Full professor, Institute of Mathematics and Statistics
University of São Paulo, Brazil
sinai.robins@gmail.com (434) 358-2880
(NEW!) [pdf] Sinai Robins, Ehrhart quasi-polynomials via Barnes polynomials and discrete moments of parallelepipeds, submitted (2026).
I will add more expository notes and examples in the Research page here, regarding this new paper.
My research interests include Data science, Machine learning, Neural networks, Discrete and Computational Geometry, Harmonic analysis, Combinatorial optimization, Combinatorics, Number Theory.
Basically, I enjoy solving problems.
Fourier Analysis on Polytopes, and the Geometry of Numbers, Part I: A Friendly Introduction
Published in 2024, by the American Mathematical Society, in the book series "Student Mathematical Library":
https://bookstore.ams.org/view?ProductCode=STML/107
(this is the published version that can be cited)
There is also an informal, longer version of the latter book, which is free and located on the math arxives, but which is not to be cited: https://arxiv.org/abs/2104.06407
Computing the Continuous Discretely, Integer-Point Enumeration in Polyhedra, 2'nd Edition, 2015, Springer.
Click here for a free downloadable copy
(please respect the Springer copyright agreement)
Here are some reviews of our book
Here are 5 videos that I made for IMPA's YouTube presentations, as part of the 33'rd Brasilian Colloquium:
www.youtube.com/playlist?list=PLvvfpeSf1IRKy1PhJqxVy-148xbnUCHmI
(This new version of my homepage, using googlesites, was created February 19, 2024)