AARMS/DMSGSA Summer School 2016 Student Conference

Saturday, July 23, 2016, MacMechan Auditorium, 1st Floor, Killam Memorial Library, Halifax


About

Funded by the Dalhousie Mathematics and Statistics Graduate Students' Association (DMSGSA), this conference aims to complement the Summer School being run at Dalhousie University by the Atlantic Association for Research in the Mathematical Sciences (AARMS).

Conference Organiser: Darien DeWolf, President, DMSGSA

Summer School Organisers: Dr. Dorette Pronk, Dalhousie and Dr. Geoffrey Cruttwell, Mount Allison

Location

Saturday, July 23, 2016.
MacMechan Auditorium, 1st Floor, Killam Memorial Library, 6225 University Ave. Halifax, Nova Scotia

Schedule

Time Slot Description
10h00 Asymptotics of the median of the beta distribution

Dimitrios Askitis University of Copenhagen
We investigate the median of the beta distribution as a function of one of its two parameters. In particular, we shall see its monotonicity properties and its asymptotic behaviour at 0 and at infinity, through the study of an auxiliary function related to its logarithm.
10h30 The Lean Theorem Prover

Jacob Gross University of Pittsburgh
Computer-assisted theorem proving is increasing in importance in pure mathematics. In this talk, we attempt to present the current status of automated proof assistants as well as introduce the Lean Theorem Prover. Lean is a proof assistant being developed principally by Leonardo de Moura at Microsoft Research. It is based on intuitionistic dependent type theory, but is compatible with classical logic as well as with homotopy type theory.
11h00 Standard Quantum Error Correction

Comfort Mintah University of Guelph
The theory of Quantum Error Correction plays an important role in the study of Quantum Information. This is based on the assumption of completely positive maps. We discuss completely positive maps and develop the notion of quantum error correction that applies to linear maps. We state the necessary and sufficient condition (Knill and Laflamme theorem ) for an error set to be correctable and use an example to show how the theorem applies to quantum error correction.
11h30 Spatially Anisotropic Einstein -Aether Cosmological Harmonic Potential Model

Bassemah Alhulaimi Dalhousie University
We use a dynamical systems analysis to investigate the qualitative behaviour of a class of spatially anisotropic cosmological models in Einstein -Aether theory with a homogeneous scalar field. Particularly, we study the harmonic-like self interaction potential which depends on the time-like aether vector field through the expansion and the shear scalars. We use the Friedmann equation and the Klein-Gordon equation to derive the evolution equations. The stability (the behaviour) of the equilibrium solutions are analysed and the results are compared with the standard inflationary cosmological solutions and previously studied Einstein-Aether cosmological models. We then analyse this model, with special emphasis on the future asymptotic behaviour for different values of the parameters. In addition, we investigate the slow role regime for the case when the potential does not depend on the shear.
12h00 Lunch -
13h00 A problem of Chowla and its generalizations

Siddhi Pathak Queen's University
In the early 1960s, S. Chowla investigated the non-vanishing of Dirichlet series with periodic coefficients at the point s=1. We introduce this problem and discuss a few generalizations.
13h30 Asymptotic analysis of an aircraft wing model in subsonic airflow
PDF Slides

László Kindrat University of New Hampshire
My presentation will start with a short introduction to aeroelastic flutter and its mathematical modelling. I will describe the coupled bending-torsion vibration model with special boundary conditions that forms the starting point of my research. Main steps of the investigation of the underlying matrix differential operator will be outlined, and some results presented. Finally, I will talk about the goals and future direction of my research, as well as its applications in engineering.
14h00 Introduction to Tensor Differential Categories

JS Lemay University of Calgary
In 2005, Blute, Cockett and Seely introduced the notion of a tensor differential category, which formalises the concept of differentiation by axiomatizing a structure on a category using the rules of differentiation. These rules include the differentiation formulas for constants and linear functions, the product rule and the chain rule. There are many examples of tensor differential categories, in particular, the category of vector spaces, where the differential structure coincides with the usual differentiation of multivariable polynomial functions. More surprising examples of differential categories include the category of sets and relations and any category of modules over rigs (rings without negatives). In this talk we will present the definition and structure of tensor differential categories while also exploring some of the examples listed above. Given enough time, we may take a peek at tensor integral categories (my current research project). References: 1. -R. Blute, R. Cockett, R. Seely, Differential Categories , Mathematical Structures in Computer Science Volume 1616, pp 1049-1083, 2006 2. -R. Blute, R. Cockett, T. Porter, R. Seely, Kahler Categories , Cahiers de Topologie et Geometrie Differentielle 52, pp. 253-268, 2012
14h30 Break -
15h00 Towards a type theory for differential geometry

Jonathan Gallagher University of Calgary
In this talk, we will introduce the differential lambda calculus of Ehrhard and Regnier. The differential lambda calculus is to smooth functions as the lambda calculus is to usual functions. First, we will give the categorical semantics of the simply typed differential lambda calculus. We will then consider some extensions to this calculus, and why these extensions might be geometrically interesting.
15h30 Cartesian Double Categories

Evangelia Aleiferi Dalhousie University
We extend the theory of Cartesian categories to Cartesian double categories, with a specific interest on those ones that are fibrant. Also, we apply the structure of monads and modules, which will allow us to show that the double category of profunctors over a category with pullbacks and terminal object, is Cartesian.
16h00 How monoidal can it get? Monads, and adjunctions in monoidal bicategories

Ramón Abud Alcalá Macquarie University
Street's Formal Theory of Monads provides an excellent account of the notions of adjunction and monad in a bicategory. If one works in a monoidal bicategory instead, one might define objects, arrows and cells that have a (weak) monoidal structure. It is of particular interest when this monoidal structures interact with adjunctions and monads. In this talk, I will expose a situation that one might find, which is given by three teorems: two of them are a particular case Kelly's Doctrinal Adjunction, which characterise adjunctions between (skew) monoidales in which the right adjoint is monoidal and strong monoidal; and the third one, a generalisation of Moerdijk's Monads in Tensor Categories, which characterises opmonoidal monads on a (skew) monoidale.