Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Dynamics, Geometry, & Groups - Neil MacVicar (Queen's University)

Friday, November 22nd, 2019

Time: 10:30 a.m Place: Jeffery Hall 319

Speaker: Neil MacVicar (Queen's University)

Title: Bratteli Diagrams and Cantor Minimal Systems.

Abstract: A Bratteli diagram is a kind of infinite graph for which a transformation can be defined on its path space. This talk will introduce the diagrams, their associated dynamical systems, and the relationship between these systems and systems described by a minimal homeomorphism acting on a Cantor space.

Number Theory Seminar - Richard Leyland

Thursday, November 21st, 2019

Time: 4:30-5:30 p.m.  Place: Jeffery Hall 422

Speaker: Richard Leyland

Title: Isogenies of Elliptic Curves with Complex Multiplication.

Abstract: In my thesis work I seek to answer Mazur's Question which asks if there exists any isomorphisms of mod $N$ Galois representations attached to elliptic curves that are not induced by isogenies. The first step in answering this question is determining which isogenies of elliptic curves are defined over a field $F$. In this talk, I will show how to construct isogenies between CM elliptic curves by using ideals of the endomorphism rings. In particular, we will see that if the field of definition $F$ does not contain the CM field, then we can reduce the problem to finding cyclic isogenies.

Curves Seminar - Gregory G. Smith (Queen's University)

Wednesday, November 20th, 2019

Time: 4:00-5:30 p.m Place: Jeffery Hall 319

Speaker: Gregory G. Smith (Queen's University)

Title: Patterns in the Betti tables.

Abstract: We will examine some of the numerical restrictions on the Betti numbers appearing in the minimal free resolution of the homogeneous coordinate ring of a canonical curve. We will also highlight the consequences of these conditions on low genus curves.

Statistics & Biostatistics - Qingling Duan (Queen's University)

Wednesday, November 20th, 2019

Time: 11:30-12:30 Place: Jeffery Hall 225

Speaker: Qingling Duan (Queen's National Scholar in Bioinformatics, School of Computing and Dept. of Biomedical & Molecular Sciences, Queen's University)

Title: Statistical methods for the study of genomic risk factors of complex traits

Abstract: The overarching goal of my research program is to identify and characterize genomic factors that modulate multifactorial traits such as drug response, allergies and asthma. My team leads the collection and analysis of multiple types of ‘omics (i.e. genomics, transcriptomics, epigenomics and metagenomics) datasets from human cohorts. Specifically, we hypothesize that gene-gene and gene-environment interactions account in part for the missing heritability of complex traits. We test this using additive and multiplicative models in addition to network analysis and data integration to characterize novel biological pathways and underlying disease mechanisms. For example, we have identified main and interaction effects of genetic variants and environmental exposures (e.g., smoking, dog ownership, breastfeeding) on risk of early childhood asthma. In addition, we report novel gene networks associated with risk of asthma and response to chemotherapy among cancer patients. I am a lead investigator of the Canadian Healthy Infant Longitudinal Development (CHILD) cohort study and the Canadian Respiratory Research Network which supports the Canadian Chronic Obstructive Lung Disease (CanCOLD). My laboratory is currently funded by the Canadian Institute of Health Research, Queen’s University and the Canadian Foundation for Innovation.

Topological Data Analysis - Multiple Speakers

Monday, November 18th, 2019

Time: 2:30 p.m. Place: Goodes Hall 120

Speaker: Jordan Kokocinski, Arne Kuhrs, Catherine Pfaff, David Riegert Luke Steverango

Topics:  The graduate students have a well-prepared presentation on the Bubenik worksheet. This is highly recommended, even if you've missed a few meetings &/or are confused about homology. With leftover time Pfaff will provide some supplement to last week's presentation.

All are welcome!

Geometry & Representation - Gregory G. Smith

Monday, November 18th, 2019

Time: 4:30-5:30 p.m.  Place: Jeffery Hall 319

Speaker: Gregory G. Smith (Queen's University)

Title: Smooth Hilbert schemes.

Abstract:  In algebraic geometry, Hilbert schemes are the prototypical parameter spaces: their points correspond to closed subschemes in a projective space with a fixed Hilbert polynomial. After surveying some of their known features, we will present new numerical conditions on the polynomial that completely characterize when the associated Hilbert scheme is smooth. In this smooth situation, our explicit description of the subschemes being parametrized also provides new insights into the global geometry of Hilbert schemes. This talk is based on joint work with Roy Skjelnes (KTH).

