Together with Matilde Marcolli, I am co-organizing the Information, Geometry & Physics Seminar at Caltech.
| Time | Winter 2025, 15:00-16:00 on Wednesdays |
|---|---|
| Location | 310 Linde Hall |
| Date | Speaker | Title | Abstract |
|---|---|---|---|
| Feb. 26th 2025 | Terrence George (UCLA) | Electrical networks and Lagrangian Grassmannians | An electrical network is a planar graph with weights on its edges called conductances. Thomas Lam showed that electrical networks form a subset of the totally nonnegative part of the Grassmannian and described the subset as a linear slice. We show that this linear slice consists of points that are isotropic for a particular symplectic form. This is joint work with Sunita Chepuri and David Speyer. |
| Apr. 23rd 2025 | Colleen Delaney (Perdue) | An "efficient" classical algorithm for some 3-manifold TQFT invariants | We will share some recent results that are instructive for approaching the classification of 3D TQFTs and topological order by computational complexity. We explain how the Turaev-Viro-Barrett-Westbury state-sum invariants that arise from Tambara-Yamagami categories are efficient to compute for 3-manifolds, provided there is a bound on their first Betti number. On the one hand, this is a pretty good algorithm given the fact that these TQFT invariants are #P-hard to compute for the smallest member of the family of Tambara-Yamagami categories (and should be hard to compute more generally). On the other hand, it isn't too surprising given that Tambara-Yamagami categories are only a slight generalization of the finite dimensional representation category of a finite abelian group, whose associated TVBW invariants are easy to compute. In any case, one can interpret our parametrized algorithm to mean that our inability to classically compute these quantum invariants in polynomial time is due to the fact that 3-manifolds can have a large first Betti number. This talk is based on joint work with Clément Maria and Eric Samperton. |
| Apr. 30th 2025 | Svala Sverrisdóttir (UC Berkeley) | Kinematic varieties for massless particles | We study algebraic varieties that encode the kinematic data for n massless particles in $d$-dimensional spacetime subject to momentum conservation. Their coordinates are spinor brackets, which we derive from the Clifford algebra associated to the Lorentz group. This was proposed for $d=5$ in the recent physics literature. Our kinematic varieties are given by polynomial constraints on tensors with both symmetric and skew symmetric slices. |
| May. 14th 2025 | Jonathan Beardsley (University of Reno) | TBA | TBA |
| May. 21st 2025 | Jane Panangaden (Pitzer College) | TBA | TBA |
| June. 4th 2025 | Yulia Alexandr (UCLA) | Maximum information divergence from linear and toric models | I will revisit the problem of maximizing information divergence from a new perspective using logarithmic Voronoi polytopes. We will see that for linear models, the maximum is always achieved at the boundary of the probability simplex. For toric models, I will describe an algorithm that combines the combinatorics of the chamber complex with numerical algebraic geometry. I will pay special attention to reducible models and models of maximum likelihood degree one, with many colorful examples. This talk is based on joint work with Serkan Hoşten. |
| June. 18th 2025 | Leo Shaposhnik (Freie Universität Berlin) | TBA | TBA |