Tue, 30 Jan 2024

16:00 - 17:00
L6

Characteristic polynomials, the Hybrid model, and the Ratios Conjecture

Andrew Pearce-Crump
(University of York)
Abstract

In the 1960s Shanks conjectured that the  ζ'(ρ), where ρ is a non-trivial zero of zeta, is both real and positive in the mean. Conjecturing and proving this result has a rich history, but efforts to generalise it to higher moments have so far failed. Building on the work of Keating and Snaith using characteristic polynomials from Random Matrix Theory, the Hybrid model of Gonek, Hughes and Keating, and the Ratios Conjecture of Conrey, Farmer, and Zirnbauer, we have been able to produce new conjectures for the full asymptotics of higher moments of the derivatives of zeta. This is joint work with Chris Hughes.

Tue, 24 Oct 2023

14:00 - 15:00
L5

Existence and rotatability of the two-colored Jones–Wenzl projector

Amit Hazi
(University of York)
Abstract

The two-colored Temperley-Lieb algebra is a generalization of the Temperley-Lieb algebra. The analogous two-colored Jones-Wenzl projector plays an important role in the Elias-Williamson construction of the diagrammatic Hecke category. In this talk, I will give conditions for the existence and rotatability of the two-colored Jones-Wenzl projector in terms of the invertibility and vanishing of certain two-colored quantum binomial coefficients. As a consequence, we prove that Abe’s category of Soergel bimodules is equivalent to the diagrammatic Hecke category in complete generality.

 

Tue, 01 Jun 2021
14:15
Virtual

p-Kazhdan—Lusztig theory for Hecke algebras of complex reflection groups

Chris Bowman
(University of York)
Abstract

Riche—Williamson recently proved that the characters of tilting modules for GL_h are given by non-singular p-Kazhdan—Lusztig polynomials providing p>h.  This is equivalent to calculating the decomposition numbers for symmetric groups labelled by partitions with at most h columns.  We discuss how this result can be generalised to all cyclotomic quiver Hecke algebras via a new and explicit isomorphism between (truncations of) quiver Hecke algebras and Elias–Williamson’s diagrammatic endomorphism algebras of Bott–Samelson bimodules. 

This allows us to give an elementary and explicit proof of the main theorem of Riche–Williamson’s recent monograph and extend their categorical equivalence to all cyclotomic quiver Hecke algebras, thus solving Libedinsky–Plaza’s categorical blob conjecture.  Furthermore, it allows us to classify and construct the homogeneous simple modules of quiver Hecke algebras via BGG resolutions.   
 
This is joint work with A. Cox, A. Hazi, D.Michailidis, E. Norton, and J. Simental.  
 

Tue, 15 Jun 2021

15:30 - 16:30
Virtual

Are random matrix models useful in biological systems?

Jon Pitchford
(University of York)
Abstract

For five decades, mathematicians have exploited the beauties of random matrix theory (RMT) in the hope of discovering principles which govern complex ecosystems. While RMT lies at the heart of the ideas, their translation toward biological reality requires some heavy lifting: dynamical systems theory, statistics, and large-scale computations are involved, and any predictions should be challenged with empirical data. This can become very awkward.

In addition to a morose journey through some of my personal failures to make RMT meet reality, I will try to sketch out some more constructive future perspectives. In particular, new methods for microbial community composition, dynamics and evolution might allow us to apply RMT ideas to the treatment of cystic fibrosis. In addition, in fisheries I will argue that sometimes the very absence of an empirical dataset can add to the practical value of models as tools to influence policy.

 

Tue, 24 Nov 2020
12:00
Virtual

Symmetries and Master Ward Identity in perturbative Algebraic QFT

Kasia Reijzner
(University of York)
Abstract

In this talk I will explain how theories with local symmetries are treated in perturbative Algebraic Quantum Field Theory (pAQFT). The main mathematical tool used here is the Batalin Vilkovisky (BV) formalism. I will show how the perturbative Master Ward Identity can be applied in this formalism to make sense of the renormalised Quantum Master Equation. I will also comment on perspectives for a non-perturbative formulation.

 

Fri, 18 Oct 2019

16:00 - 17:00
L1

Geometry as a key to the virosphere: Mathematics as a driver of discovery in virology and anti-viral therapy

Reidun Twarock
(University of York)
Further Information

The Oxford Mathematics Colloquia are generously sponsored by Oxford University Press.

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 an overarching theory of virus architecture, that contains the seminal Caspar Klug theory as a special case and solves long-standing open problems in structural virology. Combining insights into virus structure with a range of different mathematical modelling techniques, such as Gillespie algorithms, I will show how viral life cycles can be better understood through the lens of viral geometry. In particular, I will discuss a recent model for genome release from the viral capsid. I will also demonstrate the instrumental role of the Hamiltonian path concept in the discovery of a virus assembly mechanism that occurs in many human pathogens, such as Picornaviruses – a family that includes the common cold virus– and Hepatitis B and C virus. I will use multi-scale models of a viral infection and implicit fitness landscapes in order to demonstrate that therapeutic interventions directed against this mechanism have advantages over conventional forms of anti-viral therapy. The talk will finish with a discussion of how the new mathematical and mechanistic insights can be exploited in bio-nanotechnology for applications in vaccination and gene therapy.

Thu, 10 May 2018

16:00 - 17:00
L6

On spectra of Diophantine approximation exponents

Antoine Marnat
(University of York)
Abstract

Exponents of Diophantine approximation are defined to study specific sets of real numbers for which Dirichlet's pigeonhole principle can be improved. Khintchine stated a transference principle between the two exponents in the cases  of simultaneous approximation and approximation by linear forms. This shows that exponents of Diophantine approximation are related, and these relations can be studied via so called spectra. In this talk, we provide an optimal bound for the ratio between ordinary and uniform exponents of Diophantine approximation for both simultaneous approximation and approximation by linear forms. This is joint work with Nikolay Moshchevitin.

Mon, 11 Jun 2018

14:15 - 15:15
L3

Gradient estimates and applications to nonlinear filtering

CHRISTIAN LITTERER
(University of York)
Abstract

We present sharp gradient estimates for the solution of the filtering equation and report on its applications in a high order cubature method for the nonlinear filtering problem.

Tue, 05 Jun 2018

12:00 - 13:15
L4

A Cohomological Perspective on Algebraic Quantum Field Theory

Eli Hawkins
(University of York)
Abstract

After outlining the principles of Algebraic Quantum Field Theory (AQFT) I will describe the generalization of Hochschild cohomology that is relevant to describing deformations in AQFT. An interaction is described by a cohomology class.

Tue, 24 Oct 2017

12:00 - 13:15
L4

Convergence and new perspectives in perturbative algebraic quantum field theory

Kasia Rejzner
(University of York)
Abstract

In this talk I will present recent results obtained within the
framework of perturbative algebraic quantum field theory. This novel
approach to mathematical foundations of quantum field theory allows to
combine the axiomatic framework of algebraic QFT by Haag and Kastler with
perturbative methods. Recently also non-perturbative results have been
obtained within this approach. I will report on these results and present
new perspectives that they open for better understanding of foundations of
QFT.

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