures I will present the calculation of the title in the case of the star-shaped quivers related to character varieties based on my joint work with E.

January 18, 2007

Math, Puzzles and Computers

In the early 2000’s while monkeying around with lattice polygons, I came up with a puzzle that looked interesting. I named it Blet after my daughter Malena saying one day out of the blue: Blet, suena como un tomat. (To this day nobody can really figure out what she meant by it.) I discussed the puzzle with my then colleagues at UT, Austin, Felipe Voloch and Lorenzo Sadun, and together worked out pretty much the whole thing and published the results.

January 18, 2006

Complex Analysis

These are notes of a graduate course in Complex Analysis at UT Austin in 2006. Pretty standard stuff for a first course in Complex Analysis. The history of the proof of Cauchy’s theorem has its twists and turns. I always liked Goursat’s proof that does not require continuity of first partial derivatives.

April 1, 2002

K-theory and L-functions

These are notes (taken by M. Lalín) for a course on $K$-theory and $L$-functions I gave at Harvard University in the Spring of 2002. Notes for the first few lectures were taken by S. Valverde. The main goal of the course was to explain how to frame conceptually the numerical examples of D. Boyd relating the Mahler measure of certain two variable polynomials $A(x,y)$ and $L(E,2)$ for $E$ the elliptic curve defined by the zeros of $A$.

June 7, 1999

La Función Zeta de Hasse-Weil (in Spanish)

These are notes for a course in Spanish on the Hasse-Weil zeta function given en Mérida, Venezuela in 1999.