NUMBER THEORY SEMINAR: | Shai HaranTechnion, Israel |
New Foundations for Arithmetical Geometry, Pt 1 (Follow up talk at MIT on 5/5/16) |

on Wednesday, May 04, 2016, at 3:00 PM in Science Center 507 | ||

We shall give a simple generalization of commutative rings. The category GR of such generalized rings contains ordinary commutative rings (fully, faithfully), but also the "integers" and the "residue field" at a real or complex place of a number field ; the "field with one element" F1 (the initial object of GR) ; the "Arithmetical Surface" (the categorical sum of the integers Z with them self). We shall show this geometry sees the real and complex places of a number field K : the valuation sub GR of K correspond to the finite and infinite primes of K, and there is a compactification of the spectrum of the integers of K. One can develope algebraic geometry using generalized rings following Grothendieck's paradigm, with Quillen's homotopical algebra replacing homological algebra. There is a theory of differentials which satisfy all the usual properties, as well as an analogue of Quillen's cotangent complex. We compute the differentials of the integers Z over F1. We associate with any compact topologic |

CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM: | Hirosi OoguriCalifornia Institute of Technology |
String Theory And Its Applications in Mathematics and Physics |

on Wednesday, May 04, 2016, at 4:30 PM in CMSA Building, 20 Garden Street, Room G10 | ||

In the past few decades, we have discovered several new connections between mathematics and physics via study of string theory. In this talk, I will review some of these connections, focusing on topological string theory, the mirror symmetry, the large N duality, and the Mathieu moonshine. I will also discuss a new perspective that is emerging at the interface between information theory and geometry. The talk is aimed at a general audience in mathematics and physics. |

CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS GENERAL RELATIVITY SEMINAR: | Robert PennaMIT |
BMS Invariance and the membrane paradigm |

on Wednesday, May 04, 2016, at 12:00 - 1:00 PM in CMSA Building, 20 Garden Street, Room G10 | ||

The Bondi-van der Burg-Metzner-Sachs (BMS) group is the asymptotic symmetry group of asymptotically flat spacetime. It is infinite dimensional and entails an infinite number of conservation laws. According to the black hole membrane paradigm, null infinity (in asymptotically flat spacetime) and black hole event horizons behave like fluid membranes. Membrane fluid dynamics is governed by an infinite set of symmetries and conservation laws. Our main result is to point out that the infinite set of symmetries and conserved charges of the BMS group and the membrane paradigm are the same. This relationship sheds light on the physical interpretation of BMS conservation laws, generalizes the BMS conservation laws to arbitrary subregions of arbitrary null surfaces, and clarifies the identification of the superrotation subgroup of the BMS group. |

CENTER OF MATHEMATICAL SCIENCES AND APPLICATIONS COLLOQUIUM: | Juerg FroehlichETH and IAS |
Implications of the Chiral Anomaly - From the Quantum Hall Effect to Topological Insulators and Out to Space |

on Wednesday, May 11, 2016, at 4:30 PM in CMSA Building, 20 Garden Street, Room G10 | ||

Starting with an analysis of chiral edge currents in 2D electron gases exhibiting the quantum Hall effect, I will discuss the role of anomalous chiral edge currents and of anomaly inflow in 2D insulators with explicitly broken parity and time-reversal and in time-reversal invariant 2D topological insulators exhibiting edge spin-currents. I will derive the topological Chern-Simons theories that yield the correct response equations for the 2D bulk of such materials. After an excursion into the theory of 3D topological insulators, including “axionic insulators”, I discuss a model of Dark Matter and Dark Energy involving an axion coupled to the instanton density of a gauge field. |