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# Scientific

## Abelian Varieties Multi-Site Seminar Series: Drew Sutherland

Speaker:
Drew Sutherland
Date:
Tue, Jan 12, 2016
Location:
PIMS, University of Washington
Conference:
PIMS CRG in Explicit Methods for Abelian Varieties
Abstract:
Let A be an abelian variety of dimension g over a number field K. The Sato-Tate group ST(A) is a compact subgroup of the unitary symplectic group USp(2g) that can be defined in terms of the l-adic Galois representation associated to A. Under the generalized Sato-Tate conjecture, the Haar measure of ST(A) governs the distribution of various arithmetic statistics associated to A, including the distribution of normalized Frobenius traces at primes of good reduction. The Sato-Tate groups that can and do arise for g=1 and g=2 have been completely determined, but the case g=3 remains open. I will give a brief overview of the classification for g=2 and then discuss the current state of progress for g=3.

## OM representation of prime ideals and applications in function fields

Speaker:
Jens Bauch
Date:
Thu, Dec 10, 2015
Location:
PIMS, Simon Fraser University
Conference:
PIMS CRG in Explicit Methods for Abelian Varieties
Abstract:
Let $A$ be a Dedekind domain, $K$ the fraction field of $A$, and $f\in A[x]$ a monic irreducible separable polynomial. Denote by $\theta\in K^{\mathrm{sep}}$ a root of $f$ and let $F=K(\theta)$ be the finite separable extension of $K$ generated by $\theta$. We consider $\mathcal{O}$ the integral closure of $A$ in $L$. For a given non-zero prime ideal $\mathfrak{p}$ of $A$ the Montes algorithm determines a parametrization (OM representation) for every prime ideal $\mathfrak{P}$ of $\mathcal{O}$ lying over $\mathfrak{p}$. For a field $k$ and $f\in k[t,x]$ this yields a new representation of places of the function field $F/k$ determined by $f$. In this talk we summarize some applications which improve the arithmetic in the divisor class group of $F$ using this new representation.

## The long road to 0.075: a statistician’s perspective of the process for setting ozone standards

Speaker:
Jim Zidek
Date:
Thu, Nov 26, 2015
Location:
PIMS, University of British Columbia
Conference:
UBC Statistics Distinguished Speaker
Abstract:
The presentation will take us along the road to the ozone standard for the United States, announced in Mar 2008 by the US Environmental Protection Agency, and then the new proposal in 2014. That agency is responsible for monitoring that nation’s air quality standards under the Clean Air Act of 1970. I will describe how I, a Canadian statistician, came to serve on the US Clean Air Scientific Advisory Committee (CASAC) for Ozone that recommended the standard and my perspectives on the process of developing it. I will introduce the rich cast of players involved including the Committee, the EPA staff, “blackhats,” “whitehats,” “gunslingers,” politicians and an unrevealed character waiting in the wings who appeared onstage only as the 2008 standards had been formulated. And we will encounter a couple of tricky statistical problems that arose along with approaches, developed by the speaker and his coresearchers, which could be used to address them. The first was about how a computational model based on things like meteorology could be combined with statistical models to infer a certain unmeasurable but hugely important ozone level, the “policy related background level” generated by things like lightning, below which the ozone standard could not go. The second was about estimating the actual human exposure to ozone that may differ considerably from measurements taken at fixed site monitoring locations. Above all, the talk will be a narrative about the interaction between science and public policy - in an environment that harbors a lot of stakeholders with varying but legitimate perspectives, a lot of uncertainty in spite of the great body of knowledge about ozone and above all, a lot of potential risk to human health and welfare.

## An arithmetic intersection formula for denominators of Igusa class polynomials

Speaker:
Bianca Viray
Date:
Thu, Nov 12, 2015
Location:
PIMS, University of Washington
Conference:
PIMS CRG in Explicit Methods for Abelian Varieties
Abstract:
Igusa class polynomials are the genus 2 analogue of Hilbert class polynomials; their roots are invariants of genus 2 curves that have complex multiplication by a fixed order. The coefficients of Igusa class polynomials are rational, but, unlike in genus 1, are not integral. An exact formula, or tight upper bound, for these denominators is needed to compute Igusa class polynomials and has applications to cryptography. In this talk, we explain how to obtain a formula for the arithmetic intersection number G1.CM(K) and how this results in a bound for denominators of Igusa class polynomials. We also explain how the formula for G1.CM(K) leads us to a generalization of Gross and Zagier's formula for differences of CM j-invariants. This is joint work with Kristin Lauter.

