Events

Elcim Elgun, Pure Mathematics Department, University of Waterloo

"The Construction a West Compactication of Z"

Abstract: Given a locally compact group G, a compact semigroup S is called a semigroup compactication if it contains a dense homomorphic image of G. We study the question of extending continuous bounded functions on G to its various semigroup compactications.

Robert Garbary, Pure Mathematics Department, University of Waterloo

"The Zariski Topology"

For a ring R, let Spec(R) denote the set of its prime ideals. We are going to topologize Spec(R) by demanding that R is the ring of continuous functions (into where?) defined on Spec(R). This is called the Zariski Topology. It is so named because, in the case that R is the coordinate ring of an affine variety X, we will see that Spec(R) is almost equal to (whatever that means) X, and that the topology on Spec(R) is almost the same as the usual Zariski topology on X.

Yen-Liang Kuan National Central University, Taiwan

“On the distribution of torsion points modulo primes - Part III.”

Let A be a commutative algebraic group defined over a number field K. For a prime ℘ in K where A has good reduction, let N℘,n be the number of n-torsion F℘-rational points of the reduction of A modulo ℘ where F℘ is the residue field of ℘ and n is a positive integer.

Matthew Harrison-Trainor, Pure Mathematics Department University of Waterloo

"One dimensional Zariski geometries - Part II"

We will introduce three axioms on a Noetherian topological structure which, together with the Krull dimension, are sufficient to make the topological structure a one-dimensional presmooth Zariski structure. We will show that such a structure has quantifier elimination, and satisfies the addition formula AF if the fibre condition FC holds.

Ross Willard, Pure Mathematics Department, University of Waterloo

“Solving group constraints - Part II”

This is the second of several lectures in which I will describe an algorithm for problems whose constraints are cosets of subgroups of powers of a fixed group.

Matthew Beckett, Pure Mathematics, University of Waterloo

"Scaling arguments for the Yang-Mills action"

This talk will introduce the Yang-Mills action on the space of connections as a setting to demonstrate the use of scaling arguments in gaining information about critical points of the energy functional.

Matthew Harrison-Trainor, Pure Mathematics University of Waterloo

“Omitting Partial Types and Hyperimmune Degrees - Part II”

We will show that hyperimmune degrees are able to omit non-principal partial types, and in fact are the only such types. By seeing that this proof can be carried out in RCA0, we will show that omitting partial types and the existence of hyperimmune degrees are equivalent over RCA0.

Tyrone Ghaswala, Department of Pure Mathematics, University of Waterloo

“Spec-tacular”

We will continue talking about the Zariski topology on Spec(R) for R a ring, getting our hands dirty proving some basic properties about it.

Shuntaro Yamagishi, Pure Mathematics Department, University of Waterloo

"Circle Method on Waring's Problem (Major Arcs)"

Abstract: A classic application of Hardy-Littlewood circle method
is the Warding's problem. This talk is meant to be an
introduction to circle method. I will cover the major arcs in the
first week.

Omar Leon Sanchez, Pure Mathematics Department, University of Waterloo

"Examples of Zariski Structures"

In the following two weeks we will see why the following are examples of Zariski structures:

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