Scientific

The Ostrowski Quotient for a finite extension of number fields

Speaker: 
Abbas Maarefparvar
Date: 
Wed, Nov 20, 2024
Location: 
PIMS, University of British Columbia
Zoom
Online
Conference: 
UBC Number Theory Seminar
Abstract: 

For a number field $K$, the P\'olya group of $K$, denoted by $Po(K)$, is the subgroup of the ideal class group of $K$ generated by the classes of the products of maximal ideals of $K$ with the same norm. In this talk, after reviewing some results concerning $Po(K)$, I will generalize this notion to the relative P\'olya group $Po(K/F)$, for $K/F$ a finite extension of number fields. Accordingly, I will generalize some results in the literature about P\'olya groups to the relative case. Then, due to some essential observations, I will explain why we need to modify the notion of the relative P\'olya group to the Ostrowski quotient $Ost(K/F)$ to get a more 'accurate' generalization of $Po(K)$. The talk is based on a joint work with Ali Rajaei (Tarbiat Modares University) and Ehsan Shahoseini (Institute For Research In Fundamental Sciences).

Class: 

Mean values of Hardy's Z-function and weak Gram's laws

Speaker: 
Hung M. Bui
Date: 
Tue, Nov 19, 2024
Location: 
PIMS, University of Northern British Columbia
Zoom
Online
Abstract: 

We establish the fourth moments of the real and imaginary parts of the Riemann zeta-function, as well as the fourth power mean value of Hardy's Z-function at the Gram points. We also study two weak versions of Gram's law. We show that those weak Gram's laws hold a positive proportion of time. This is joint work with Richard Hall.

Class: 

On the vertical distribution of the zeros of the Riemann zeta-function

Speaker: 
Emily Quesada Herrera
Date: 
Fri, Nov 8, 2024
Location: 
PIMS, University of British Columbia
Zoom
Online
Conference: 
UBC Number Theory Seminar
Abstract: 

In 1973, assuming the Riemann hypothesis (RH), Montgomery studied the vertical distribution of zeta zeros, and conjectured that they behave like the eigenvalues of some random matrices. We will discuss some models for zeta zeros starting from the random matrix model but going beyond it and related questions, conjectures and results on statistical information on the zeros. In particular, assuming RH and a conjecture of Chan for how often gaps between zeros can be close to a fixed non-zero value, we will discuss our proof of a conjecture of Berry (1988) for the number variance of zeta zeros, in a regime where random matrix models alone do not accurately predict the actual behavior (based on joint work with Meghann Moriah Lugar and Micah B. Milinovich).

Class: 

On the average least negative Hecke eigenvalue

Speaker: 
Jackie Voros
Date: 
Tue, Nov 5, 2024
Location: 
PIMS, University of British Columbia
Online
Zoom
Abstract: 

The least quadratic non-residue has been a central problem in number theory for centuries. The average least quadratic non-residue was explored by Erdős in the 1960s, and many extensions of this problem such as to the average least character non-residue (Martin, Pollack) have been explored. In this talk, we look in to the average first sign change of Fourier coefficients of newforms (equivalently Hecke eigenvalues). We discuss the distribution of Hecke eigenvalues through the so-called 'horizontal' and 'vertical' Sato-Tate distributions, and we also discuss large sieve inequalities for cusp forms that are uniform in both the weight and the level.

Class: 

Skeletal muscle: modeling and computation

Speaker: 
Nilima Nigam
Date: 
Wed, Oct 16, 2024
Location: 
PIMS, University of British Columbia
Conference: 
UBC Math Biology Seminar Series
Abstract: 

Skeletal muscle is composed of cells collectively referred to as fibers, which themselves contain contractile proteins arranged longtitudinally into sarcomeres. These latter respond to signals from the nervous system, and contract; unlike cardiac muscle, skeletal muscles can respond to voluntary control. Muscles react to mechanical forces - they contain connective tissue and fluid, and are linked via tendons to the skeletal system - but they also are capable of activation via stimulation (and hence, contraction) of the sacromeres. The restorative along-fibre force introduce strong mechanical anisotropy, and depend on departures from a characteristic length of the sarcomeres; diseases such as cerebral palsy cause this characteristic length to change, thereby impacting muscle force. In the 1910s, A.V. Hill [1] posited a mathematical description of skeletal muscles which approximated muscle as a 1-dimensional nonlinear and massless spring. This has been a remarkably successful model, and remains in wide use. Yet skeletal muscle is three dimensional, has mass, and a fairly complicated structure. Are these features important? What insights are gained if we include some of this complexity in our models? Many mathematical questions of interest in skeletal muscle mechanics arise: how to model this system, how to discretize it, and what theoretical properties does it have? In this talk, we survey recent work on the modeling, parameter estimation, simulation and validation of a fully 3-D continuum elasticity approach for skeletal muscle dynamics. This is joint work based on a long-standing collaboration with James Wakeling (Dept. of Biomedical Physiology and Kinesiology, SFU).

