## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

**Returning to in-person experiences in February:** Visit the COVID-19 website for more information.

Wednesday, April 17, 2019 — 3:30 PM EDT

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

"Non-triviality of the Bounded Jump Hierarchy - Part 3"

We finish the proof that for all $B$, there is some set $A$ with $B <_{bT} A <_{bT} B^b$. We determine $\hat{h}_A$ and $\hat{h}_C$ as promised, taking into account the restrictions imposed by the construction, and prove that our choices are correct.

MC 5413

Monday, April 15, 2019 — 11:30 AM EDT

**Nigel Pynn-Coates, University of Illinois at Urbana-Champaign**

"Asymptotic valued differential fields and differential-henselianity"

Wednesday, April 10, 2019 — 3:30 PM EDT

**Clifford Bearden, University of Texas at Tyler**

"A module version of the weak expectation property"

Wednesday, April 10, 2019 — 3:30 PM EDT

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

"Non-triviality of the Bounded Jump Hierarchy - Part 2"

We continue with the proof that for all $B$, there is some set $A$ with $B <_{bT} A <_{bT} B^b$. We start the main construction itself, check that the requirements eventually settle and are met, and we investigate the correct $\hat{h}_A$ and $\hat{h}_C$ as promised.

MC 5413

Friday, April 5, 2019 — 2:30 PM EDT

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

"A curious system of second order nonlinear PDEs for $\mathrm{U}(m)$-structures on manifolds"

Thursday, April 4, 2019 — 12:00 PM EDT

**Nick Manor, Unviersity of Waterloo**

"Exact Groups"

There are two notions of exactness for groups, but they are not known to be equivalent outside the discrete case. I will show how we can extend this equivalence to include two larger classes of groups.

MC 5403

Wednesday, April 3, 2019 — 4:30 PM EDT

**Ben Moore, University of Waterloo**

"A proof of the Hell-Neˇsetˇril Dichotomy via Siggers Polymorphism"

Wednesday, April 3, 2019 — 3:30 PM EDT

"The numerical range of quaternion matrices with respect to involutions"

Wednesday, April 3, 2019 — 3:30 PM EDT

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

“Non-triviality of the Bounded Jump Hierarchy - Part 1”

Monday, April 1, 2019 — 4:00 PM EDT

**Jan Minac, University of Western Ontario**

"The 13th mysterious room of a palace of absolute Galois groups"

Friday, March 29, 2019 — 2:30 PM EDT

**Martin Pinsonnault, Western University**

"Stability of Symplectomorphism Groups of Small Rational Surfaces"

Thursday, March 28, 2019 — 4:00 PM EDT

**Tobias Fritz, Perimeter Institute for Theoretical Physics**

"Real algebra, random walks, and information theory"

Wednesday, March 27, 2019 — 3:30 PM EDT

**Andre Kornell, UC Davis**

"Quantum Extensions of Ordinary Maps"

Wednesday, March 27, 2019 — 3:30 PM EDT

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

"Generalizing $\omega^k$-c.e. for Relativization - Part 2"

We finish the proof of a characterization of $A \leq_{bT} B^b$ that we started last time. We then use this to motivate a more general characterization, namely when $A \leq{bT} B^{nb}$. Finally, we begin the proof of a weak non-collapse theorem which uses this expanded characterization.

MC 5413

Tuesday, March 26, 2019 — 5:00 PM EDT

**Ragini Singhal, Department of Pure Mathematics, University of Waterloo**

"Surfaces, Minimal surfaces, Willmore surfaces and much more"

Tuesday, March 26, 2019 — 2:30 PM EDT

**Ben Webster, Department of Pure Mathematics, University of Waterloo**

"Coulomb, Galois, Gelfand-Tsetlin"

In the grand tradition of naming objects after mathematicians who knew nothing about them, I'll talk a bit about Galois orders, their Gelfand-Tsetlin modules, and how most important examples are Coulomb branches.

Tuesday, March 26, 2019 — 12:30 PM EDT

**Vandita Patel, University of Toronto**

"A Galois property of even degree Bernoulli polynomials"

Let $k$ be an even integer such that $k$ is at least $2$. We give a (natural) density result to show that for almost all $d$ at least $2$, the equation $(x+1)^k + (x+2)^k + ... + (x+d)^k = y^n$ with $n$ at least $2$, has no integer solutions $(x,y,n)$. The proof relies upon some Galois theory and group theory, whereby we deduce some interesting properties of the Bernoulli polynomials. This is joint work with Samir Siksek (University of Warwick).

