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.
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.
Friday January 22, 2016.
12.05 - 12.30: Tom Lenagan, Totally nonnegative
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.