## 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

Thursday, June 29, 2023 4:00 PM EDT

**Florin Pop, Wagner College**

"Detecting certain properties of C*-algebras"

A C*-algebra $A$ is said to detect a certain property $\mathcal{P}$ (or is a $\mathcal{P}$-detector) if, for any C*-algebra $B$, we have $A\otimes_{\min}B=A\otimes_{\max}B$ is and only if $B$ has property $\mathcal{P}$. In this talk we will survey several properties that can be detected, as well as present the algebras which play the detector's part.

MC 5479

Thursday, June 29, 2023 2:30 PM EDT

**Joey Lakerdas-Gayle, Department of Pure Mathematics, University of Waterloo**

"Reverse Math - VI"

In this talk, we will be presenting material from a recent book by Damir Dzhafarov and Carl Mummert. In particular, we will begin Chapter 5, studying subsystems of second order arithmetic.

MC 5403

Thursday, June 29, 2023 2:30 PM EDT

**Jesse Madnick, University of Oregon**

**"Cohomogeneity-One Lagrangian Mean Curvature Flow"**

In C^n, mean curvature flow preserves the class of Lagrangian submanifolds, a fact known as "Lagrangian mean curvature flow" (LMCF). As LMCF typically forms finite-time singularities, it is of interest to understand the blowup models of such singularities, as well as the soliton solutions.

Thursday, June 29, 2023 11:00 AM EDT

**Cynthia Dai, Department of Pure Mathematics, University of Waterloo**

"Properties of Schemes"

We will talk about some properties of schemes, including possibly integral, separated, and proper, if time permits.

MC 5403

Wednesday, June 28, 2023 3:00 PM EDT

**Leo Jimenez, Department of Pure Mathematics, University of Waterloo**

"Restricted Zilber Trichotomy"

We continue to read Ben Castle’s paper.

MC 5479

Wednesday, June 28, 2023 2:30 PM EDT

**Hanming Liu, Department of Pure Mathematics, University of Waterloo**

"Proof of Smale's Theorem"

I will present the proof of Smale's theorem about the existence of gradient-like vector fields satisfying the Smale condition.

M3 4206

Wednesday, June 28, 2023 1:00 PM EDT

**Eric Boulter, Department of Pure Mathematics, University of Waterloo**

"Spectral curves and the Hitchin system"

I will give an overview of how spectral curves are constructed in the context of Higgs bundles, and discuss how they are used in the study of the Hitchin system.

MC 5479

Zoom link: https://uwaterloo.zoom.us/j/94942581597?pwd=cWhzelpQWXBVakkrZUVWVkFhMmV1dz09

Tuesday, June 27, 2023 9:30 PM EDT

**Talk #1 Valentio Iverson: Powerfree Sieve on Prime Inputs**

Abstract: In recent years, there have been several results on the density of integer tuples (a_1,...,a_n) such that f(a_1,...,a_n), for some fixed integer polynomial f, is squarefree. In this talk, we restrict to the case of prime inputs and prove similar results.

**Talk #2 Gian Sanjaya: Density of Restricted Polynomials with Squarefree Discriminant**

Tuesday, June 27, 2023 1:00 PM EDT

Talk #1: (1:00pm-2:00pm)**Amanda Petcu**

"The $G_2$ Laplacian flow and Laplacian solitons"

Tuesday, June 27, 2023 12:30 PM EDT

**Erik Seguin, Department of Pure Mathematics, University of Waterloo**

"Haagerup's noncommutative Grothendieck inequality (cont.)"

We will continue to prove things related to and on the subject of the NCG theorem. Possibly we will finish the proof of the theorem this week, and possibly not; we conjecture that no third option exists, but we are unable to prove this claim at present. Time permitting, we may attempt to prove this rigorously; this attempt is unlikely to be successful, veracity of the claim notwithstanding.

Tuesday, June 27, 2023 11:00 AM EDT

**Francisco Villacis, Pure Mathematics, University of Waterloo**

"D-Modules on Smooth Varieties"

Abstract: In this talk I will continue talking about D-modules on smooth varieties and the Riemann-Hilbert Correspondence.

MC 5403

Thursday, June 22, 2023 11:00 AM EDT

**Cynthia Dai, Department of Pure Mathematics, University of Waterloo**

**"Properties of Schemes"**

We will talk about some properties of schemes, including possibly integral, separated, and proper, if time permits.

