Friday, November 14, 2025
Location: Fariborz Maseeh Hall (FMH), room 462
Time: 3:15pm - 4:15pm
Speaker: Dr. J.J.P. Veerman
Title: Birkhoff Sums of Irrational Rotations
Abstract: We investigate the distribution of a sequence of points in the circle generated by rotations by a fixed irrational number rho with initial condition x, that is: frac{ x + i rho } for i from 1 to infinity. The discrepancy as defined by Pisot and Van Der Corput in the 1930's quantifies how evenly distributed such a sequence is. It plays a prominent role in numerical analysis, dynamical systems, and ergodic theory.
We associate a measure (the Birkhoff measure) to the distribution of Sum frac{ x + i \rho } over i in {1,..., n} and show that the graph of the density of that measure varies strongly with n. Nonetheless, it always tiles \R. We discuss various other aspects of these measures, including connections with the theory of continued fractions. Finally, we outline more efficient proofs of two classical results.
Biography: J. J. P. Veerman received his Ph.D. from Cornell University in 1986. After postdocs in Spain (1 year) and at Cornell University/Rockefeller University (2 years), he held visiting positions in the U.S. (Rockefeller University, CUNY, Stony Brook University, Georgia Tech, Penn State), as well as in Spain (Aut´oma Madrid, Aut´onoma Barcelona), and Brazil (IMPA, PUC-Rio, UFPe). He came to Portland State University in 2000. Since coming to Portland, he has held visiting positions in Spain (Granada), Italy (Pisa, Salerno), Greece (University of Crete), and Rockefeller University in NYC.
Selected Awards:
In 2018, he was offered the (full year) Fulbright-Czech Distinguished Professorship for 2019-2020 at the Czech Technical University in Prague. In 2022, he was the Joseph Meyerhoff Visiting Professor at the Weizmann Institute of Science in Israel. In 2023, he was Visiting Fellow at the Institute of Advanced Studies of the University of Bologna, Italy.