12, 14 и 17 сентября в институте физико-математических наук и ИТ состоятся лекции профессора Грэма Холла (Абердин, Шотландия).
Грэм Холл — член Королевского Общества Эдинбурга, Общества общей относительности и Гравитации, Эдинбургского математического общества, европейского математического общества и Королевского астрономического общества.
Место проведения лекций: ул. А. Невского 14, корпус института ФМН и ИТ.
12 сентября (среда) в 17.00 (229 ауд.)
«Краткое введение в общую теорию относительности Эйнштейна»
14 сентября (пятница) в 13.30 (118 ауд.)
«Евклидова геометрия и аксиомы Гильберта»
17 сентября (понедельник) в 17.00 (233 ауд.)
«Теория конвергенции в топологии»
Приглашаются студенты, магистранты, аспиранты и преподаватели.
A Brief Introduction to Einstein’s General Theory of Relativity
This talk will attempt to explain the basic ideas of general relativity theory and their connection with classical differential geometry. Einstein’s theory is a theory of gravity and so the talk begins with a discussion of the problems with classical Newtonian gravitational theory as it existed in about 1900. The separate ideas and steps used by Einstein to address each of these problems will then be described. These include the principles of covariance and equivalence, the formulation of a differential-geometric foundation for his work, the role of geometric curvature in physics and, of course, Einstein’s field equations. Some of the consequences of Einstein’s work can then be summarised, such as the theory of exact solutions of his equations, a general theory of cosmology (including light bending, dark matter and dark energy), black holes and gravitational waves.
Student talk 1, Euclidean Geometry and Hilbert’s axioms
This talk will consider the foundations of (2-dimensional) Euclidean Geometry as given by David Hilbert. The intuitive reasons for the axioms will be discussed first and then the axioms themselves will be described in the order; (i) Axioms of incidence, (ii) Axioms of betweenness, (iii) Axioms of congruence for length and angle, (iv) The completeness axiom and (v) the parallel axiom. Some extra discussion will be given on the completeness axiom (which is the only non-intuitive axiom in the list) and its relationship to Dedekind’s idea of a cut in the construction of the real numbers. It will then be described how there are exactly two choices for the parallel axiom, one of which leads uniquely to Euclidean geometry and the other which leads uniquely to the (non-Euclidean) geometry of Lobachevski and Bolyai.
Student talk 2, The Theory of Convergence in Topology
This talk discusses the theory of convergence in topology. It starts by describing the usual (sequential) convergence in terms of sequences and proving some classical theorems in this area. These theorems will highlight the restrictive nature of sequential convergence but will also suggest how such restrictions can be avoided by making certain generalisations. These generalisations will then be described in terms of directed sets and nets. The classical theorems mentioned above are then re-visited using nets and it will be shown how the restrictions encountered for sequences are removed.
