Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Lorne Campbell Lectureship - Olgica Milenkovic (UIUC)

Olgica Milenkovic (UIUC)

This is the second in a lecture series named in honour of Lorne Campbell, emeritus professor in the department, made possible by a generous donation from alumnus Vijay K. Bhargava, Professor of Electrical and Computer Engineering at the University of British Columbia.

Wednesday, November 27th, 2019

Time: 3:30 p.m.  Place: Jeffery Hall 127

Speaker: Olgica Milenkovic (UIUC)

Title: String reconstruction problems in molecular storage.

Abstract: String reconstruction problems frequently arise in many areas of genomic data processing, molecular storage, and synthetic biology. In the most general setting, they may be described as follows: one is given a single or multiple copies of a coded or uncodedstring, and the string copies are subsequently subjected to some form of (random) processing such as fragmentation or repeated transmission through a noise-inducing channel. The goal of the reconstruction method is to obtain an exact or approximate version of the string based on the processed outputs. Examples of string reconstruction questions include reconstruction from noisy traces, reconstruction from substrings and k-decks and reconstruction from compositional substring information. We review the above and some related problems and then proceed to describe coding methods that lead to strings that can be accurately reconstructed from their noisy traces, substrings and compositions. (This is a joint work with Ryan Gabrys, Han Mao Kiah, Srilakshmi Pattabiraman and Gregory Puleo.

Olgica Milenkovic is a professor of Electrical and Computer Engineering at the University of Illinois, Urbana-Champaign (UIUC), and Research Professor at the Coordinated Science Laboratory. She obtained her PhD from the University of Michigan, Ann Arbor. Her research interests include coding theory, bioinformatics, machine learning and signal processing.

Among her accolades, she received an NSF CAREER grant, the DARPA Young Faculty Award, the Dean’s Excellence in Research Award, and several best paper awards. She was elected a UIUC Center for Advanced Study Associate and Willett Scholar (2013) and became a Distinguished Lecturer of the Information Theory Society (2015). She is an IEEE Fellow and has served as Associate Editor and Guest-Editor-in-Chief of several leading IEEE journals.

Images from Olgica Milenkovic's Lecture - Nov. 28th, 2019

Lorne Campbell Lectureship - Olgica Milenkovic (UIUC)
Lorne Campbell Lectureship - Olgica Milenkovic (UIUC)
Lorne Campbell Lectureship - Olgica Milenkovic (UIUC)
Lorne Campbell Lectureship - Olgica Milenkovic (UIUC)

Department Colloquium - Undergraduate Summer Projects

Undergraduate Summer Projects

Friday, November 22nd, 2019

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

Speaker: Multiple Speakers

Title: Undergraduate Summer Projects.

This week colloquium will consists of ten 9 minutes presentations, starting at 2:30pm and
in the following order, by:

  • Rebecca Carter - RabbitMath animations: bringing dynamical systems to high school mathematics.
  • Daniel Cloutier - Computation of Beta Invariants on Toric Varieties I.
  • Keenan McPhail - Computation of Beta Invariants on Toric Varieties II.
  • Luca Sardellitti - Modelling and analyzing antibiotic resistance using artificial life
  • Adam Gronowski - Deep Variational Information Bottleneck.
  • Paul Wilson - Error control codes for two-way multiplying channels.
  • Ian Hogeboom-Burr - Comparison of information structures for zero-sum games and Blackwell ordering in standard Borel spaces.
  • Matt Spragge - Differential Equations Driven by Rough Paths.
  • Shikai Liu - Extensions of the Kalman lter I.
  • Linke Li - Extensions of the Kalman lter II.

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.