Memorial Mathematics Working Seminar
Winter Schedule: TBD
| December 2nd | Graham Cox - Geometry of
infinite-dimensional manifolds (part 3) This is an introductory talk on differential geometry in infinite dimensions. I will try to keep prerequisites to a minimum, just assuming familiarity with basic concepts from differential geometry and functional analysis (in particular, Banach spaces and finite-dimensional smooth manifolds). Many of the definitions and constructions are identical to those in finite dimensions, so I will instead focus on some of the subtleties and differences that arise in infinite dimensions. In a future talk I will describe some classical examples of this theory, such as manifolds of mappings and their application to incompressible fluid flow. |
| November 25th | Serhii Koval - Algebra of
symplectic reduction (part 2) In classical mechanics, symplectic (or Hamiltonian) reduction allows simplifying the equations of motion by considering symmetries of the phase space and its furter foliation into symplectic leaves. In this talk, I will give an introduction to the process of symplectic reduction from an algebraic perspective in the framework of affine schemes and actions of reductive groups. I will give an example of computation of Hamiltonian reduction for the commuting scheme. Time permitting, I will discuss Hamiltonian reduction along coadjoint orbit and give the construction of Calogero-Moser space of Kazhdan, Kostant and Sternberg. This talk is based on the lecture notes of P. Etingof on Calogero-Moser systems. Reference: arXiv:0606233. |
| November 18th | Graham Cox - Geometry of
infinite-dimensional manifolds (part 2) This is an introductory talk on differential geometry in infinite dimensions. I will try to keep prerequisites to a minimum, just assuming familiarity with basic concepts from differential geometry and functional analysis (in particular, Banach spaces and finite-dimensional smooth manifolds). Many of the definitions and constructions are identical to those in finite dimensions, so I will instead focus on some of the subtleties and differences that arise in infinite dimensions. In a future talk I will describe some classical examples of this theory, such as manifolds of mappings and their application to incompressible fluid flow. |
| November 12th | Graham Cox - Geometry of
infinite-dimensional manifolds (part 1) This is an introductory talk on differential geometry in infinite dimensions. I will try to keep prerequisites to a minimum, just assuming familiarity with basic concepts from differential geometry and functional analysis (in particular, Banach spaces and finite-dimensional smooth manifolds). Many of the definitions and constructions are identical to those in finite dimensions, so I will instead focus on some of the subtleties and differences that arise in infinite dimensions. In a future talk I will describe some classical examples of this theory, such as manifolds of mappings and their application to incompressible fluid flow. |
| November 4th | Tom Baird - An introduction to
Cohomological Field Theories (part 2) Having introduced moduli spaces of curves and Gromov-Witten theory last week, this week I will present the abstract definition of a cohomological field theory, explore some of its properties, and describe the Givental-Teleman classification of semisimple cohomological field theories. Reference: arXiv:1712.02528. |
| October 28th | Christopher Lang - An introduction
to topological recursion (part 2) Topological recursion is a construction in algebraic geometry that recursively computes invariants of spectral curves. In this talk, I will (finally) introduce topological recursion, examine the connection between topological recursion and Airy ideals, and explore some applications of this construction. Reference: arXiv:2409.06657. |
| October 21th | Serhii Koval - Algebra of
symplectic reduction (part 1) In classical mechanics, symplectic (or Hamiltonian) reduction allows simplifying the equations of motion by considering symmetries of the phase space and its furter foliation into symplectic leaves. In this talk, I will give an introduction to the process of symplectic reduction from an algebraic perspective in the framework of affine schemes and actions of reductive groups. I will give an example of computation of Hamiltonian reduction for the commuting scheme. Time permitting, I will discuss Hamiltonian reduction along coadjoint orbit and give the construction of Calogero-Moser space of Kazhdan, Kostant and Sternberg. This talk is based on the lecture notes of P. Etingof on Calogero-Moser systems. Reference: arXiv:0606233. |
| October 16th | Tom Baird - An introduction to
Cohomological Field Theories (part 1) In this expository lecture, I will give an introduction to cohomological field theories in the sense of Kontsevich and Manin. Along the way, we will learn about moduli spaces of complex curves, Gromov-Witten theory, and 2D topological field theories. I hope to make my presentation accessible to anyone acquainted with manifolds and cohomology (singular or de Rham). Reference: arXiv:1712.02528. |
| October 7th | Christopher Lang - An introduction
to topological recursion (part 1) Topological recursion is a construction in algebraic geometry that recursively computes invariants of spectral curves. It has applications to enumerative geometry, string theory, knot theory, mathematical physics, and random matrix theory, among others. In this talk, I will introduce some of the components of this construction. Reference: arXiv:2409.06657. |
| September 30th | Organizational
Meeting We will set up a preliminary schedule of speakers for the term. |