Monday, March 27, 2023
03/27/2023 - 4:00pm
The classical Klein Combination Theorem provides sufficient conditions to construct new Kleinian groups. Subsequently, Maskit gave far-reaching generalizations to the Klein Combination Theorem. A special feature of Maskit's theorems is that they furnish sufficient conditions so that the combined group retains nice geometric features, such as convex-cocompactness or geometric-finiteness. In recent years, Anosov subgroups have emerged as a natural higher-rank generalization of the convex-cocompact Kleinian groups, exhibiting their robust geometric and dynamical properties. This talk will discuss my recent joint work with Michael Kapovich on the Combination Theorems in the setting of Anosov subgroups.
03/27/2023 - 4:30pm
In this talk, I discuss how an infinite dimensional convex geometry of interest to physicists exhibits "flattening," which manifests as emergent equalities among naively independent coordinates. This flattening behavior is intrinsically tied to the infinite dimensional nature of the convex geometry, as these emergent equalities only appear in the infinite dimensional limit. In more detail, the space of causal and unitary theories, called the EFT-Hedron, is identified as the intersection of a convex region given by the Minkowski sum of two moment curves and a hyperplane in an infinite dimensional projective space. I use linear programming to provide strong numeric evidence that the EFT-hedron "flattens out." For example, restricting a finite fraction of the coordinates to be even-zeta values, the remaining coordinates are (conjecturally) fixed to take odd-zeta values. I will conclude by briefly sketching how this conjecture relates to Type-I superstring theory, which corresponds to a particular point in the EFThedron.