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Math & Stats Department Colloquium

Friday, October 7th, 2022

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

Speaker: Changbao Wu (University of Waterloo)

Title: Recent Developments in Analysis of Non-Probability Survey Samples

Abstract: We provide a critical review and some extended discussions on theoretical and practical issues with analysis of non-probability survey samples. We attempt to present rigorous inferential frameworks and valid statistical procedures under commonly used assumptions, and address issues on the justification and verification of assumptions in practical applications. Some current methodological developments are showcased, and problems which require further investigation are mentioned. While the focus of the talk is on non-probability samples, the essential role of probability survey samples with rich and relevant information on auxiliary variables is highlighted.

Changbao Wu is Professor of Statistics and Chair of the Department of Statistics and Actuarial Science at the University of Waterloo. His main research interests include design and analysis of complex surveys, resampling techniques, missing data analysis and causal inference, and integration of data from multiple sources. He is Fellow of ASA, Fellow of IMS, Elected Member of ISI, and was the winner of the CRM-SSC Prize in Statistics in 2012. He has served on several editorial boards including Survey Methodology, The Canadian Journal of Statistics, Journal of the American Statistical Association (Theory \& Methods) and Biometrika. He is the lead author of the book “Sampling Theory and Practice” (with Mary Thompson) published by Springer in 2020. He has also served on Statistics Canada’s Advisory Committee on Statistical Methods since 2015.

Curves Seminar

Wednesday, September 21st, 2022

Time: 1:00 p.m.  Place: Jeffery Hall, Room 222

Speaker: Deepanshu Prasad

Title: Introduction to Affine Toric Varieties

Abstract: We will see two more constructions of affine toric varieties, via toric ideals and affine semigroup, and then we'll see how these various constructions are related to one another.

Number Theory Seminar

Tuesday, September 20th, 2022

Time: 2:00 p.m.  Place: Jeffery Hall, Room 422

Speaker: David Nguyen (���ϳԹ���Դ)

Title: Variance of the k-fold divisor function in arithmetic progressions for individual modulus

Abstract: We discuss some background and the proof of Corollary 1 in arXiv:2205.02354. This result is closely related to moments of Dirichlet L-functions and confirms a smoothed version of a recent conjecture of Keating–Rodgers–Roditty-Gershon–Rudnick-Soundararajan on the variance of the k-fold divisor function in arithmetic progressions to individual composite moduli, in a restricted range.

Curves Seminar

Wednesday, September 14th, 2022

Time: 1:00 p.m.  Place: Jeffery Hall, Room 222

Speaker: Alexandre (Sasha) Zotine

Title: Introduction to Affine Toric Varieties

Abstract: Toric geometry is a rich field of algebraic geometry with heavy ties to combinatorial methods, which in turn make them very computationally accessible, while still demonstrating non-trivial behavior. The field has varied applications to representation theory, symplectic geometry, algebraic statistics, as well as coding theory, biology, and mirror symmetry in physics.

In this talk, I will give an introduction to affine toric varieties. We will discuss two constructions, and depending on timing, we may discuss polyhedral cones.

Number Theory Seminar

Tuesday, September 13th, 2022

Time: 2:00 p.m.  Place: Jeffery Hall, Room 422

Speaker: Sneha Chaubey (Indraprastha Institute of Information Technology, Delhi)

Title: Zeros of Derivatives of L-functions in the Selberg Class

Abstract: Spieser in 1935 showed that the Riemann Hypothesis is equivalent to the first derivative of the Riemann zeta function having no non-real zeros to the left of the critical line. This was reported by Levinson and Montgomery in 1974 in a quantitative form. Analogous results have been proven for other L-functions, including Dirichlet L-functions associated to primitive characters. In this talk, we are interested in extending these results to the Selberg class. This is a joint work with Ade Irma Suriajaya and Suraj Singh Khurana.

Math & Stats Department Colloquium

Friday, September 23rd, 2022

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

Speaker: Daniel Litt (University of Toronto)

Title: The search for special symmetries

Abstract: What are the canonical sets of symmetries of n-dimensional space? I'll describe the history of this question, going back to Schwarz, Fuchs, Painlevé, and others, and some new answers to it, obtained jointly with Aaron Landesman. While our results rely on low-dimensional topology, Hodge theory, and the Langlands program, and we'll get a peek into how these areas come into play, no knowledge of them will be assumed.

Daniel Litt is an Assistant Professor of mathematics at the University of Toronto. He was in a similar position at the University of Georgia from 2019-2022. He completed his PhD at Stanford in 2015; from 2015-2018 was an NSF Postdoc at Columbia; and from 2018-2019 was a member at the Institute for Advanced Study.

