Quanlei Fang, CUNY BCC (Jingbo Xia)
Revisiting Arveson’s Dirac operator of a commuting tuple
4:00PM, Wed Oct 16 2019, Room 250 Mathematics Bldg
About twenty years ago, Arveson introduced an abstract Dirac operator based on Taylor spectrum and functional calculus. He showed that every Dirac operator is associated with a commuting tuple. The Dirac operator of a commuting tuple has inspired several interesting problems in multivariable operator theory. In this talk, we will revisit the Dirac operator and discuss some related problems.
Colloquium: Barry Fox
A Quant’s Journey Toward Diversification
4:00PM, Thu Oct 17 2019
Portfolio diversification is a useful technique that has the potential to improve risk-adjusted returns for an investment portfolio. In this presentation we take a detailed look at diversification through theoretical considerations as well as empirical results. We analyze the degree of potential benefit of diversification as well as its limitations and trade-offs. This provides a glimpse into quantitative research conducted by Graham Capital’s systematic investment team.
Applied math seminar: Mark Hoefer
4:00PM, Tue Oct 22 2019
Han Li, Wesleyan University ( Hanfeng Li)
Masser’s conjecture on equivalence of integral quadratic forms
4:00PM, Wed Oct 23 2019
A classical problem in the theory of quadratic forms is to decide whether two given integral quadratic forms are equivalent. Formulated in terms of matrices the problem asks, for given symmetric n-by-n integral matrices A and B, whether there is a unimodular integral matrix X satisfying A=X’BX, where X’ is the transpose of X. For definite forms one can construct a simple decision procedure. Somewhat surprisingly, no such procedure was known for indefinite forms until the work of C. L. Siegel in the early 1970s. In the late 1990s D. W. Masser conjectured for n at least 3, there exists a polynomial search bound for X in terms of the heights of A and B. In this talk we shall discuss our recent resolution of this problem based on a joint work with Professor Gregory A. Margulis, and explain how ergodic theory is used to understand integral quadratic forms.
Anita T. Layton (University of Waterloo)
4:00PM, Tue Nov 19 2019