Events

Jonathan Herman, Department of Pure Mathematics, University of Waterloo

"Momentum and Position Forms"

We first recall the theory of the classical momentum and position functions on the phase space of a manifold. The Poisson bracket relations between these functions form the bridging gap from classical to quantum mechanics. We extend the Poisson bracket to multisymplectic geometry and show that a more general relationship holds between 'momentum and position forms' on an $n$-plectic manifold.

MC 5479

Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo

"Muchnik and Medvedev Reducibilities"

Even though both reducibilities seemed to behave in a similar way, we could see (without proof), that they differ at how they get affected by adding a constant to the structures. We give a proof this time and also show in another result that the difference is more than just the reactions to adding constants. The latter result will require a version of the Slaman-Wehner structure.

MC 5403

Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo

"A new construction of compact $G_2$~manifolds by glueing Eguchi-Hanson spaces, Part II: Modifying the identification with the normal bundle"

Shouzhen Gu, Department of Pure Mathematics, University of Waterloo

"The Hales-Jewett Theorem"

Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo

"Faizrahmanov-Kalimullin Theorem"

This week we finish the proof of Faizrahmanov-Kalimullin Theorem which says that there is a structure whose degree spectra is all the non-computable degrees, but unlike the Slaman-Wehner structure, there is no uniform computable way that gives us a copy of the structure from any non-computable set.

MC 5403

Brendan Nolan, University of Kent

"A gentle overview of some quantum algebras, quantum groups, and their prime and primitive ideals"

I will introduce some examples of quantum algebras and quantum groups, outlining some behaviour which they share with their classical counterparts. I will discuss the Goodearl--Letzter stratification of quantum algebras with respect to the actions of algebraic tori, which gives deep insights into the prime and primitive spectra of various quantum algebras. 

MC 5417

Ertan Elma, Department of Pure Mathematics, University of Waterloo

"Brun's Sieve"

First, we will have a look at Brun's Main Theorem (section 6.2 of the book An Introduction to Sieve Methods and Their  Applications, by R. Murty, C. Cojojaru) and then prove that there are  infinitely many natural numbers n such that n and n+2 have at most 7  prime factors.

MC 5403

Diana Castaneda Santos, Department of Pure Mathematics, University of Waterloo

"Affine-local properties"

We will continue working on Section 5.3  of Ravi Vail's notes. Last time we discussed about the affine communication lemma. Now, we will use it to define properties on schemes that can be verified locally on its affine pieces. Properties such as being Noetherian, being reduced or being of finite type over a ring $A$, can be verified in this way. Finally we will define affine and projective varieties over a field $k$ and show examples of these.