Calendar

Supersymmetric QFT’s are of long-standing interest for their high degree of solvability, phenomenological implications, and rich connections to mathematics. In my talk, I will describe how the holomorphic twist isolates the protected quantities which give SUSY QFTs their potency by restricting to the cohomology of one supercharge. I will briefly introduce infinite dimensional symmetry algebras, generalizing Virasoro and Kac-Moody symmetries, which emerge. Finally, I will explain a potential novel UV manifestation of confinement, dubbed “holomorphic confinement,” in the example of pure SU(N) super Yang-Mills. Based on arXiv:2207.14321 and 2 forthcoming works with Kasia Budzik, Davide Gaiotto, Brian Williams, Jingxiang Wu, and Matthew Yu.

For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/quantum-matter-seminar/

Quantitative reasoning tasks which can involve mathematics, science, and programming are often challenging for machine learning models in general and for language models in particular. We show that transformer-based language models obtain significantly better performance on math and science questions when trained in an unsupervised way on a large, math-focused dataset. Performance can be further improved using prompting and sampling techniques including chain-of-thought and majority voting. Minerva, a model that combines these techniques, achieves SOTA on several math and science benchmarks. I will describe the model, its capabilities and limitations.

For more information, please see: https://cmsa.fas.harvard.edu/tech-in-math/

This seminar will be held in Science Center 530 at 4:00pm on Wednesday, October 5th.

Please see the seminar page for more details: https://math.harvard.edu/~ctm/sem/.

The Sachdev-Ye-Kitaev model was introduced as a toy model of interacting fermions without any particle-like excitations. I will describe how this toy model yields the universal low energy quantum theory of generic charged black holes in asymptotically 3+1 dimensional Minkowski space. I will also discuss how extensions of the SYK model yield a realistic theory of the strange metal phase of correlated electron systems.

In this talk, we construct special Lagrangian fibrations for log Calabi–Yau surfaces and scattering diagrams from Lagrangian Floer theory of the fibers. These scattering diagrams recover the algebro-geometric scattering diagrams of Gross–Pandharipande–Siebert and Gross–Hacking–Keel. The argument relies on a holomorphic/tropical disc correspondence to control the behavior of holomorphic discs, allowing us to relate open Gromov–Witten invariants to log Gromov-Witten invariants. This talk is based on joint work with Man-Wai Mandy Cheung, Hansol Hong, and Yu-Shen Lin.

For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/algebraic-geometry-in-string-theory/

We will talk about our recent construction of the smallest closed exotic 4-manifolds with signature zero known to date. Our novel examples are derived from fairly special small Lefschetz fibrations we build, with spin and non-spin monodromies. This is joint work with N. Hamada.