MU Talk + Social: Lattices

 

Jonathan Love, U of T math grad and Stanford PhD student, will be giving a talk on Lattices and Basis Reduction!
INFO: Nov. 22, 4-6 pm // BAB025 // stay for the social happening afterwards, from 6-8 pm
Abstract: A lattice is a discrete collection of points inside a vector space which in many ways behaves like a vector space itself. But for many problems that are simple to solve for vector spaces, the corresponding lattice problems are extremely difficult to solve – so hard, in fact, that there are cryptosystems based on them which are expected to be secure even under quantum attacks.

In addition to discussing a few of these problems, this talk will develop the beginnings of the theory used to try and solve them, through the notion of a fundamental domain for a moduli space and related concepts.

Facebook Event here: https://www.facebook.com/events/161085384488953/

MU Presents: Deformations on Low Dimensional Topology

This talk will be given by Jaimal Thind. Food will be served at 4:30pm in the graduate lounge on the 6th floor of Bahen!

Imagine that the surfaces in the picture on this poster are made of a very stretchable rubber. Without cutting, tearing or puncturing the surfaces, can you start with the surface on the top and turn it into the surface below it? Would you like to know how it’s possible? If so, this talk is for you!

In this interactive talk we will introduce some ideas related to surfaces and their generalizations (called manifolds), mostly focussed on dimensions 2 and 3. We will introduce the notion of a manifold, equivalence of manifolds, and look at examples and constructions in low dimension. The audience will have the opportunity to use models to understand the solution to the above problem, and some others like it.

We will put an emphasis on developing geometric intuition, so the only pre-requisite demanded is an open imagination. (Familiarity with the notion of continuity and basic geometry will help.)

https://www.facebook.com/events/729837150509396/

The Hallway Probelm

This talk will be given by Jason Siefken!

The hallway problem considers adjacent parallel hallways of unit width each with a single doorway (aligned with integer lattice points) of unit width. It then asks: what are the properties of lines that pass through each doorway? Configurations of doorways closely correspond to Sturmian words, and so properties of these configurations may be lifted to properties of Sturmian words. This talk will explore lines of sight, lines that pass through each doorway, for both the case for both a finite number of parallel hallways and an infinite number, and their consequences for Sturmian words. We then produce a metric on configurations with an infinite number of hallways that preserves the property of admitting a line of sight under limits.

Refreshments will be served at 4:30pm in the graduate lounge on the 6th floor of Bahen.

Math Union Presents: The Importance of Being Integral

Many practical optimization problems require integer solutions. For example, it doesn’t make sense to give 8.4 dimes in change, to assign 1.3 workers to a shift, or to produce 6.71 chairs. In this talk, we will explore a recently discovered method for attacking this type of optimization problem that uses tools originally developed to understand collections of polynomials. Along the way, we will see why our usual methods for solving optimization problems do not work when integer solutions are required, exchange coins with computational algebra, and explore connections between polynomials and geometry.

Refreshments will be served in the graduate lounge on the 6th floor of Bahen before the talk, at 4:30pm!

Find the event on Facebook here.

Knots and Graphs: Better Together

https://www.facebook.com/events/1417764968295754/

We will explore the areas of knot theory and graph theory, and then show how these two theories can be combined to prove a property of Jones Polunomial. In the end, we will discuss recent discoveries about what the underlying graph structure can tell us about a knot.

Refreshments will be served at 4:30 in the mathematics graduate lounge on the 6th floor of Bahen.

MUGS VI: How many ways to the coffee house?

Join Dr. Brendan Kelly on Friday for the Math Union’s first MUGS Talk of the semester! Refreshments, as always, will be provided.

The ability to pose good questions is critical in the problem solving process. This talk will begin with a simple question that will frame a conversation on mathematics, education, and your college experience. The mathematical enterprise of digging deeper will send us down the rabbit hole as we investigate variations of the title question. We will explore the importance of asking good questions and techniques to empower students to ask good questions. The only prerequisite for this talk is an inquisitive mind and a willingness to actively participate.

Math Union Book Sale

The Math Union will be holding its book sale some time in the first week of classes. Fantastic deals guaranteed on all kinds of books, from STEM textbooks to scifi novels. For a small preview, here’s what we’ll have in stock.
See if there’s anything you’re interested in here.

MUGS 3: Gotta Catch ‘em All! with Prof. Dror Bar-Natan

Join us this Thursday on Oct 22nd, 2015 at Medical Science Building Room 2173 from 4-6PM for the Math Union’s third instalment: The 17 Tiling Patterns – Gotta Catch ‘em All with Professor Dror Bar-Natan. He is going to uncover all kinds the patterns for plane tiling in mathematical terms and essentially get you obsessed with the game of finding these patterns in everyday life. For those who are interested in symmetries, geometries, and their connections to group theory and topology or simply need new inspirations on tiling designs, do not miss out this excellent opportunity!

Refreshments will be provided. Hope to see you there.

Link to Dror’s bio http://www.math.toronto.edu/drorbn/, and his tiling pattern collection http://www.math.toronto.edu/~drorbn/Gallery/Symmetry/Tilings/