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Dynamics, Geometry and Groups Seminar

Friday, September 30th, 2022

Time: 10:00 a.m.  Place: Jeffery Hall, Room 422

Speaker: Neil MacVicar (Queen's University)

Title: Multiplicative Invariance in the Complex Plane

Abstract: In the late 60s, Hillel Furstenberg proved results and made conjectures concerning the fractal nature of subsets of the unit interval that are invariant under the map that scales a real number by a positive integer r and then kills the integer part. Since then, these sets have been deeply studied. Considerably less has been said about analogous sets in the complex plane. I will review what is known for the case when r is a positive integer that scales real numbers and then introduce a notion of times b invariance in the plane where b is a Gaussian integer. The fractal dimension of these times b invariant sets will be discussed.

Curves Seminar

Wednesday, September 28th, 2022

Time: 1:00 p.m.  Place: Jeffery Hall, Room 319

Speaker: Sonja Ruzic

Title: Review of Affine Varieties

Abstract: We will backtrack to cover some prerequisite topics including affine varieties, the Zariski topology, the coordinate rings.

Algebra & Geometry Seminar

Monday, October 3rd, 2022

Time: 4:30 p.m.  Place: TBA

Speaker: Ruiran Sun (McGill University)

Title: On slope and valuative K-semistability for big and nef birational divisors

Abstract:

Website details here: https://mast.queensu.ca/~georep/Fall%20'22.html

Number Theory Seminar

Tuesday, September 27th, 2022

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

Speaker: Nic Fellini (���ϳԹ���Դ)

Title: Fermat quotients and the Ankeny-Artin-Chowla conjecture

Abstract: In 1952, Ankeny, Artin, and Chowla proved a congruence relation mod p relating the class number of the real quadratic field Q(√p), the fundamental unit of Q(√p), and some Bernoulli number. I will present joint work with Professor Murty where we generalize the results of Ankeny, Artin, and Chowla and will discuss some consequences of a conjecture related to their work.

Dynamics, Geometry and Groups Seminar

Friday, September 23rd, 2022

Time: 10:00 a.m.  Place: Jeffery Hall, Room 422

Speaker: Henry Kavle (Queen's University)

Title: A Morse index-Maslov index correspondence for convex billiards

Abstract: In 1976, J.J. Duistermaat proved a general correspondence between the Morse index of a trajectory arising as a critical point of a variational problem and the Maslov index of a path of symplectic matrices describing the linearized flow along the trajectory in phase space. We will sketch an analogous correspondence for discrete time dynamics, emphasizing concrete computations for periodic orbits in smooth convex billiard tables. Time permitting, we will show that these indices allow us to determine the linear stability of periodic trajectories.

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.