GAMES -- General Audience Maths Edinburgh Seminar

Dates: January 22,   February 5,   February 26,   March 11,   April 1;
Time: 12.05 -- 1.00pm;
Room: JCMB 4325A.

About:

In this seminar, speakers from Edinburgh explain their research to a general mathematical audience including final year undergraduate students, PhD students, postdocs and faculty from the School of Mathematics. We'll try to have a good mix of speakers coming from all the different research areas within the school. We'll typically have two talks of 25 minutes each.

Motivation:

  • Learn about the diverse research interests and projects within the school.
  • Learn/improve to give a understandable research talk to a general (mathematical) audience.

    Give a talk:

    Please contact the organisers if you are interested in giving a talk in the seminar
    (m (dot) kalck (at) ed (dot) ac (dot) uk ; m (dot) lanini (at) ed (dot) ac (dot) uk).

    Mairi Walker (new Mathematics Engagement Officer) kindly offered support in preparing the talks.

    Schedule:

    Friday January 22, 2016.

    12.05 - 12.30:   Tom Lenagan,   Totally nonnegative matrices.

                            Abstract: A real matrix is totally nonnegative if each of the
                            determinants of its square submatrices is nonnegative, and is totally
                            positive if each of the determinants of its square submatrices is
                            strictly positive. Such matrices have applications in a variety of
                            fields. I will give an elementary talk giving some of the properties
                            of these matrices. The only thing you need to know at the start is the
                            definition of a determinant.

    12.35 - 13.00:   Mairi Walker,   Continued fractions and hyperbolic geometry.

                            Abstract: Continued fractions have been studied by mathematicians
                            for many hundreds of years, but it is only much more recently that
                            geometric representations of them have been explored. This talk will
                            look at how continued fractions can be studied in an intuitive and
                            elementary way using hyperbolic geometry. No previous knowledge of
                            continued fractions or hyperbolic geometry is necessary!

    Friday February 5, 2016.

    12.05 - 12.30:   Andrew Ranicki,   Roots of polynomials and quadratic forms.

                            Abstract: In 1829 Sturm used the Euclidean algorithm for polynomials
                            to obtain an algebraic formula for the number of real roots of a
                            polynomial P(X) ∈ R[X] in an interval [a,b]. In 1853 Sylvester used
                            continued fractions to express the formula in terms of the signature
                            of a quadratic form - indeed the Law of Inertia required for proving
                            that the signature is an invariant was established for just this purpose.
                            In 2015 Etienne Ghys and I obtained this expression from the calculation
                            of the Witt group of quadratic forms over the function field R(X).

    12.35 - 13.00:   Jim Wright,   Roots of polynomials: some elementary properties.

                            Abstract: In this talk we explore a few elementary relationships
                            between the roots of a polynomial and its coefficients. These
                            arise when investigating structural properties of various diverse
                            objects, from the Fourier transform in analysis to polynomial
                            congruences in number theory.

    Friday February 26, 2016.

    12.10 - 12.35:  José Figueroa-O'Farrill,   What is supersymmetry?

                            Abstract: I will review how our concepts of space and
                            time have evolved since Newton to the present and hopefully
                            explain that the concept of space and time which supersymmetry
                            suggests requires additional “quantum” coordinates. If time allows
                            I will say something about the uses of supersymmetry in mathematics.

    Friday March 11, 2016.

    12.10 - 12.35:   Joan Simon,   The unbearable (amusing) finitude (interconnectivity) of ideas.

                            Abstract: Just as points can be labelled by different coordinates,
                            seemingly different relativistic theories can in fact be equivalent.
                            We will discuss the extension of these ideas (duality) to describe gravitational
                            theories, such as General Relativity, using the language of Hilbert spaces and
                            inner products (holography & quantum gravity). It is the ability to describe the
                            same phenomena using a different language that may give us the clues to unravel
                            what the fabric of space-time is.

    Friday April 1, 2016.

    12.10 - 12.35:   Gergö Nemes,   The asymptotics of the gamma function via resurgence.

                            Abstract: This talk will be about the divergent asymptotic
                            expansion of the gamma function. The divergence of this asymptotic
                            expansion is caused by the singularities of its Borel transform.
                            We exploit these singularities to obtain explicit formulae for the
                            coefficients and remainder term of the asymptotic expansion of the
                            gamma function. These formulae then will be used to obtain realistic
                            error bounds for the asymptotics of the gamma function. All related
                            concepcts will be explained during the talk.

    See GAMES in autumn 2015 for information about last semester's seminar including slides, notes and a video!

    Organisers: Martin Kalck, Martina Lanini.