Scientific

Exponential Sums Over Multiplicative Groups in Fields of Prime Order and Related Combinatorial Problems

Author: 
Sergei Konyagin
Date: 
Thu, Apr 1, 2004
Location: 
University of British Columbia, Vancouver, Canada
Conference: 
PIMS Distinguished Chair Lectures
Abstract: 
Let $p$ be a prime. The main subject of my talks is the estimation of exponential sums over an arbitrary subgroup $G$ of the multiplicative group ${\mathbb Z}^*_p$: $$S(a, G) = \sum_{x\in G} \exp(2\pi iax/p), a \in \mathbb Z_p.$$ These sums have numerous applications in additive problems modulo $p$, pseudo-random generators, coding theory, theory of algebraic curves and other problems.
Notes: 
PDF icon Konyagin_Lectures.pdf
Class: 
Scientific
Subject: 
Discrete Mathematics
Group Theory

PDE from a probability point of view

Author: 
Richard Bass
Date: 
Thu, Jan 1, 2004
Location: 
UBC, Vancouver, Canada
Abstract: 

These notes are for a course I gave while on sabbatical at UBC. The topics covered are: stochastic differential equations, solving PDEs using probability, Harnack inequalities for nondivergence form elliptic operators, martingale problems, and divergence form elliptic operators.

This course presupposes the reader is familiar with stochastic calculus; see the notes on my web page for Stochastic Calculus, for example. These notes for the most part are based on my book Diffusions and Elliptic Operators, Springer-Verlag, 1997.

Notes: 
PDF icon Bass.pdf
Class: 
Scientific
Subject: 
Partial Differential Equations
Probability

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