I gave some version of this lecture on the Mathematics of the football/soccer ball several times, in different places and in various languages. Florence 20/05/2024 Gonit Sora (online) 14/06/2021 Form their website: Gonit Sora is a multi lingual (English and Assamese) web magazine devoted to publishing well written and original articles related to science in general and mathematics in particular. One of its founders and current editor is Manjil P. Saikia, a former ICTP Diploma student, who invited me to give this online talk.

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.

These are the slides of my talk at Bill Duke’s birthday conference held at ETH in Zurich. I later wrote an extended abstract of this talk. It includes a proof of the calculation of the mixed Hodge numbers of a hypergeometric motive. The original conjecture on Hodge numbers of is a paper of Corti and Golyshev. A proof was given by Fedorov.

In 2018 I was invited by my former ICTP Diploma student Manjil P. Saikia to give a mini-course at the University of Vienna. I also gave then a general talk about the puzzle Blet. Later in the year I gave a Basic Notions Seminar on the puzzle at ICTP. As an experiment I got the transcript of the talk from youtube and then ran it through ChatGPT. After some light editing here is the result.

These are the slides of my talk at the 2018 conference “Perspectives on the Riemann Hypothesis” held in Bristol.

These are the slides of my Beeger Lecture at the 2018 Dutch Mathematical Congress.

These are notes of a talk a gave in a workshop on the arithmetic of curves held in Barcelona in 2017.

Frequently groups of high-school students come to visit ICTP. One of their standard activities is to attend a short talk by a scientist. A number of times I gave one of these talks. In this case it was a talk for Italian students and I discussed a bit the mathematics of information transmission.

I gave a the kick-off Basic Notions talk at ICTP in 2014 on Impartial Games (one of the topics of the course Math, Puzzles and Computers). I expected students in the class to connect to puzzles and eventually to the corresponding mathematics through a chilhood experience. It is certainly what happened to me while preparing the lectures. I have a somewhat vague but powerful memory of being introduced to the standard version of the game of Nim at an early age.

These are the slides of my talk at the first Abel conference in honor of John Tate at the University of Minessota in 2011. It is a summary of my work with T. Hausel and E. Letellier.

These are the slides of a talk I gave in the UT Odyssey public lecture series in 2007. It was a partly historical talk on the way certain puzzles seem to grab the public’s attention and become an obsession for a period of time, Rubik’s cube being a classic example of the recent past. Another wildly popular puzzle was the Famous Trick Donkeys 1858 puzzle by Sam Lloyd. The original links on the slides don’t seem to work anymore.

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.

At UT Austin there is a wonderful program of lectures for high-school students on some Saturday mornings. I gave a number of the talks there including one about lattice polygons and the number 12.

These are slides of a talk of the late 2000’s (don’t remember where) on my early work with T. Hausel on character varieties. It has some details on the combinatorics involved in computing the key quantity $C_\tau$.

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.

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 $A$.

Part of the 2001 University of Texas Lectures on the Clay Institute Millennium Problems. On the Birch-Swinnerton–Dyer Conjecture

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

These are the slides of my talk at the 1998 Pacific Northwest Number Theory Meeting.

These are the slides of a talk I gave some time in 1997 on my joint work with Farshid Hajir on defining explicit elliptic units; basically trying, and to some degree succeeding, to tame the 24-th roots of unity that arise from the transformation formula of Dedekind’s eta function.

These are notes on approaching Bernoulli polynomials as eigenvalues of certain operators acting on polynomials. It is my re-interpretation of work of E. H. Lehmer. (A new approach to Bernoulli polynomials, Amer. Math. Monthly 95(1988), 905-911.) I wrote this note at the end of my Ph.D. studies around 1989.

These are the notes of one my first research talks in the US, at OSU in the Spring of 1989. It is on my thesis (original, published versions).

These are unpublished notes in Spanish, written in 1985 when I was finishing my undergraduate degree in Buenos Aires, on defining a group law on degenerate cubics. More precisely, on cubics consisting of a smooth conic and a line. Depending on the number of intersection points of the conic and the line over the given ground field (0,1, or 2 points) you get the circle, the additive or the multiplicative group respectively.