MC 5417

Tuesday, March 26, 2019 — 10:30 AM EDT

**Remi Jaoui, Department of Pure Mathematics, University of Waterloo**

"Failure of essential surjectivity"

We consider Example 3.2 of the Bakker-Brunebarbe-Tsimerman paper, of an analytic line bundle on **G**_{m} that does not definably trivialise.

MC 5479

Tuesday, March 26, 2019 — 9:00 AM EDT

**Patrick Naylor, Department of Pure Mathematics, University of Waterloo**

"Trisections of 4-manifolds"

Trisections were introduced by Gay and Kirby in 2013 as a way to study 4-manifolds. They are similar in spirit to a common tool in a lower dimension: Heegaard splittings of 3-manifolds. These both have the advantage of changing problems about manifolds into problems about combinatorics of curves on surfaces. This talk will be a relaxed introduction to these decompositions. Time permitting, we will talk about some recent applications.

MC 5413

Thursday, March 21, 2019 — 4:00 PM EDT

**Rahim Moosa, Department of Pure Mathematics, University of Waterloo**

"Pseudo-finite dimensions IX"

I will discuss the description of approximate subgroups of simple algebraic groups in Udi's "Stable groups and approximate subgroups".

MC 5403

Wednesday, March 20, 2019 — 4:30 PM EDT

**Patrick Naylor, Department of Pure Mathematics, University of Waterloo**

“Is any knot not the unknot?”

Ever wanted to learn something about knots? This is your chance! We'll talk about some basics of knot theory, including how to prove some intuitively `obvious' but mathematically tricky results. Along the way, we'll see knot coloring invariants, polynomial invariants, and more. We'll even show how to produce a knotted surface: a sphere ($S^2$) in $\mathbb{R}^4$ that is `knotted'. This talk will be very accessible and will include many cool pictures.

Wednesday, March 20, 2019 — 3:30 PM EDT

**Yuanhang Zhang, Jilin University**

"Connecting invertible analytic Toeplitz operators in $G(\mathcal{T}(\mathcal{P}^{\perp}))$"

We prove that there exists an orthonormal basis $\mathcal{F}$ for classical Hardy space $H^2$, such that each invertible analytic Toeplitz operator $T_\phi$ (i.e. $\phi$ is invertible in $H^\infty$) could be connected to the identity operator via a norm continuous path of invertible elements of the lower triangular operators with respect to $\mathcal{F}$.

Wednesday, March 20, 2019 — 3:30 PM EDT

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

"Generalizing $\omega^k$-c.e. for Relativization"

Just as the arithmetic hierarchy characterizes reductions below various Turing jumps of $\emptyset$, Anderson and Csima showed that the Ershov hierarchy -- related to the notion of $\omega^k$-c.e. -- characterizes reductions of bounded Turing jumps of $\emptyset$. We discuss how to relativize this to reductions below bounded Turing jumps of an arbitrary set.

MC 5413

Thursday, March 14, 2019 — 4:30 PM EDT

**Patrick Naylor, Department of Pure Mathematics, University of Waterloo**

"Is any knot not the unknot?"

Ever wanted to learn something about knots? This is your chance! We'll talk about some basics of knot theory, including how to prove some intuitively `obvious' but mathematically tricky results. Along the way, we'll see knot coloring invariants, polynomial invariants, and more. We'll even show how to produce a knotted surface: a sphere ($S^2$) in $\mathbb{R}^4$ that is `knotted'. This talk will be very accessible and will include many cool pictures.

Wednesday, March 13, 2019 — 3:30 PM EDT

**Adam Fuller, Ohio University**

"Describing *C**-algebras in terms of topological groupoids"

Unital abelian *C**-algebras are well understood. They are necessarily isomorphic to *C*(*X*), the continuous functions on a compact Hausdorff space *X*. Studying the topological dynamics on $X$ gives rise to the study of crossed product *C**-algebras: a class of relatively well understood of non-abelian operator algebras constructed from a dynamical system.

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

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

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Indigenous Initiatives Office.