Generating functions of intersection numbers on moduli spaces of curves provide geometric solutions to integrable systems. Notable examples are the Kontsevich-Witten tau function and Brezin-Gross-Witt...
In this talk, we discuss the reduction-quantization diagram in terms of formality. First, we propose a reduction scheme for multivector fields and multidifferential operators, phrased in terms of L∞ m...
Bridgeland stability conditions have been introduced about 20 years ago, with motivations both from algebraic geometry, representation theory and physics. One of the fundamental problems is that we cu...
I will illustrate the most recent results on how to enhance triangulated categories (and exact functors) of geometric nature. We will then move to the problem of lifting equivalences between various t...
AKSZ sigma models are physical models constructed from dg manifolds (Q-manifolds). One of important AKSZ sigma models is the Poisson sigma model, which gives the Kontsevich formula in the deformation ...
In this talk I will report on work on elliptic cohomology with Tomasini and Scherotzke. With Tomasini we give a new construction of equivariant elliptic cohomology in terms of a stack of maps out of t...
The Donaldson-Thomas invariants count stable coherent sheaves on Calabi-Yau 3-folds which were introduced by Thomas around 1998. Later Joyce-Song, Kontsevich-Soibelman and Davison-Meinhardt introduced...
Modified Patankar-Runge-Kutta (MPRK) schemes are numerical methods for the solution of positive and conservative production-destruction systems. They adapt explicit Runge-Kutta schemes in a way to ens...
