[Alta-Logic] CUMC festival on Friday

[Kristine Bauer]

Hello all,

Thanks to everyone who pointed out the conflict between the CUMC talks and Lauren DeDieu’s talk on Friday.  We are working on resolving this conflict, so please stay tuned and I will send an adjusted schedule.

Also, I seem to have made a cut-and-paste error.  There is indeed a 5th CUMC talk, whose title and abstract are below.  My apologies to Adam Humeniuk for the oversight!

Cheers,
Kristine

Speaker: Adam Humeniuk

Title: Rings of Functions and the Gelfand Transform: an Intro to C*-algebras

Abstract: The set $C(X)$ of continuous complex-valued functions on a space $X$ is simultaneously a commutative ring, a vector space, and a topological space (a commutative Banach algebra). Algebraic properties of this ring encode geometric properties of the space, e.g. ideals correspond naturally to closed subspaces. Consider a dual problem: given a commutative Banach algebra $\mathcal{A}$, can we build a space $X$ on which $\mathcal{A}$ is the ring of functions $C(X)$? I will sketch how to do so; this is called the Gelfand transform. I'll identify the class of algebras for which $\mathcal{A}\cong C(X)$. These are the commutative C*-algebras. Time permitting, I'll give a categorical perspective of the Gelfand transform.

> On Jul 11, 2017, at 10:00 AM, Kristine Bauer <bauerk at ucalgary.ca> wrote:
> 
> 
> 
> Dear colleagues,
> 
> I would like to invite you to preview the Calgary contributions to the Canadian Undergraduate Math Conference which will take place next week in Montreal.  The five students who are giving talks have agreed to give their talks locally in Calgary first, and will do so on Friday afternoon.  I will provide written feedback forms which can be used to record comments to help the students improve their talks, and there will be time for questions and comments between the talks and following the session.  The talks are 20 minutes each and we will offer them in parallel sessions, as in the schedule below.  Please drop in as you would like!  It will be a really good opportunity to see what kind of things our undergraduates are doing in math outside the classroom.
> 
> Cheers,
> Kristine
> 
> 
> Session 1: MS 319
> 
> 2:30 pm
> Speaker: Vanessa Pizante
> Title: The Mean Variance Hedging Problem for a Contingent Claim in a Two Dimensional Binomial Model
> 
> Abstract: In this presentation, we will specifically find the mean variance hedging portfolio for an exchange option in a two period, two dimensional binomial model. The problem of or finding the mean variance hedging portfolio for any contingent claim involves an incomplete market, meaning there is no replicating portfolio corresponding to the claim. Equivalently, there does not exist a unique risk neutral probability corresponding to the model. We utilize dynamical programming to find the optimal replicating strategy for the exchange option in this market. We then use the optimal policy to find a  price for the exchange option.
> 
> 3:00pm
> Speaker: Aiden Huffman
> Title: SIC(K) Measurements
> Abstract: Measurements lay at the heart of how we interpret quantum mechanics. One class of measurements of interest are SIC-POVMs, Positive Operator Valued Measurements which are both Symmetric and Informationally Complete. This class of measurements gives a nice framework for understanding finite dimensional quantum states probabilistically. In this talk we will introduce the SIC representation of quantum states and their relationship to the Bloch sphere, we will also investigate how quantum channels can be viewed in this representation.
> 
> Session 2: MS 371
> 
> 2:30pm 
> Speaker: Ethan White
> Title: Different Necklaces
> Abstract: At the 2000 World Puzzle Championship Bernardo Santos asked if the integers 1 to 15 could be arranged in a chain such that adjacent numbers summed to squares. This problem has inspired many variations, including the generalization to arbitrary length, and examination of square differences, instead of sums. With Renate Scheidler, Richard Guy and I answered this question, and began to investigate necklaces where any two differences are allowed. The numbers of such necklaces always seems to satisfy a linear recurrence relation, but a proof of this result appears elusive for all but the smallest difference values. 
> 
> 3:00 pm
> Speaker: Reginald Lybbert
> Title: Blowing Up Singularities: A Foray into Algebraic Geometry
> Abstract: Algebraic geometry is the study of solution sets to multivariate polynomial equations via algebraic methods.  These solution sets are known as algebraic varieties.  Oftentimes, we will run into special points on these varieties, known as singularities.  We desire to find other varieties, which are 'nearly' isomorphic to these singular varieties, but which lack any singularities.  This is known as resolving the singularities.  In this talk, we will introduce these concepts and discuss the process of blowing up singularities, through which they can be resolved._______________________________________________
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