宅男视频

Monday, 19 October 2020, 3-4pm Zoom

• Speaker: Reidun Twarock (University of York)
  
  Title: Mathematical Virology: Geometry as a key to the discovery of novel anti-viral solutions
  
  Abstract: Viruses encapsulate their genetic material into protein containers that act akin to molecular Trojan horses, protecting viral genomes between rounds of infection and facilitating their release into the host cell environment. In the majority of viruses, including major human pathogens, these containers have icosahedral symmetry. Mathematical techniques from group, graph and tiling theory can therefore be used to better understand how viruses form, evolve and infect their hosts, and point the way to novel antiviral solutions. In this talk, I will present a theory of virus architecture, that contains the seminal Caspar Klug theory as a special case and solves long-standing open problems in structural virology. I will also introduce mathematical models of symmetry breaking in viral capsids and discuss their consequences for our understanding of more complex viral geometries. By combining these geometric insights with a range of different mathematical and computational modelling techniques, I will demonstrate how viral life cycles can be better understood through the lens of viral geometry, and how such insights can act as drivers of discovery of novel anti-viral solutions.

Monday, 2 November 2020, 3-4pm Zoom

• Speaker: Colin Guillarmou (Orsay)
  
  Title: The Conformal Bootstrap in Liouville Conformal Field Theory
  
  Abstract: Liouville Conformal Field Theory (LCFT) is a 2 dimensional quantum field theory with conformal symmetries. It was introduced and heavily studied in theoretical physics by Belavin, Polyakov, Zamolodchikov etc in the 80s/90s. It is a field theory corresponding to random Riemannian metrics, it corresponds to defining a path integral on the set of metrics in a conformal class on a closed surface, the measure being of the form exp(S_g(\phi))d\phi where \phi are (generalized) functions, g is a background Riemannian metric and the conformal metrics are represented by e^{\phi}g; here S_g(\phi) is the so-called Liouville action whose miminizers lead to constant curvature metrics. LCFT is now considered solved in theoretical physics in the sense that the n-point correlation functions enjoy explicit closed formulas, involving some structure constants called DOZZ constants for the 3-point correlation function, and the conformal blocks associated to Vrasoro algebras. The formula for the n-point correlations are obtained from (n-k)-points function for k>0 through an iterative method called the "conformal bootstrap". In this talk, I'll review recent works based on probability to construct mathematically the path integral of LCFT using the Gaussian Free Field, and will explain our mathematical proof to the formulas proposed by Zamolodchikov and others in physics for the n-point correlation functions. Our proof is a mathematical proof of the conformal bootstrap for this theory, it uses tools from probability, from spectral/scattering theory and from the use of certain representations of Virasoro algebras. This work gives a bridge between the statistical physics approach and the algebraic approach for studying confomal field theories in 2 dim with an uncountable family of primary fields. This is a joint work with A.Kupiainen, R.Rhodes and V.Vargas.

Monday, 7 December 2020, 3-4pm Zoom

• Speaker: Keith Ball (Warwick)
  
  Title: Rational approximations to the zeta function
  
  Abstract: I will describe the construction of a sequence of rational functions with rational coefficients that converge to the zeta function. These approximations extend and make precise the spectral interpretations of the Riemann zeros found by Connes and by Berry and Keating.