Mathematics

Read more about Summer at the HUB Britiania Summer Camp
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Ranks of elliptic curves

Speaker:

Brian Conrey

Date:

Thu, Jun 2, 2011

Location:

PIMS, University of Calgary

Conference:

Analytic Aspects of L-functions and Applications to Number Theory

Abstract:

We show how to use conjectures for moments of L-functions to get insight into the frequency of rank 2 elliptic curves within a family of quadratic twists.

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Optimal Investment for an Insurance Company

Speaker:

Alexandru Badescu

Location:

Calgary Place Tower (Shell)

University of Calgary, Calgary, Canada

Conference:

Shell Lunchbox Lectures

Abstract:

Optimal investment is a key problem in asset-liability management of an insurance company. Rather than allocating wealth optimally so as to maximize the overall investment return, an insurance company is interested in assessing the risk exposure where both assets and liabilities are included and minimizing the risk of mismatches between them. Different approaches for solving optimization problems by minimizing standard risk measures such as the value at risk (VaR) or the conditional value at risk (CVaR) have been proposed in the literature. In this paper we focus on some Solvency II applications by investigating several novel problems for jointly quantifying the optimal initial capital requirement and the optimal portfolio investment under various constraints.

Discussions on the convexity of these problems are also provided. Using a Monte Carlo simulation and a semi-parametric approach based on different assumptions for the loss distribution, we compute the insurer optimal capital needed to be efficiently invested in a portfolio formed by two or more assets. Finally, a detailed numerical experiment is conducted to assess the robustness and sensitivity of our optimal solutions relative to the model factors.

This paper was written in collaboration with Alexandru V. Asimit (Cass Business School, City University, UK), Tak Kuen Siu (Faculty of Business and Economics, Macquarie University, Australia)and Yuriy Zinchenko (Department of Mathematics and Statistics, University of Calgary).

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Moments of zeta and L-functions on the critical Line II (3 of 3)

Speaker:

K. Soundararajan

Date:

Fri, Jun 3, 2011

Location:

University of Calgary, Calgary, Canada

Conference:

Analytic Aspects of L-functions and Applications to Number Theory

Abstract:

I will discuss techniques to get upper and lower bounds for moments of zeta and L-functions. The lower bounds are unconditional and the upper bounds in general rely on the Riemann Hypothesis. In several cases of low moments, one can obtain asymptotics, and I may discuss a couple of such recent cases.

This lecture is part of a series of 3

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Moments of zeta and L-functions on the critical Line I (2 of 3)

Speaker:

K. Soundararajan

Date:

Thu, Jun 2, 2011

Location:

PIMS, University of Calgary

Conference:

Analytic Aspects of L-functions and Applications to Number Theory

Abstract:

I will discuss techniques to get upper and lower bounds for moments of zeta and L-functions. The lower bounds are unconditional and the upper bounds in general rely on the Riemann Hypothesis. In several cases of low moments, one can obtain asymptotics, and I may discuss a couple of such recent cases.

This lecture is part of a series of 3

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Subject:

Distribution of Values of zeta and L-functions (1 of 3)

Speaker:

K. Soundararajan

Date:

Thu, Jun 2, 2011

Location:

PIMS, University of Calgary

Conference:

Analytic Aspects of L-functions and Applications to Number Theory

Abstract:

I will discuss the distribution of values of zeta and L-functions when restricted to the right of the critical line. Here the values are well understood by probabilistic models involving “random Euler products”. This fails on the critical line, and the L-values here have a different flavor here with Selberg’s theorem on log normality being a representative result.

This lecture is part of a series of 3

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Embedding questions in symplectic geometry

PIMS/UBC Distinguished Colloquium: Dusa McDuff

Conference:

PIMS/UBC Distinguished Colloquium Series

Date:

Fri, Nov 4, 2011

Reference:

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Subject:

Hugh C. Morris Lecture: George Papanicolaou

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Inaugural Hugh C Morris Lecture - George Papanicolaou

PIMS was pleased to present the inaugural lecture in the new Hugh C Morris series with speaker George Papanicolaou from Stanford University.

Conference:

Hugh C. Morris Lecture

Date:

Mon, Nov 7, 2011

Reference:

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Subject:

Special values of Artin L-series (3 of 3)

Speaker:

Ram Murty

Date:

Thu, Jun 2, 2011

Location:

PIMS, University of Calgary

Conference:

Analytic Aspects of L-functions and Applications to Number Theory

Abstract:

Dirichlet’s class number formula has a nice conjectural generalization in the form of Stark’s conjectures. These conjectures pertain to the value of Artin L-series at s = 1. However, the special values at other integer points also are interesting and in this context, there is a famous conjecture of Zagier. We will give a brief outline of this and display some recent results.

This lecture is part of a series of 3.

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Read more about Special values of Artin L-series (3 of 3)
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Artin’s holomorphy conjecture and recent progress (2 of 3)

Speaker:

Ram Murty

Date:

Thu, Jun 2, 2011

Location:

PIMS, University of Calgary

Conference:

Analytic Aspects of L-functions and Applications to Number Theory

Abstract:

Artin conjectured that each of his non-abelian L-series extends to an entire function if the associated Galois representation is nontrivial and irreducible. We will discuss the status of this conjecture and discuss briefly its relation to the Langlands program.

This lecture is part of a series of 3.

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