Events

Jason Bell, Pure Mathematics, University of Waterloo

"Gromov's theorem VII: linear groups, continued"

We have seen that Gromov's theorem for linear groups reduces to three claims. We will quickly recall these claims and then work on proving the last claim, which shows that under very general conditions that a linear group must have subexponential growth.

Jordan Hamilton, Pure Mathematics, University of Waterloo

"Once Morse Unto The Breach, Dear Friends"

In this final talk of the term we will finish our discussion regarding the existence of Morse functions on manifolds in Euclidean space. In fact, as was teased at the end of the last talk, we will be able to find a very large number of such functions. This has some interesting applications, which we will also examine.

Omar Leon Sanchez, Pure Mathematics, University of Waterloo

"NIP X"

We correct the argument from the last talk to prove that every formula has an honest definition.

Chris Ramsey, Pure Mathematics, University of Waterloo

"Maximal Ideal Space Techniques in Non-Selfadjoint Operator Algebras"

The following thesis is divided into two main parts. In the first part we study the problem of characterizing algebras of functions living on analytic varieties.

Jamie Murdoch, Pure Mathematics, University of Waterloo

"Almost every set of the correct density is Λ(p)"

I give an overview of Bourgain’s argument in his 1989 paper, Bounded orthogonal systems and the Λ(p)-set problem. Through a rather complex argument, Bourgain was able to show, using elementary probabilistic methods, that for any 2 < p < ∞, almost every random set is Λ(p), where the mean density of the random sets is 2/p. Prior attempts at this problem

Oded Yacobi, University of Toronto

Subquotients of Yangians and categorical representation theory

Yangians were originally introduced by Drinfeld in the 1980's to
quantize current Lie algebras. In geometric representation theory
subquotients of Yangians arise as quantizations of symplectic leaves of
the affine grassmannian. We will discuss ongoing work with Kamnitzer,
Webster, and Weekes to study categories of representations of these
subquotients. We will begin by explaining the construction of these

Shuntario Yamagishi, Pure Mathematics Department, University of Waterloo

“Sidon Problem”

Given a sequence of natural numbers ω, we define rn(ω) = |{(a, b) : a+b = n, a < b, and a, b ∈ ω}|. In this talk, we present the proof that there exists a sequence ω such that log n ≪ rn(ω) ≪ log n.

Rahim Moosa, Department of Pure Mathematics, University of Waterloo

“NIP Theories XI”

I will continue my aside on full versus emptyset-induced structure and the connection with stable embedability and weak stable embedability. I will then continue with section 3.2 of Simon’s notes.

Jason Bell, Department of Pure Mathematics, University of Waterloo

“Gromov’s Theorem VIII: solvable linear groups”

This week we look at groups of matrices with the property that all of the eigenvalues of each element are roots of unity. Modifying an argument due to Burnside and Schur, we show that all such groups have the property that they have a normal solvable subgroup of finite index.

Blake Madill, Pure Mathematics, University of Waterloo

"Small Salem Numbers"

A great deal is known about the Pisot-Vijayaraghavan (P.V.) numbers. However, less is known about the set of Salem numbers. The main
result in this area, due to Salem, is that each P.V. number is a limit
point of the set of Salem numbers. The smallest known P.V. number is
approximately $\theta_0=1.3247$. Any interval $(0,a)$, $a\geq\theta_0,$ contains infinitely many Salem numbers. Therefore it is reasonable to be interested in small Salem numbers.

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Algebra seminar

Jason Bell, Pure Mathematics, University of Waterloo

"Gromov's theorem VII: linear groups, continued"

Graduate student Geometry and Topology learning seminar

Jordan Hamilton, Pure Mathematics, University of Waterloo

"Once Morse Unto The Breach, Dear Friends"

Model Theory learning seminar

Omar Leon Sanchez, Pure Mathematics, University of Waterloo

"NIP X"

PhD thesis defense seminar

Chris Ramsey, Pure Mathematics, University of Waterloo

"Maximal Ideal Space Techniques in Non-Selfadjoint Operator Algebras"

USRA seminar

Jamie Murdoch, Pure Mathematics, University of Waterloo

"Almost every set of the correct density is Λ(p)"

Algebra seminar

Oded Yacobi, University of Toronto

Subquotients of Yangians and categorical representation theory

Student Number Theory seminar

Shuntario Yamagishi, Pure Mathematics Department, University of Waterloo

“Sidon Problem”

Model Theory seminar

Rahim Moosa, Department of Pure Mathematics, University of Waterloo

“NIP Theories XI”

Algebra seminar

Jason Bell, Department of Pure Mathematics, University of Waterloo

“Gromov’s Theorem VIII: solvable linear groups”

Student Number Theory seminar

Blake Madill, Pure Mathematics, University of Waterloo

"Small Salem Numbers"

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