Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
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Department Colloquium - Hector Pasten (Harvard University)

Hector Pasten (Harvard University)

Friday, November 10th, 2017

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

Speaker: Hector Pasten

Title: In Quest of Arithmetic Derivatives

Abstract: There are well-known arithmetic analogies between integers and polynomials (or more generally, holomorphic functions), specially with respect to solutions of Diophantine equations. A crucial aspect that is missing in this analogy is that for polynomials and holomorphic functions one can use derivatives, while for integers there is no direct substitute of this operation. After some motivation, I will discuss a couple of possible candidates for arithmetic derivatives.

Hector Pasten (Harvard University): Hector Pasten (Chile, 1988) is since 2014 a Benjamin Peirce Fellow at Harvard University. He was also a member of the Institute for Advanced Study at Princeton (2015-2016). Pasten received a Ph.D. in 2010 from Universidad de Concepcion in the subject of mathematical logic and non-archimedean analysis. Then he received a Ph.D. in 2014 from Queen's University in the subject of number theory. Among other distinctions, Pasten was awarded the Governor-General of Canada Academic Gold Medal (2014), the Doctoral Prize of the Canadian Mathematical Society (2015), and the Mathematical Council of the Americas Prize (2017). His current research is in number theory and related areas, addressing topics such as decidability of arithmetic structures, Diophantine approximation, and analogies between number theory and value distribution.

Number Theory - Francesco Cellarosi (Queen's University)

Wednesday, November 8th, 2017

Time: 1:30 p.m.  Place: Jeffery Hall 319

Speaker: Francesco Cellarosi

Title: Smooth Sums over Smooth k-Free Integers

Abstract: We provide an asymptotic estimate for certain sums over k-free integers with small prime factors. These sums depend upon a complex parameter $\alpha$ and involve a smooth cut-off $f$. They are a variation of several classical number-theoretical sums. One term in the asymptotics is an integral operator whose kernel is the $\alpha$-convolution of the Dickman-de Bruijn distribution, and the other term is explicitly estimated. The trade-off between the value of $\alpha$ and the regularity of $f$ is discussed.

Department Colloquium - Nasser Sadeghkhani (Queen's University)

Nasser Sadeghkhani (Queen's University)

Friday, November 3rd, 2017

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

Speaker: Nasser Sadeghkhani

Title: Bayesian Predictive Density Estimation with Additional Information

Abstract: In the context of Bayesian theory and decision theory, the estimation of a predictive density of a random variable represents an important and challenging problem. Often the times there is some additional information at our disposal which is unduly being ignored. In this talk, we deal with strategies to take into account this kind of information, in order to obtain e ective and sometimes better performing predictive densities than others in the literature.

Nasser Sadeghkhani (Queen's University): Nasser Sadeghkhani earned his Ph.D in Mathematics (Statistics) from the Universite de Sherbrooke in 2017 under the supervision of Eric Marchand. He recently joined the Department of Mathematics and Statistics at Queen's University as a Coleman Postdoctoral Fellow. Dr Sadeghkhani's research interests include Bayesian Statistics, Multivariate Statistics, Survival Analysis, Decision Theory, and Predictive Inference.

Number Theory - Siddhi Pathak (Queen's University)

Wednesday, November 1st, 2017

Time: 3:30 p.m.  Place: Jeffery Hall 319

Speaker: Siddhi Pathak

Title: On a conjecture of Erdos

Abstract: In a written correspondence with A. Livingston in the 1960s, Erdos conjectured that for an arithmetic function f, periodic with period q satisfying: (i) f(n) is 1 or -1 if q does not divide n and (ii) f(n) = 0 if q divides n, the series \sum_{n=1}^{\infty} f(n)/n is not zero (and hence, evaluates to a transcendental number) whenever it converges. In 2007, this conjecture was proved by M. Ram Murty and N. Saradha for q congruent to 3 modulo 4 and is still open when q is congruent to 1 modulo 4. In this talk, we present some new developments toward this conjecture.

Department Colloquium - Daniel Wise (McGill University)

Daniel Wise (McGill University)

Friday, October 27th, 2017

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

Speaker: Daniel Wise

Title: The Cubical Route to Understanding Groups

Abstract: Cube complexes have come to play an increasingly central role within geometric group theory, as their connection to right-angled Artin groups provides a powerful combinatorial bridge between geometry and algebra. This talk will introduce nonpositively curved cube complexes, and then describe the developments that recently culminated in the resolution of the virtual Haken conjecture for 3-manifolds, and simultaneously dramatically extended our understanding of many in nite groups.

Daniel Wise (McGill University): Daniel Wise earned his Ph.D. in Mathematics from Princeton University in 1996, with a thesis on "Non Positively Curved Squared Complexes, Aperiodic Tilings and Non-Residually Finite Groups". After a NSF Postdoctoral Fellowship at UC Berkeley (1996-1997), he became H.C. Wang Assistant Professor at Cornell (1997-2000), Visiting Assistant Professor at Brandeis (2000-2001), and Assistant Professor at McGill University (2001-2004). Wise was promoted to Associate Professor in 2004, Full Professor in 2009, and appointed James McGill Professor in 2013. He has also served as Chair of the Institut Henri Poincare (2015-2016). Prof Wise received the Oswald Weblen Prize in Geometry in 2013, and the Je ery-Williams the CRM-Fields-PIMS Prizes in 2016. In 2014, he was ICM speaker and became Fellow of the Royal Society of Canada and, in 2016, he became Guggenheim Fellow. Wise's research is dedicated to the theory of in nite groups - with applications to Geometry and Topology. Specically, he studies geometric group theory, metric spaces of nonpositive curvature, residually finite groups, subgroup separability, 3-dimensional manifolds, coherence.

Number Theory - Richard Leyland (Queen's University)

Wednesday, October 25th, 2017

Time: 1:30 p.m.  Place: Jeffery Hall 319

Speaker: Richard Leyland

Title: Galois representations of CM Elliptic Curves

Abstract: We introduce the notion of the mod-N Galois representation $\rho_{E/F,N}$ attached to an elliptic curve $E/F$. Motivated by conjectures of Frey and Mazur, we aim to determine all elliptic curves $E’/F$ such that $\rho_{E’/F,N}\cong \rho_{E/F,N}$ in the case where both $E$ and $E’$ have complex multiplication. In this talk, we introduce the problems, terminology currently being worked on and present a small result in the case where $E$ and $E’$ have complex multiplication by different imaginary quadratic fields.