Talks

Many of the rich interactions between mathematics and physics arise using general mathematical frameworks that describe a host of physical phenomena: from differential equations, to algebra, to topology and geometry. On the other hand, mathematics also possesses many examples of "exceptional objects": they constitute the finite set of leftovers that appear in numerous classification problems. For example, groups of symmetries in three dimensions appear in two infinite families (cyclic groups and dihedral groups of n-sided polygons) and the symmetry groups of the five Platonic solids--- the 'exceptional' structures. 

The mathematical subject of moonshine refers to surprising relationships between other kinds of special/exceptional objects that arise from the theory of finite groups and from number theory. Increasingly, string theory has been a source of insights in and explanations for moonshine. It is even the source of new examples of moonshine that further implicate special objects in geometry. We will review moonshine, survey these developments, and highlight some of the (many!) exciting mysteries that remain.

It is known that there is a relationship between conformal Carroll transformations and BMS symmetry. In this talk I will explore the geometry of generic Carroll structures which may be thought of as the basic underlying geometric structure on null hypersurfaces. A Carroll structure can be thought of as a fibre bundle with Ehresmann connection, and one finds that (generalized) BMS symmetry emerges as the conformal symmetry of this bundle and connection. I’ll briefly also describe how this story fits into the physics of ’soft modes.’

Mirror sectors -- hidden sectors that are approximate copies of the Standard Model -- are a generic prediction of many models, notably the Mirror Twin Higgs model. Such models can have a rich cosmology and many interesting detection signatures beyond the realm of colliders. In this talk, I will focus on the possibility that mirror matter can form stars which undergo mirror nuclear fusion in their cores. I will discuss the mechanisms by which these objects can emit Standard Model light and estimate their luminosity and prospects for their detection.

An assessment of the particle standard model and an alternative formulation of
the model are presented. An ultraviolet complete particle model is constructed
for the observed particles of the standard model. The quantum field theory
associates infinite derivative entire functions with propagators and vertices, which
make perturbative quantum loops finite and maintain Poincaré invariance and
unitarity of the model. The electroweak model SU(2) X U(1) group is treated as a
broken symmetry group with non-vanishing experimentally determined boson
and fermion masses. A spontaneous symmetry breaking of the vacuum by a
scalar Higgs field is not invoked to restore boson and fermion masses to the
initially massless SU(2) X U(1) Lagrangian of the standard model. The hierarchy
naturalness problem of the Higgs boson mass is resolved and the model
contains only experimentally observed masses and coupling constants. The
renormalization group features of the scalar Higgs field are investigated and the
model is shown to be asymptotically safe and free from the triviality problem. It is
demonstrated that the finite nonlocal quantum field theory satisfies
microcausality. The model can predict a stable vacuum evolution. Experimental
tests to distinguish the standard model from the alternative model are proposed.
The finite quantum field theory can be extended to quantum gravity.