Broadly speaking, he is interested in the interplay between algebraic geometry and number theory (and, to a lesser extent, topology). Most of his work has focused on using arithmetic techniques to study classical questions about, for example, complex algebraic varieties. Currently, he is thinking about the arithmetic structures on the fundamental group of an algebraic variety, and the relationships between those structures and the geometry of the variety. Some of his other interests include questions about positivity and vanishing theorems, dynamics of algebraic varieties, and Hodge theory (broadly construed).

Public Lecture

Tuesday, September 20th, 2022

Time: 6:30 p.m.  Place: Biosciences Auditorium, ���ϳԹ���Դ, 116 Barrie St.

Speaker: Professor David J. D. Earn (McMaster)

Title: Learning from the pandemics of the last seven centuries

Abstract: Historical records allow us to reconstruct patterns of disease spread in the past, in some cases going back hundreds of years. I will present data, going back as far as 1348, which we have acquired and studied at McMaster in the last few years. I will discuss insights obtained from mathematical modelling inspired by these data, and the opportunities we have to improve our understanding of plague, influenza, COVID-19, and other diseases that cause pandemics.

David Earn is a Professor of Mathematics and Statistics and the Faculty of Science Research Chair in Mathematical Epidemiology at McMaster University. He has been Chair of the  of the  for COVID-19. Modeling from his group has helped guide the governmental response to COVID-19.

Professor Earn is a recipient of the Canadian Applied and Industrial Mathematics Society Research Prize and is an Elected Fellow of the Canadian Academy of Health Sciences.

This lecture is presented as part of the Natural Sciences and Engineering Research Council of Canada’s Mathematics Literacy Week. Attendance is free but please RSVP.

Math & Stats Department Colloquium

Friday, September 16th, 2022

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

Speaker: Duncan McCoy (UQAM)

Title: The unknotting number

Abstract: This talk will be a gentle introduction to the unknotting number. A mathematical knot is a tangled up circle in 3-dimensional space -- think of your shoe laces but with the ends fused together. The unknotting number of a knot is the minimum number of times the knot must be passed through each other in order to transform it into a standard round circle (the 'unknot'). Despite its simple definition, the unknotting number is in general very hard to compute. I will discuss some examples and explain a little of what is known and unknown about the unknotting number.

Dynamics, Geometry and Groups Seminar

Thursday, August 11th, 2022

Time: 2:30 p.m.  Place: Jeffery Hall 422

Speaker: Marco Lenci (Università di Bologna)

Title: Random walks in one-dimensional Lévy random media

Abstract: One speaks of anomalous diffusion when a process (e.g., a mechanical system of particles or a stochastic process) diffuses through space with a different law than that of the Brownian motion. These types of systems are observed both in physics (rarefied gases, certain glassy materials, etc.) and in other sciences (e.g., ethology, social sciences, financial mathematics, etc.). The most realistic models of anomalous diffusion are those where the anomalous behavior is caused by particular properties of the media the process lives in. The mathematical literature on such systems is rather scant. We present a continuous-time random walk in random medium which generalizes a system known in the physical literature as Lévy-Lorentz Gas: a particle travels at constant speed between “target points” that are randomly placed on the real line with fat-tailed interdistances. Depending on the decay of the tail of the distribution, this process may exhibit different types of anomalous diffusion.

Dynamics, Geometry and Groups Seminar

Wednesday, August 3rd, 2022

Time: 2:30 p.m.  Place: Jeffery Hall 422

Speaker: Marco Lenci (Università di Bologna)

Title: Internal-wave billiards in trapezoids and similar tables

Abstract: We call internal-wave billiard the dynamical system of a point particle that moves freely inside a planar domain (the table) and is reflected by its boundary according to this rule: reflections are standard Fresnel reflections but with the pretense that the boundary at any collision point is either horizontal or vertical (relative to a predetermined direction representing gravity). These systems are point particle approximations for the motion of internal gravity waves in closed containers, hence the name. The phenomenon of internal waves in a fluid occurs in many situations and has been intensively studied by physicists. One of the first experiments, which became paradigmatic, was done in a container shaped like a rectangular trapezoid (with some thickness). For a class of tables including rectangular trapezoids, we prove that the dynamics has only three asymptotic regimes: (1) there exist a global attractor and a global repellor, which are periodic and might coincide; (2) there exists a beam of periodic trajectories, whose boundary (if any) comprises an attractor and a repellor for all the other trajectories; (3) all trajectories are dense (that is, the system is minimal). If time permits, we will also discuss the prominent case where the table is an actual trapezoid, studying the sets in parameter space relative to the three regimes. We prove in particular that the set for (1) has positive measure (giving a rigorous proof of the existence of Arnold tongues for internal-wave billiards), whereas the sets for (2) and (3) are non-empty but have measure zero. Joint work with C. Bonanno and G. Cristadoro.