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
Michael Deveau, Department of Pure Mathematics, University of Waterloo
"Nontriviality 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
Nigel PynnCoates, University of Illinois at UrbanaChampaign
"Asymptotic valued differential fields and differentialhenselianity"
Clifford Bearden, University of Texas at Tyler
"A module version of the weak expectation property"
Michael Deveau, Department of Pure Mathematics, University of Waterloo
"Nontriviality 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
Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo
"A curious system of second order nonlinear PDEs for $\mathrm{U}(m)$structures on manifolds"
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
Ben Moore, University of Waterloo
"A proof of the HellNeˇsetˇril Dichotomy via Siggers Polymorphism"
Michael Deveau, Department of Pure Mathematics, University of Waterloo
“Nontriviality of the Bounded Jump Hierarchy  Part 1”
Jan Minac, University of Western Ontario
"The 13th mysterious room of a palace of absolute Galois groups"
Martin Pinsonnault, Western University
"Stability of Symplectomorphism Groups of Small Rational Surfaces"
Tobias Fritz, Perimeter Institute for Theoretical Physics
"Real algebra, random walks, and information theory"
Andre Kornell, UC Davis
"Quantum Extensions of Ordinary Maps"
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 noncollapse theorem which uses this expanded characterization.
MC 5413
Ragini Singhal, Department of Pure Mathematics, University of Waterloo
"Surfaces, Minimal surfaces, Willmore surfaces and much more"
Ben Webster, Department of Pure Mathematics, University of Waterloo
"Coulomb, Galois, GelfandTsetlin"
In the grand tradition of naming objects after mathematicians who knew nothing about them, I'll talk a bit about Galois orders, their GelfandTsetlin modules, and how most important examples are Coulomb branches.
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
Remi Jaoui, Department of Pure Mathematics, University of Waterloo
"Failure of essential surjectivity"
We consider Example 3.2 of the BakkerBrunebarbeTsimerman paper, of an analytic line bundle on G_{m} that does not definably trivialise.
MC 5479
Patrick Naylor, Department of Pure Mathematics, University of Waterloo
"Trisections of 4manifolds"
Trisections were introduced by Gay and Kirby in 2013 as a way to study 4manifolds. They are similar in spirit to a common tool in a lower dimension: Heegaard splittings of 3manifolds. 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
Rahim Moosa, Department of Pure Mathematics, University of Waterloo
"Pseudofinite dimensions IX"
I will discuss the description of approximate subgroups of simple algebraic groups in Udi's "Stable groups and approximate subgroups".
MC 5403
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.
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 $\mathcal{F}$.
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
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.
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 nonabelian operator algebras constructed from a dynamical system.
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Departmental office: MC 5304
Phone: 519 888 4567 x43484
Fax: 519 725 0160
Email: puremath@uwaterloo.ca
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.