Class: 

Computational Modeling for Medical Devices

Speaker: 
Pras Pathmanathan
Date: 
Wed, Oct 30, 2024
Location: 
PIMS, University of British Columbia
Zoom
Online
Conference: 
UBC Math Biology Seminar Series
Abstract: 

The Food and Drug Administration (FDA) is responsible for ensuring the safety and effectiveness of medical devices marketed in the US. For several decades, in a handful of niche applications, medical device industry has used computational modeling to provide evidence for safety or effectiveness, complementing bench, animal, or clinical testing. In recent years, the use of computational modeling in medical device regulatory submissions has grown significantly. FDA’s medical device Center is now tasked with evaluating a wide range of computational models of medical devices, as well as computational models implemented in medical device software (for example, patient-specific model-based software devices, closely related to the concept of a digital twin), and in silico clinical trials. This talk will discuss how computational models are relevant to medical devices, and then delve in model credibility assessment. We will discuss key activities involved in evaluating computational models for medical devices, overview recent FDA-led Standards and Guidances, and summarize recent work expanding these methods to the new frontiers of patient-specific models and in silico clinical trials.

Class: 

Environmental feedback maintains cooperation in phage $\Phi_6$

Speaker: 
Jaye Sudweeks
Date: 
Wed, Sep 25, 2024
Location: 
PIMS, University of British Columbia
Zoom
Online
Conference: 
UBC Math Biology Seminar Series
Abstract: 

The evolution and maintenance of cooperation is a fundamental problem in evolutionary biology. Because cooperative behaviors impose a cost, Cooperators are vulnerable to exploitation by Defectors that do not pay the cost to cooperate but still benefit from the cooperation of others. The bacteriophage $\Phi_6$ exhibits cooperative and defective phenotypes in infection: during replication, phages produce essential proteins in the host cell cytoplasm. Coinfection between multiple phages is possible. A given phage cannot guarantee exclusive access to its own proteins, so Cooperators contribute to the common pool of proteins while Defectors contribute less and instead appropriate proteins from Cooperators. Previous experimental work found that $\Phi_6$ was trapped in a prisoner's dilemma, predicting that the cooperative phenotype should disappear. Here we propose that environmental feedback, or interplay between phage and host densities, can maintain cooperation in $\Phi_6$ populations by modulating the rate of co-infection and shifting the advantages of cooperation vs. defection. We build and analyze an ODE model and find that for a wide range of parameter values, environmental feedback allows Cooperation to survive.

Class: 

Torsion of Rational Elliptic Curves over the Cyclotomic Extensions of ℚ

Speaker: 
Omer Avci
Date: 
Thu, Oct 31, 2024
Location: 
PIMS, University of Calgary
Conference: 
UCalgary Algebra and Number Theory Seminar
Abstract: 

Let E be an elliptic curve defined over ℚ. Let p > 3 be a prime such that p - 1 is not divisible by 3, 4, 5, 7, 11. In this article, we classify the groups that can arise as E(ℚ(ζp))tors up to isomorphism. The method illustrates techniques for eliminating possible structures that can appear as a subgroup of E(ℚab)tors.

Class: 

Subconvexity for GL(2) L-functions and Shifted MDS

Speaker: 
Henry Twiss
Date: 
Wed, Oct 30, 2024
Location: 
PIMS, University of Northern British Columbia
Online
Zoom
Abstract: 

Subconvexity problems have maintained extreme interest in analytic number theory for decades. Critical barriers such as the convexity, Burgess, and Weyl bounds hold particular interest because one usually needs to drastically adjust the analytic techniques involved in order to break through them. It has recently come to light that shifted Dirichlet series can be used to obtain subconvexity results. While these Dirichlet series do not admit Euler products, they are amenable to study via spectral methods. In this talk, we construct a shifted multiple Dirichlet series (MDS) and leverage its analytic continuation via spectral decompositions to obtain the Weyl bound in the conductor-aspect for the L-function of a holomorphic cusp form twisted by an arbitrary Dirichlet character. This improves upon the corresponding bound for quadratic characters obtained by Iwaniec-Conrey in 2000. This work is joint with Jeff Hoffstein, Nikos Diamantis, and Min Lee.

Class: 

Mathematical modeling applied to women's health

Speaker: 
Leah Edelstein-Keshet
Date: 
Wed, Sep 11, 2024
Location: 
PIMS, University of British Columbia
Zoom
Online
Conference: 
UBC Math Biology Seminar Series
Abstract: 

Several years ago, Dr Kathryn Isaac, a UBC professor and clinical surgeon contacted me with an intriguing problem. In her work on cosmetic reconstructive for post-breast-cancer-surgery patients, she encounters cases of failure that result (weeks or months later) in "capsular contraction" (CC). This painful condition arises when the healing tissue (the "capsule") that forms surrounding a breast implant undergoes pathological contraction and deformation - necessitating a new rounds of surgery. In this talk, I describe work in our team to help understand the root causes of CC, the risk factors, and possible preventative treatments. We use mathematical modeling to depict and investigate hypotheses for cell-level mechanisms involved in initiating CC. I will describe two rounds of modeling, the earliest joint with Cheryl Dyck MacDonald, and the latest joint with Ms Yuqi Xiao (UBC MSc student) and Prof. Alain Goriely (Oxford).

Class: 

Pages