June 14th, 2021

When a new variant of COVID-19 recently appeared, with the ability to spread much faster than the original virus, many people were taken by surprise. 

But not Troy Day.

Dr. Day is an applied mathematician at Queen’s University who for years has been studying the evolution of microbes that cause infectious diseases, and he knows how quickly these can mutate into new versions. His expertise has now made him a key member of the Ontario COVID-19 Modelling Consensus Table, a group of experts trying to forecast where the virus is headed next...

Read more on the Queen's Alumni Review...

Thursday, June 10th, 2021

Congratulations to graduating Mathematics and Engineering (MTHE) students who received awards in 2021. 

For a list of the award recipients, click here.

Friday, April 16th, 2021

Time: 2:30 p.m.  Place: Online (via Zoom)

Speaker: Michael Perlman (Queen's University)

Title: Measuring hypersurface singularities via differential operators and Hodge theory.

Abstract: Given a polynomial with complex coefficients, its set of zeros is a geometric object known as an algebraic hypersurface. We will discuss two invariants defined via differential operators that can detect and measure singularities of these hypersurfaces: the Bernstein-Sato polynomial and the Hodge ideals. Via the example of the hypersurface defined by the n x n determinant, we will illustrate that these invariants are two sides of the same coin: the mixed Hodge structure.

Michael Perlman is Coleman Postdoctoral Fellow in the Department of Mathematics and Statistics at Queen's University. He obtained his Ph.D. in Mathematics in May 2020 from the University of Notre Dame. His research is in Algebraic Geometry, Commutative Algebra, and their interactions with Representation Theory.

Friday, March 26th, 2021

Time: 2:30 p.m.  Place: Online (via Zoom)

Speaker: Qiyang Han (Rutgers University)

Title: Multiple isotonic regression: limit distribution theory and confidence intervals.

Abstract: In the first part of the talk, we study limit distributions for the tuning-free max-min block estimators in multiple isotonic regression under both fixed lattice design and random design settings. We show that at a fixed interior point in the design space, the estimation error of the max-min block estimator converges in distribution to a non-Gaussian limit at certain rate depending on the number of vanishing derivatives and certain effective dimension and sample size that drive the asymptotic theory. The limiting distribution can be viewed as a generalization of the well-known Chernoff distribution in univariate problems. The convergence rate is optimal in a local asymptotic minimax sense. In the second part of the talk, we demonstrate how to use this limiting distribution to construct tuning-free pointwise nonparametric confidence intervals in this model, despite the existence of an infinite-dimensional nuisance parameter in the limit distribution that involves multiple unknown partial derivatives of the true regression function. We show that this difficult nuisance parameter can be effectively eliminated by taking advantage of information beyond point estimates in the block max-min and min-max estimators through random weighting. Notably, the construction of the confidence intervals, even new in the univariate setting, requires no more efforts than performing an isotonic regression for once using the block max-min and min-max estimators, and can be easily adapted to other common monotone models. This talk is based on joint work with Hang Deng and Cun-Hui Zhang.

Qiyang Han is an Assistant Professor of Statistics at Rutgers University. He received his Ph.D. in Statistics from University of Washington in 2018. He is broadly interested in mathematical statistics and high dimensional probability. His current research is concentrated on abstract empirical process theory and its applications to nonparametric function estimation, Bayes nonparametrics, and high dimensional statistics.

Friday, March 19th, 2021

Time: 2:30 p.m.  Place: Online (via Zoom)

Speaker: Mike Hill (UCLA)

Title: Counting exotic spheres.

Abstract: The circle, surfaces, and three manifolds have essentially one smooth structure on them: there is a unique way to "do calculus" on these. For dimensions at least 5, ordinary Euclidean space does too. In 1956, Milnor shocked the mathematical community by showing that this is not the case for spheres: the 7-sphere has "exotic" smooth structures! In this talk, I will discuss the question "how many distinct smooth structures are there on a given sphere?'' In particular, I will describe some work addressing when the only smooth structure on a sphere is the usual one.

Mike Hill is a Professor at the University of California, Los Angeles. His research focus is in algebraic topology. Prof. Hill completed his Ph.D. at the Massachusetts Institute of Technology in 2006. Prior to joining UCLA in 2015, he was a faculty member at the University of Virginia. He is an editor for Mathematische Zeitschrift, Documenta Mathematica and the Transactions of the American Mathematical Society.