## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Wednesday, May 31, 2017 — 5:00 PM EDT

****This talk has been cancelled****

**Ertan Elma, Department of Pure Mathematics, University of Waterloo**

"Selberg's Sieve"

We will start reading Chapter 7 of the book An Introduction to Sieve Methods and Their Applications, by R. Murty, C. Cojocaru.

MC 5403

Wednesday, May 31, 2017 — 4:30 PM EDT

**Nick Rollick, Department of Pure Mathematics, University of Waterloo**

"Dots, lines, and arrows"

Wednesday, May 31, 2017 — 3:30 PM EDT

**Hongdi Huang, Department of Pure Mathematics, University of Waterloo**

"Skew polynomial rings and their prime ideals"

The skew polynomial rings (Ore extensions) are of the form $T=R[x, \sigma, \delta],$ where $\sigma$ is a ring endomorphism of $R$ and $\delta$ is $\sigma$-derivation on $R$ such that $ax=x\sigma(a)+\delta(a)$. If both $\sigma$ and $\delta$ are non-trival, and $P$ is a prime ideal of $T$, we are interested in the prime ideal restriction $R\cap P$. In this talk, we will introduce some result when $R$ is commutative noetherian.

Tuesday, May 30, 2017 — 3:30 PM EDT

**Michael Deveau, Department of Pure Mathematics, University of Waterloo**

"Effective Bi-interpretability"

We extend the definition of effective interpretability presented last time to get the notion of effective bi-interpretability, and prove that a number of useful properties hold when two structures are effectively bi-interpretable.

MC 5403

Tuesday, May 30, 2017 — 2:30 PM EDT

**Panagiotis Gianniotis, Department of Pure Mathematics, University of Waterloo**

"Relating diameter and mean curvature for submanifolds of Euclidean space"

Monday, May 29, 2017 — 10:00 AM EDT

**Letian Chen, University of Waterloo**

"Algebraic Function Fields and the Riemann-Roch Theorem"

We will introduce the concept of algebraic function fields and state the Riemann-Roch theorem. We will see some natural analogues between number fields and algebraic function fields. In particular we will define primes and divisors and study how prime factorization works in the function field case. As a consequence we will be able to prove that the class number of a function field over finite field is finite. Time permitting we will also talk about ramifications.

Friday, May 26, 2017 — 1:30 PM EDT

**Trevor Gunn, Department of Pure Mathematics, University of Waterloo **

“Hyperfields for Tropical Geometry”

Thursday, May 25, 2017 — 2:30 PM EDT

**Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo **

“A new construction of compact G2 manifolds by glueing Eguchi-Hanson spaces, Part III: Fibrewise blow-up by a family of Eguchi-Hanson spaces”

Wednesday, May 24, 2017 — 5:00 PM EDT

**Ertan Elma, Department of Pure Mathematics, University of Waterloo **

“Brun’s Sieve, Part 2”

We will finish the proof of the main theorem of Brun’s sieve (section 6.2 of the book An Introduction to Sieve Methods and Their Applications, by R. Murty, C. Cojocaru).

MC 5403

Tuesday, May 23, 2017 — 3:30 PM EDT

**Vilmos Komornik, University of Strasbourg**

"Topological and fractal properties of non-integer base expansions"

Given a base $1<q\le 2$, following R\'enyi (1957) we consider expansions of the form

\begin{equation*}

x=\sum_{i=1}^{\infty}\frac{c_i}{q^i}

\end{equation*}

with digits $c_i$ belonging to $\{0,1\}$. In case $q=2$ of the familiar binary expansions every $x\in [0,1]$ has an expansion, and this is unique except the dyadic rational numbers that have two expansions.

Tuesday, May 23, 2017 — 2:30 PM EDT

**Anthony McCormick, Department of Pure Mathematics, University of Waterloo **

“The Spencer Complex Part 3”

Tuesday, May 23, 2017 — 11:30 AM EDT

**Stephen Wen, Department of Pure Mathematics, University of Waterloo**

“Applications of the zeta function over function fields.”

Tuesday, May 23, 2017 — 11:00 AM EDT

**Michael Deveau, Department of Pure Mathematics, University of Waterloo**

“Computable Functors and Effective Interpretability”

Friday, May 19, 2017 — 1:30 PM EDT

**Trevor Gunn, Department of Pure Mathematics, University of Waterloo **

“Valuated Matroids”

Thursday, May 18, 2017 — 2:30 PM EDT

**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.

Thursday, May 18, 2017 — 2:30 PM EDT

**Spiro Karigiannis, Department of Pure Mathematics University of Waterloo **

“A new construction of compact G2 manifolds by glueing Eguchi-Hanson spaces, Part II.B: Modifying the identification with the normal bundle”

Wednesday, May 17, 2017 — 5:00 PM EDT

**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

Wednesday, May 17, 2017 — 3:30 PM EDT

**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

Tuesday, May 16, 2017 — 3:30 PM EDT

**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

Monday, May 15, 2017 — 10:00 AM EDT

**Shouzhen Gu, Department of Pure Mathematics, University of Waterloo**

"The Hales-Jewett Theorem"

Thursday, May 11, 2017 — 2:30 PM EDT

**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"

Tuesday, May 9, 2017 — 3:30 PM EDT

**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

Tuesday, May 9, 2017 — 2:30 PM EDT

**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

Monday, May 8, 2017 — 10:00 AM EDT

**Wentang Kuo, Department of Pure Mathematics, University of Waterloo**

"Number Theory in Function Fields"

Friday, May 5, 2017 — 2:00 PM EDT

**Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo**

"A new construction of compact G_{2}~manifolds by glueing Eguchi-Hanson spaces, Part I: Overview"

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1