Infosheet (November 28th, 2017) 
Queen's University  Department of Mathematics and Statistics 
Tuesday, November 28 
Biostatistics Seminar Time: 1:00 p.m. Place: Bracken 124 (Health Sciences Library) 
Speaker: Debaraj Sen Title: Inference concerning intraclass correlation for binary responses Abstract Attached 
Wednesday, November 29 
Number Theory Seminar Time: 1:30 p.m. Place: Jeffery 319 
1^{st} Speaker: M. Ram Murty Title: Hilbert’s tenth problem over number fields 2^{nd} Speaker: François Séguin Title: A lower bound for the twovariable Artin conjecture 3^{rd} Speaker: Arpita Kar Title: On a Conjecture of Bateman about $r_5(n)$ 4^{th} Speaker: Siddhi Pathak Title: Derivatives of Lseries and generalized Stieltjes constants Abstracts Attached 
Wednesday, November 29

Special Colloquium Time: 3:30 p.m. Place: Jeffery 234 
Speaker: Jason Klusowski, Yale University Title: Counting motifs and connected components of large graphs via subgraph sampling Abstract Attached 
Thursday, November 30 
Seminar in Free Probability and Random Matrices Time: 4:00 p.m. Place: Jeffery 319 
Speaker: PeiLun Tseng, Queen’s University Title: Infinitesimal Laws of noncommutative random variables, II Abstract Attached 
Items for the Info Sheet should reach Anne ( burnsa@queensu.ca) by noon on Monday. The Info Sheet is published every Tuesday.
Tuesday, November 28, 1:00 p.m. Bracken 124 (Health Sciences Library) Biostatistics Seminar
Speaker: Debaraj Sen
Title: Inference concerning intraclass correlation for binary responses
Abstract: In the analysis of several treatment groups for binary outcome data, it is often interesting to determine if the treatments may have stabilizing effects. This inference problem can be done based on the confidence interval for a common intraclass correlation coefficient, and in many applications of epidemiological studies it is preferable by practitioners. Inference procedures concerning the intraclass correlation have been well developed for singlesample problems; little attention has been paid to extend these inference procedures for multiplesample problems. In this talk, we focus on constructing the confidence interval procedures for a common intraclass correlation coefficient of several treatment groups. We compare different approaches with a large sample procedure in terms of coverage and expected length through a simulation study. An application to a solar protection study is used to illustrate the proposed methods.
Wednesday, November 29, 1:30 p.m. Jeffery 319 Number Theory Seminar
1^{st} Speaker: M. Ram Murty
Title: Hilbert’s tenth problem over number fields
Abstract: Hilbert's tenth problem for rings of integers of number fields remains open in general,
although a conditional negative solution was obtained by Mazur and Rubin assuming some unproved conjectures about the ShafarevichTate groups of elliptic curves. In this talk, we highlight how the nonvanishing of certain Lfunctions is related to this problem. In particular, we show that Hilbert's tenth problem for rings of integers of number fields is unsolvable assuming the automorphy of Lfunctions attached to elliptic curves and the rank part of the Birch and SwinnertonDyer conjecture. This is joint work with Hector Pasten.
2^{nd} Speaker: François Séguin
Title: A lower bound for the twovariable Artin conjecture
Abstract: In 1927, Artin conjectured that any integer other than 1 or a perfect square generates the multiplicative group Z/pZ× for infinitely many p. In a 2000 article, Moree and Stevenhagen considered a twovariable version of this problem, and proved a positive density result conditionally to the generalized Riemann Hypothesis by adapting a 1967 proof by Hooley for the original conjecture. During this talk, we will prove an unconditional lower bound for this twovariable problem. This is joint work with Ram Murty and Cameron Stewart.
3^{rd} Speaker: Arpita Kar
Title: On a Conjecture of Bateman about $r_5(n)$
Abstract: Let $r_5(n)$ be the number of ways of writing $n$ as a sum of five integer squares. In his study of this function, Bateman was led to formulate a conjecture regarding the sum $$\sum_{j \leq \sqrt{n}}\sigma(nj^2)$$ where $\sigma(n)$ is the sum of positive divisors of $n$. We give a proof of Bateman's conjecture in the case $n$ is squarefree and congruent to $1$ (mod $4$). This is joint work with Prof. Ram Murty.
4^{th} Speaker: Siddhi Pathak
Title: Derivatives of Lseries and generalized Stieltjes constants
Abstract: Generalized Stieltjes constants occur as coefficients of (s1)^k in the Laurent series expansion of certain Dirichlet series around s=1. The connection between these generalized Stieltjes constants and derivatives of L(s,f) for periodic arithmetical functions f, at s=1 is known. We utilize this link to throw light on the arithmetic nature of L'(1,f) and certain Stieltjes constants. In particular, if p is an odd prime greater than 7, then we deduce the transcendence of at least (p7)/2 of the generalized Stieltjes constants, {gamma_1(a,p) : 1 \leq a < p }, conditional on a conjecture of S. Gun, M. Ram Murty and P. Rath.
Wednesday, November 29, 3:30 p.m. Jeffery 234 Special Colloquium
Speaker: Jason Klusowski
Title: Counting motifs and connected components of large graphs via subgraph sampling
Abstract: Learning properties of large graphs from samples is an important problem in statistical network analysis. We revisit the problem of estimating the numbers of connected components in a graph of $N$ vertices based on the subgraph sampling model, where we observe the subgraph induced by $n$ vertices drawn uniformly at random. The key question is whether it is possible to achieve accurate estimation, i.e., vanishing normalized meansquare error, by sampling a vanishing fraction of the vertices. We show that it is possible by accessing only sublinear number of samples if the graph does not contains highdegree vertices or long induced cycles; otherwise it is impossible. Optimal sample complexity bounds are obtained for several classes of graphs including forests, cliques, and chordal graphs. The methodology relies on topological identities of graph homomorphism numbers, which, in turn, also play a key role proving minimax lower bounds based on constructing random instances of graphs with matching structures of small subgraphs. We will also discuss results for the neighborhood sampling model, where we observe the edges between the sampled vertices and their neighbors.
Thursday, November 30, 4:00 p.m. Jeffery 319
Seminar in Free Probability and Random Matrices
Speaker: PeiLun Tseng
Title: Infinitesimal Laws of noncommutative random variables, II
Abstract: In this talk, we will focus on a single type B variable, and introduce the corresponding infinitesimal law. In addition, we will also define the free additive convolution for infinitesimal laws, and to see the relation between the type B laws and the infinitesimal laws.
Seminar website: http://www.mast.queensu.ca/~mingo/seminar/