## Local-global principles for quadratic forms

Author:
Raman Parimala
Date:
Fri, Oct 30, 2015
Location:
PIMS, University of British Columbia
Conference:
PIMS/UBC Distinguished Colloquium
Abstract:
The classical theorem of Hasse-Minkowski asserts that a quadratic form over a number field represents zero nontrivially provided it represents zero nontrivially over its completions at all its places. We discuss analogous local global principles over function fields of p-adic curves. Such local-global principles in the general setting for homogeneous spaces have implications to the understanding of the arithmetic of these fields.
Notes:

## Landing a Faculty Position

Author:
Phillip Loewen
Date:
Fri, Oct 23, 2015
Location:
PIMS, University of British Columbia
Conference:
PIMS-Math Job Forum
Abstract:
The PIMS-Math Job Forum is an annual Forum to help graduate students and postdoctoral fellows in the Mathematics Department with their job searches. The session is divided in two parts: short presentations from our panel followed by a discussion. Learn the secrets of writing an effective research statement, developing an outstanding CV, and giving a winning job talk. We will address questions like: Who do I ask for recommendation letters? What kind of jobs should I apply to? What can I do to maximize my chances of success?
Notes:

## Finding Your Place at a liberal arts college

Author:
Kathryn Nyman
Date:
Fri, Oct 23, 2015
Location:
PIMS, University of British Columbia
Conference:
PIMS-Math Job Forum
Abstract:
The PIMS-Math Job Forum is an annual Forum to help graduate students and postdoctoral fellows in the Mathematics Department with their job searches. The session is divided in two parts: short presentations from our panel followed by a discussion. Learn the secrets of writing an effective research statement, developing an outstanding CV, and giving a winning job talk. We will address questions like: Who do I ask for recommendation letters? What kind of jobs should I apply to? What can I do to maximize my chances of success?
Notes:

## My Life in "industry"

Author:
Richard Liang
Date:
Fri, Oct 23, 2015
Location:
PIMS, University of British Columbia
Conference:
PIMS-Math Job Forum
Abstract:
The PIMS-Math Job Forum is an annual Forum to help graduate students and postdoctoral fellows in the Mathematics Department with their job searches. The session is divided in two parts: short presentations from our panel followed by a discussion. Learn the secrets of writing an effective research statement, developing an outstanding CV, and giving a winning job talk. We will address questions like: Who do I ask for recommendation letters? What kind of jobs should I apply to? What can I do to maximize my chances of success?
Notes:

## Signs of abelian varieties and representations

Speaker:
Matthew Greenberg
Date:
Thu, Oct 15, 2015
Location:
PIMS, University of Calgary
Conference:
PIMS CRG in Explicit Methods for Abelian Varieties
Abstract:
The sign is a fundamental invariant of an abelian variety defined over a local (archimedian or p-adic) or global (number or function) field. The sign of an abelian varieties over a global field has arithmetic significance: it is the parity of Mordell-Weil group of the abelian variety. The sign also appears in the functional equation of the L-function of abelian variety, determining the parity of its order of vanishing at s=1. The modularity conjecture says that this L-function coincides with the L-function of an automorphic representation, and the sign can be expressed in terms of this representation. Although we know how to compute this sign using representation theory, this computation does not really shed any light on the representation theoretic significance of the sign. This representation theoretic significance was articulated first by Dipendra Prasad (in his thesis), where he relates the sign of a representation to branching laws — laws that govern how an irreducible group representation decomposes when restricted to a subgroup. The globalization of Prasad’s theory culminates in the conjectures of Gan, Gross and Prasad. These conjectures suggest non-torsion elements in Mordell-Weil groups of abelian varieties can be obstructions to the existence of branching laws. By exploiting p-adic variation, though, one can hope to actually produce the Mordell-Weil elements giving rise to these obstructions. Aspects of this last point are joint work with Marco Seveso.

## Juggling Mathematics & Magic

Speaker:
Ronald Graham
Date:
Thu, Sep 17, 2015
Location:
PIMS, University of Calgary
Conference:
Louise and Richard K. Guy Lecture Series
Abstract:
The popular Richard & Louise Guy lecture series celebrates the joy of discovery and wonder in mathematics for everyone. Indeed, the lecture series was a 90th birthday present from Louise Guy to Richard in recognition of his love of mathematics and his desire to share his passion with the world. Richard Guy is the author of over 100 publications including works in combinatorial game theory, number theory and graph theory. He strives to make mathematics accessible to all. Dr. Ronald Graham, Chief Scientist at the California Institute for Telecommunications and Information Technology and the Irwin and Joan Jacobs Professor in Computer Science at UC San Diego. Dr. Ronald Graham, Chief Scientist at the California Institute for Telecommunications and Information Technology and the Irwin and Joan Jacobs Professor in Computer Science at UC San Diego, will the present the lecture, Juggling Mathematics & Magic. Dr. Graham’s talk will demonstrate some of the surprising connections between the mystery of magic, the art of juggling, and the some interesting ideas from mathematics. Ronald Graham, the Irwin and Joan Jacobs Professor in Computer Science and Engineering at UC San Diego (and an accomplished trampolinist and juggler), demonstrates some of the surprising connections between the mystery of magic, the art of juggling, and some interesting ideas from mathematics. The lecture is intended for a general audience.