Talk

A surface system for a link in the 3-sphere is a collection of Seifert surfaces for the components of the links, that intersect one another transversally and in at most triple points.  The intersections are thought of as oriented manifolds.  Given two links with the same pairwise linking numbers, do they admit homeomorphic surface systems?

The idea of topologically twisting a supersymmetric field theory was introduced in the physics literature in order to generate interesting new examples of topological field theories.  The idea is very general, but systematically realising the examples it produces is not always possible using mathematical models for topological field theory (such as Atiyah-Segal's functorial field theory, or the theory of E_n-algebras).  In this talk I'll explain what it means to twist a supersymmetric field theory in the factorization algebra framework devel

A BV formalism is not only a fundamental framework of quantum field theory, but also appears in a variety of fields of mathematics and physics as an universal structure. After we prepare BV-geometry and notion of so called NS fluxes and T-duality, we reformulate geometry of T-duality by the BV-AKSZ formalism based on supergeometry. Moreover we explain that extended T-duality recently proposed in physics is also formulated and unified by this formalism.

The Hitchin fibration is a natural tool through which one can understand the moduli space of Higgs bundles and its interesting subspaces (branes). After reviewing the type of questions and methods considered in the area, we shall dedicate this talk to the study of certain branes which lie completely inside the singular fibres of the Hitchin fibrations.

A Lie pair $(L,A)$ consists of a Lie algebroid $L$ together with a Lie subalgebroid $A$. A wide range of geometric situations can be described in terms of Lie pairs including complex manifolds, foliations, and manifolds equipped with Lie algebra actions. We establish the formality theorem for Lie pairs. As an application, we obtain Kontsevich-Duflo type theorems for Lie pairs. In this talk, I'll start with the case of $\mathbf{g}$-manifolds, i.e., smooth manifolds equipped with Lie algebra actions.

Let A and B be rational functions on the Riemann sphere. The function B is
said to be semiconjugate to the function A if there exists a non-constant rational
function X such that A\circ X= X\circ B  (*).

The semiconjugacy condition generalises both the classical conjugacy relation and
the commutativity condition. In the talk we present a description of solutions of
functional equaton (*) in terms of orbifolds of non-negative Euler characteristic on
the Riemann sphere, and discuss numerous relations of this equation with complex
dynamics and number theory.