Let d and q be positive integers, and consider representing a positive integer n
For every positive, decreasing, summable sequence $a = (a_i)$, we can
construct a Cantor set $C_a$ associated with $a$. These Cantor sets
are not necessarily self-similar. Their dimensional properties and
measures have been studied in terms of the sequence $a$.
In this thesis, we extend these results to a more general collection
The classical Wielandt Theorem is about ”positivisation” of a matrix: If an indecomposable matrix A and and its modulus |A| have the same spectral radius, t
It is typically difficult to classify the irreducible representations of a given algebra A. A good first step is to try to find the primitive ideals i.e. the annihilators of the simple modules.
In this talk I will give a brief overview of a known approach to the ABC conjecture using modular forms. Then I will explain how this approach actually gives a partial result for the ABC conjecture and Szpiro’s conjecture. As a consequence, we will obtain a new effective proof of the finiteness of solutions to the S-unit equation, which does not involve linear forms in logarithms. This is joint work with Ram Murty.
The celebrated Calabi-Yau theorem is an existence result for Kahler metrics with prescribed volume form (or equivalently prescribed Ricci curvature) on a compact Kahler manifold.
Abstract - n/a
We will introduce a refinement of the ‘GPY sieve method’ for studying small gaps between primes.
We will discuss some existence results for complete Calabi-Yau metrics on crepant resolutions of singularities, and use these results to give simple examples of ALF Ricci-flat manifolds.
I will give a concise introduction to free probability theory and random matrix theory. The main focus will be on the relation between both subjects.