MC 5403

Wednesday, June 21, 2023 2:30 PM EDT

**Francisco Villacis, Department of Pure Mathematics, University of Waterloo**

**"Pseudo-Gradients and the Smale Condition"**

I will continue the discussion of pseudo-gradients that was started last time. I will talk in short detail about how the topology of the level sets change as we cross critical points of a Morse function and on the stable and unstable manifolds. I will discuss in detail the Smale condition and the space of trajectories of pseudo-gradients with a view towards the construction of the Morse complex.

M3 4206

Wednesday, June 21, 2023 1:00 PM EDT

**Yash Singh, Department of Pure Mathematics, University of Waterloo**

**"Vector bundles on toric varieties"**

We study vector bundles on toric varieties and a classification theorem due to Klyachko.

This seminar will be held both online and in person:

Tuesday, June 20, 2023 1:00 PM EDT

**Talk #1: (1:00pm-2:15pm)**

**Jing Xuan Chen**

**"Holomorphic bisectional curvature"**

The bisectional curvature on a Kähler manifold (M,J) is defined as H(X,Y)=R(X,JX,JY,Y) for unit vectors X,Y. We will see what we can prove about a compact connected Kähler manifold if we assume that it has positive bisectional curvature.

**Talk #2: (2:30pm-4:00pm)**

**Spiro Karigiannis**

**"The deTurck trick demystified"**

Tuesday, June 20, 2023 11:00 AM EDT

**Francisco Villacis, Department of Pure Mathematics, University of Waterloo**

**"D-Modules on Smooth Varieties"**

In this talk I will talk about D-modules on smooth varieties and the Riemann-Hilbert Correspondence.

MC 5403

Friday, June 16, 2023 4:30 PM EDT

**Christine Eagles, Department of Pure Mathematics, University of Waterloo**

**"BABA HAS PROOF"**

Thursday, June 15, 2023 3:00 PM EDT

**Leo Jimenez, Department of Pure Mathematics, University of Waterloo**

**"Restricted Zilber Trichotomy"**

We will be reading Ben Castle’s paper.

MC 5479

Thursday, June 15, 2023 2:30 PM EDT

**Luke MacLean, Department of Pure Mathematics, University of Waterloo**

**"Reverse Math IV"**

In this talk, we will be presenting material from a recent book by Damir Dzhafarov and Carl Mummert. In particular, we will begin on Chapter 4 studying reducibility of problems.

MC 5403

Thursday, June 15, 2023 1:00 PM EDT

**Alan Talmage, Department of Pure Mathematics, University of Waterloo**

**"Prime Solutions of Systems of Diagonal Equations"**

Thursday, June 15, 2023 11:00 AM EDT

**Francisco Villacis, Department of Pure Mathematics, University of Waterloo**

**"Functor of Points and Properties of Schemes"**

We will review the functor of points perspective of schemes which was discussed the week of May 29, and we will talk about properties of schemes.

MC 5403

Wednesday, June 14, 2023 3:00 PM EDT

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

**"Restricted Zilber Trichotomy"**

We will be reading Ben Castle's paper.

MC 4060

Wednesday, June 14, 2023 2:30 PM EDT

**Hanming Liu, Department of Pure Mathematics, University of Waterloo**

**"Introduction"**

We will be reading Audin and Damian's book "Morse Theory and Floer Homology". In this introductory talk, I will briefly talk about why symplectic geometers and geometric topologists would want to study Morse theory, and then present chapter 1 and the beginning of chapter 2.

M3 4206

Wednesday, June 14, 2023 1:00 PM EDT

**Nicolas Banks, Department of Pure Mathematics, University of Waterloo**

**"Intersection theory, Chow groups, and a generalized Bezout's Theorem"**

Bezout's Theorem is a classical result which states that two plane curves intersect in a number of points equal to the product of their degrees. This theorem has an interesting history: it was essentially known to Newton in the 17th century, while the first proof was attempted a century later by Bezout. The first rigorous, algebro-geometric proof was finally given by Serre in 1958.

Tuesday, June 13, 2023 1:00 PM EDT

**Talk #1 (1:00-2:30pm): Amanda Petcu**

**"The G_2 Laplacian flow"**

In this talk, we will introduce the G_2 Laplacian flow and attempt to show short-time existence and uniqueness following the work of Bryant and Xu.

**Talk #2 (2:30-4:00pm): Sir Michael Atiyah**

**"A Panoramic View of Mathematics "**

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 co-ordinated within our Office of Indigenous Relations.