Dynamics, Geometry, & Groups - Elizabeth Field (UIUC)

Friday, November 15th, 2019

Time: 10:30 a.m Place: Jeffery Hall 319

Speaker: Elizabeth Field (University of Illionois Urbana-Champagn)

Title: Trees, dendrites, and the Cannon-Thurston map.

Abstract: When 1 -> H -> G -> Q -> 1 is a short exact sequence of three word-hyperbolic groups, Mahan Mitra (Mj) has shown that the inclusion map from H to G extends continuously to a map between the Gromov boundaries of H and G. This boundary map is known as the Cannon-Thurston map. In this context, Mitra associates to every point z in the Gromov boundary of Q an ``ending lamination'' on H which consists of pairs of distinct points in the boundary of H. We prove that for each such z, the quotient of the Gromov boundary of H by the equivalence relation generated by this ending lamination is a dendrite, that is, a tree-like topological space. This result generalizes the work of Kapovich-Lustig and Dowdall-Kapovich-Taylor, who prove that in the case where H is a free group and Q is a convex cocompact purely atoroidal subgroup of Out(F_n), one can identify the resultant quotient space with a certain R-tree in the boundary of Culler-Vogtmann's Outer space.

Department Colloquium - Alexei Novikov (Penn State)

Alexei Novikov (Penn State)

Friday, November 15th, 2019

Time: 2:30 p.m.  Place: Jeffery Hall 234

Speaker: Alexei Novikov (Penn State)

Title: The Noise Collector for sparse recovery in high dimensions.

Abstract: The ability to detect sparse signals from noisy high-dimensional data is a top priority in modern science and engineering. A sparse solution of the linear system $Ax=b$ can be found efficiently with an $l_1$-norm minimization approach if the data is noiseless. Detection of the signal's support from data corrupted by noise is still a challenging problem, especially if the level of noise must be estimated. We propose a new efficient approach that does not require any parameter estimation. We introduce the Noise Collector (NC) matrix $C$ and solve an augmented system $Ax+Cy=b+e$, where $e$ is the noise. We show that the $l_1$-norm minimal solution of the augmented system has zero false discovery rate for any level of noise and with probability that tends to one as the dimension of $b$ increases to infinity. We also obtain exact support recovery if the noise is not too large, and develop a Fast Noise Collector Algorithm which makes the computational cost of solving the augmented system comparable to that of the original one. I'll introduce this new method and give its geometric interpretation.

Prof. Alexei Novikov obtained his Ph.D.~from Stanford in 1999 and then held postdoctoral positions at the IMA and at CalTech before joining the Pennsylvania State University where he is now a Professor in the Department of Mathematics. Prof. Novikov specializes in applied analysis and probability. His research has been supported by the NSF since 2006, as well as by the US--Israel Binational Science Foundation from 2005-2009.

CYMS Seminar - Oswaldo Sevilla

Thursday, November 14th, 2019

Time: 2:30 p.m Place: Jeffery Hall 319

Speaker: Oswaldo Sevilla (Fields Institute and Centro de Investigacion en Matematicas A.C.)

Title: Calabi Yau Threefolds arising from certain root lattices.

Abstract: I'll show my work on the construction of Calabi Yau threefolds that are constructed from the C_3 and C_4 root systems, using a construction by H. Verrill (Root lattices and pencils o f varieties, 1996) based on a paper of V. Batyrev (Dual Polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties,1994).

Number Theory Seminar - Mike Roth (Queen's University)

Thursday, November 14th, 2019

Time: 4:30-5:30 p.m.  Place: Jeffery Hall 422

Speaker: Mike Roth (Queen's University)

Title: A measure of positivity of a line bundle along a subschemes, and a simpler proof of the Ru-Vojta arithmetic theorem.

Abstract: Diophantine geometry seeks to link properties of rational solutions of a set of equations to the geometric properties of the variety they define. One of the main tools in Diophantine geometry is Diophantine approximation — results bounding how the complexity of a rational point must grow as it approaches a subvariety. In this talk I will discuss a somewhat recent new measure of the positivity of an ample line bundle along a subscheme, and show how its formal properties give a simple proof of a theorem of Ru-Vojta on Diophantine approximation. This is joint work with David McKinnon at Waterloo.