Events by month

Ada Chan, York University

"Complex Hadamard matrices and association schemes, Part 2"

This will be a continuation of Wednesday's lecture.  We will discuss the properties of the association schemes of Hadamard graphs and their associated spin models.

MC 5403

Rachael Alvir, Department of Pure Mathematics, University of Waterloo

"Reverse Math II"

In this talk, we will give a preliminary introduction to reverse mathematics. We will be working from a recent book by Damir Dzhafarov and Carl Mummert.

MC 5403

Talk #1: Kareem Alfarra

"On integers n coprime to f(n)"

In a previous discussion, we saw that the set of integers n such that gcd(n, ⌊αn⌋) = 1 for an irrational α has density 6/π2. In the same spirit, we investigate the following set of integers n such that gcd(n, f(n)) = 1 where f (1), f (2), . . . is a non-decreasing sequence of positive integers that slowly tends to infinity. Then we see once again that the density of this set is 6/π2.

Talk #2: Yash Totani

Talk #1 (1:00 - 2:30pm): Xuemiao Chen, University of Waterloo

"Boundary value problems for G2 holonomy equation and mapping problems for 3 forms on 5-d manifolds"

Michael Brannan and Nick Priebe, Department of Pure Mathematics, University of Waterloo

"Quantum symmetries of Hadamard Matrices, Revisited (Part 1)"

In this two-part talk, we will revisit quantum automorphisms of Hadamard matrices, following the preprint of D. Gromada (arxiv:2210.02047v3).  We will compare this with the original definition of Banica-Nicoara introduced in the seminar a few weeks ago, and connect it to the quantum automorphism groups of Hadamard graphs.

MC 5403

**THIS TALK HAS BEEN RESCHEDULED UNTIL NEXT WEEK**

Rahim Moosa, Department of Pure Mathematics, University of Waterloo

"Restricted Zilber Trichotomy"

We will be reading Ben Castle's paper.

MC 4060

Michael Brannan and Nick Priebe, Department of Pure Mathematics, University of Waterloo

"Quantum symmetries of Hadamard Matrices, Revisited (Part 2)"

This is the second of two talks: We will revisit quantum automorphisms of Hadamard matrices, following the preprint of D. Gromada (arxiv:2210.02047v3).  We will compare this with the original definition of Banica-Nicoara introduced in the seminar a few weeks ago, and connect it to the quantum automorphism groups of Hadamard graphs.

MC 5403

Rachael Alvir, Department of Pure Mathematics, University of Waterloo

"Reverse Math III"

In this talk, we will be presenting material from a recent book by Damir Dzhafarov and Carl Mummert. In particular, we will prove the cone avoidance basis theorem.

MC 5403

Ali Jabbari, Shahid Bahonar University of Kerman

"Affine flows, Namioka fixed points and a fixed point theorem"

Talk #1: Jack DeSerrano

"The density of integers n coprime to ⌊αn⌋"

We determine, for a real number α, the density of positive integers n such that gcd(n, ⌊αn⌋) = 1, drawing from a 1953 paper of G. L. Watson. For example, for irrational α, we show that this density is 6/π2.

Talk #2: Owen Sharpe

"Waring's Problem on Function Fields of Characteristic Two"

We review the work of Gallardo and Heath-Brown on Waring's problem in the polynomial rings F_2[t] and F_4[t].

**This talk has been postponed till next week (June 20)**

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

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 "

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.

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
 

Rahim Moosa, Department of Pure Mathematics, University of Waterloo

"Restricted Zilber Trichotomy"

We will be reading Ben Castle's paper.

MC 4060

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

Alan Talmage, Department of Pure Mathematics, University of Waterloo

"Prime Solutions of Systems of Diagonal Equations"

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

Leo Jimenez, Department of Pure Mathematics, University of Waterloo

"Restricted Zilber Trichotomy"

We will be reading Ben Castle’s paper.

MC 5479

Christine Eagles, Department of Pure Mathematics, University of Waterloo

"BABA HAS PROOF"

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

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"

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:

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

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

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

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.

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

Amanda Petcu

"The $G_2$ Laplacian flow and Laplacian solitons"

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

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

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

Leo Jimenez, Department of Pure Mathematics, University of Waterloo

"Restricted Zilber Trichotomy"

We continue to read Ben Castle’s paper.

MC 5479

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

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

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.

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