Talks

In this talk, I will present a sewing-factorization theorem for conformal blocks in arbitrary genus associated to a (possibly nonrational) $C_2$-cofinite VOA $V$. This result gives a higher genus analog of Huang-Lepowsky-Zhang's tensor product theory. Moreover, I will explain the relation between our result and pseudotraces, and confirm some of the conjectures by Gainuditnov-Runkel. The relationship between our result and coends will also be discussed. The talk is based on an ongoing project (arXiv: 2305.10180, 2411.07707) joint with Bin Gui.

In this talk, I will describe how ideas from geometry and combinatorics can help us understand the mathematical and physical properties of cosmological integrals. From efficiently deriving canonical differential equations to a systematic method for finding a minimal basis for the physical subspace. Time permitting, I will also comment on how geometry and combinatorics control the zeros of cosmological integrands.

I will introduce how to incorporate loop contributions into positivity bounds in a massless scalar theory with shift symmetry. The allowed region of Wilson coefficients is called the EFT-hedron. With loop contributions, the n=4 null constraint, which plays an important role in determining the allowed region for g3–g4 (the Wilson coefficients of dimension-10 and dimension-12 operators, respectively), is modified. This modification of the null constraint reveals new features of the EFT-hedron. We obtained a much stronger bound for g2 (the Wilson coefficient of dimension-8 operators) without using the full unitarity condition. Furthermore, we found a negative g4, which is not possible under the tree-level bound. It would be interesting to generalize our method to more complicated theory and test our results.