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Mathematics

Jacobian versus Infrastructure in Real Hyperelliptic Curves

Speaker: 
Monir Rad
Date: 
Thu, Nov 17, 2016 - Sat, Dec 17, 2016
Location: 
PIMS, University of Calgary
Conference: 
PIMS CRG in Explicit Methods for Abelian Varieties
Abstract: 

Hyperelliptic curves of low genus are good candidates for curve-based cryptography. Hyperelliptic curves comes in two models: imaginary and real. The existence of two points at infinity in real models makes them more complicated than their imaginary counterparts. However, real models are more general than the other model, every imaginary hyperelliptic curve can be transformed into a real curve over the same base field Fq , while the reverse process requires a larger base field.

Real hyperelliptic curves have not received as much attention by the cryptographic community as imaginary models, but more recent research has shown them to be suitable for cryptography. Real models admit two structures, the Jacobian (a finite abelian group) and the infrastructure (almost group just fails associativity). In this talk, we explain these two structures and compare their arithmetic based on some recent research. We show that the Jacobian makes a better performance in the real model. We also confirm our claim with some numerical evidence for genus 2 and 3 hyperelliptic curves.

 

For more information on this event, please see the event webpage

Landing a Faculty Position

Author: 
Phillip Loewen
Date: 
Tue, Oct 18, 2016
Location: 
PIMS, University of British Columbia
Conference: 
2016 PIMS-Math Job Forum for Postdoctoral Fellows and Graduate Students
Abstract: 
Slides from Phillip Loewen's presentation at the 2016 PIMS-Math Job Forum for Postdoctoral Fellows and Graduate Students.

Living the Good Life at a Liberal Arts College

Author: 
Gizem Karaali
Date: 
Tue, Oct 18, 2016
Location: 
PIMS, University of British Columbia
Conference: 
2016 PIMS-Math Job Forum for Postdoctoral Fellows and Graduate Students
Abstract: 
Slides from Gizem Karaali's presentation at the 2016 PIMS-Math Job Forum for Postdoctoral Fellows and Graduate Students.

Landing an Industry Position

Author: 
Andrew King
Date: 
Tue, Oct 18, 2016
Location: 
PIMS, University of British Columbia
Conference: 
2016 PIMS-Math Job Forum for Postdoctoral Fellows and Graduate Students
Abstract: 
Slides from Andrew King's presentation at the 2016 PIMS-Math Job Forum for Postdoctoral Fellows and Graduate Students.
Notes: 

About Irreversibility in Rarefied Gas Dynamics

Speaker: 
Laure Saint-Raymond
Date: 
Fri, Oct 7, 2016
Location: 
PIMS, University of British Columbia
Conference: 
PIMS/UBC Distinguished Colloquium
Abstract: 
About Irreversibility in Rarefied Gas Dynamics

Making Mathematics with needle and thread: Quilts as Mathematical Objects

Speaker: 
Gerda de Vries
Date: 
Thu, Aug 18, 2016
Location: 
PIMS, University of British Columbia
Conference: 
PIMS Public Lecture
Abstract: 
The connection between textiles and mathematics is intimate but not often explored, possibly because textiles and fiber arts have traditionally been the domain of women while mathematics was viewed as a male endeavour. How times have changed! Today, textiles and mathematics, like art and science, are recognized for their interwoven, complimentary attributes. In this presentation, mathematics professor Gerda de Vries will examine the connection between textiles and mathematics, in the context of both traditional and contemporary quilts. In a sense, every quilt is a mathematical object, by virtue of the fact that it has shape and dimension. But some quilts are more mathematical than others, and in very different ways. She will show how mathematical concepts such as symmetry, fractals, and algorithmic design show up in the world of quilting through serendipitous and intentional design. This lecture is for a general audience. A background in mathematics is not needed, nor the ability to sew! For more information see the event webpage.

Paths of minimal lengths on the set of exact differential k–forms

Speaker: 
Wilfrid Gangbo
Date: 
Fri, Sep 9, 2016
Location: 
PIMS, University of British Columbia
Conference: 
UBC Math Department Colloquium
Abstract: 

We initiate the study of optimal transportation of exact differential k–forms and introduce various distances as minimal actions. Our study involves dual maximization problems with constraints on the codifferential of k–forms. When k < n, only some directional derivatives of a vector field are controlled. This is in contrast with prior studies of optimal transportation of volume forms (k = n), where the full gradient of a scalar function is controlled. Furthermore, our study involves paths of bounded variations on the set of k–currents. This talk is based a joint work with B. Dacorogna and O. Kneuss.

 

For more information, see the event webpage.

On the local Langlands conjectures

Speaker: 
Rachel Ollivier
Date: 
Fri, Sep 30, 2016
Location: 
PIMS, University of British Columbia
Conference: 
UBC-PIMS Mathematical Sciences Faculty Award
Abstract: 

Abstract

The Langlands program, initiated in the 1960s, is a set of conjectures predicting a unification of number theory and the representation theory of groups. More precisely, the Langlands correspondence provides a way to interpret results in number theory in terms of group theory, and vice versa.

In this talk we sketch a few aspects of the local Langlands correspondence using elementary examples. We then comment on some questions raised by the emerging "mod p" Langlands program.

Biography

Professor Ollivier works in the Langlands Programme, a central theme in pure mathematics which predicts deep connections between number theory and representation theory. She has made profound contributions in the new branches of the "p-adic" and "mod-p" Langlands correspondence that emerged from Fontaine's work on studying the p-adic Galois representation, and is one of the pioneers shaping this new field. The first results on the mod-p Langlands correspondence were limited to the group GL2(Qp); but Dr. Ollivier has proved that this is the only group for which this holds, a surprising result which has motivated much subsequent research.

She has also made important and technically challenging contributions in the area of representation theory of p-adic groups, in particular, in the study of the Iwahori-Hecke algebra. In joint work with P. Schneider, Professor Ollivier used methods of Bruhat-Tits theory to make substantial progress in understanding these algebras. She has obtained deep results of algebraic nature, recently defining a new invariant that may shed light on the special properties of the group GL2(Qp).

Rachel Ollivier received her PhD from University Paris Diderot (Paris 7), and then held a research position at ENS Paris. She subsequently was an assistant professor at the University of Versailles and then Columbia University, before joining the UBC Department of Mathematics in 2013.

Rachel is the recepient of the 2015 UBC Mathematics and Pacific Institute for the Mathematical Sciences Faculty Award.

More information on this event is available on the event webpage

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PDE Aspects of Fluid Flows

Speaker: 
Vladimir Sverak
Date: 
Fri, Sep 23, 2016
Location: 
PIMS, University of British Columbia
Conference: 
PIMS/UBC Distinguished Colloquium
Abstract: 
We explain some of the recent results in concerning PDEs describing fluid flows, as well as some of the difficulties. Model equations will also be discussed. For more information, see the event webpage for this event.

The Arakelov Class Group

Speaker: 
Ha Tran
Date: 
Thu, Sep 22, 2016
Location: 
PIMS, University of Calgary
Conference: 
PIMS CRG in Explicit Methods for Abelian Varieties
Abstract: 
Let F be a number field. The Arakelov class group Pic_0 F of F is an analog to the Picard group of a curve. This group provides us the information of F such as the class number h_F, the class group Cl(F) and the regulator R_F. In this talk, we will first introduce Pic_0 F then show that how this group gives us the information of F. Next, we will discuss a tool to compute this group-reduced Arakelov divisors- and their properties. Finally, some open problems relating to this topic will be presented. See the event webpage for more information.
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