3 | 4  Algebraic Geometry in String Theory Seminar 10:30 am-11:30 am 12/04/2023 CMSA, 20 Garden Street, Cambridge, MA 02138 USA Algebraic Geometry in String Theory Seminar Speaker: Maksym Fedorchuk (Boston College) Title: CM-minimizers and standard models of Fano fibrations over curves Abstract: A recent achievement in K-stability of Fano varieties is an algebro-geometric construction of a projective moduli space of K-polystable Fanos. The ample line bundle on this moduli space is the CM line bundle of Tian. One of the consequences of the general theory is that given a family of K-stable Fanos over a punctured curve, the polystable filling is the one that minimizes the degree of the CM line bundle after every finite base change. A natural question is to ask what are the CM-minimizers without base change. In answering this question, we arrive at a theory of Koll\’ar stability for fibrations over one-dimensional bases, and standard models of Fano fibrations. I will explain the joint work with Hamid Abban and Igor Krylov in which we show that the CM-minimizers for del Pezzo fibrations are Corti’s standard models and related work in progress on quartic threefold hypersurfaces. - Topological Quantum Matter Seminar
2:00 pm-3:00 pm 12/04/2023 CMSA, 20 Garden Street, Cambridge, MA 02138 USA  Topological Quantum Matter Seminar Speaker: Ken K. W. Ma (Northeastern University) Title: The Fractional Quantum Hall Effect at ν=5/2: Past, Recent, and Future Abstract: The discovery of fractional quantum Hall (FQH) states started a new chapter in modern physics. Nowadays, more than 70 FQH states at different filling factors have been observed. Among them, the FQH state at the filling factor ν=5/2 in GaAs (or the 5/2 state) remains one of the most special and attractive states. Since its discovery in 1987, different possible topological orders have been proposed to describe the 5/2 state. Some of them can host an exotic type of particles, known as non-Abelian anyons. Recent experiments have provided more insights into the understanding of the 5/2 state, but its underlying nature is still under debate. In this talk, I will review the basics of the 5/2 state [1] and a more unified theoretical description of different possible topological orders of the 5/2 state that we have recently proposed [2]. I will also review the groundbreaking thermal Hall conductance experiment [3] and the follow-up quantum Hall interface experiments by the Weizmann Institute group [4, 5], and discuss what possible lessons that we can learn from the experimental results. Lastly, I will talk about some possible directions and related topics for future investigations. References: [1] K. K. W. Ma, M. R. Peterson, V. W. Scarola, and K. Yang, “Fractional quantum Hall effect at the filling factor ν = 5/2” in Encyclopedia of Condensed Matter Physics (Second Edition), edited by T. Chakraborty, Academic Press (2024).
[2] K. K. W. Ma and D. E. Feldman, “The sixteenfold way and the quantum Hall effect at half-integer filling factors”, Phys. Rev. B 100, 035302 (2019).
[3] M. Banerjee, M. Heiblum, V. Umansky, D. E. Feldman, Y. Oreg, and A. Stern, “Observation of half-integer thermal Hall conductance”, Nature (London) 559, 205 (2018).
[4] B. Dutta, W. Yang, R. Melcer, H. K. Kundu, M. Heiblum, V. Umansky, Y. Oreg, A. Stern, D. Mross, “Distinguishing between non-Abelian topological orders in a quantum Hall system”, Science 375, 193 (2021).
[5] B. Dutta, V. Umansky, M. Banerjee, and M. Heiblum, “Isolated ballistic non-Abelian interface channel”, Science 377, 1198 (2022). - Colloquium
4:30 pm-5:30 pm 12/04/2023 CMSA, 20 Garden Street, Cambridge, MA 02138 USA  Speaker: Xuwen Zhu (Northeastern) Title: Analysis of ALH* gravitational instantons Abstract: Gravitational instantons are non-compact Calabi-Yau metrics with L^2 bounded curvature and are categorized into six types. We will discuss one such type called ALH* metrics which has a non-compact end modelled by the Calabi ansatz with inhomogeneous collapsing near infinity. Such metrics appeared recently in the works on SYZ conjecture, as well as the scaling bubble limits for codimension-3 collapsing of K3 surfaces, where the study of its Laplacian played a central role. In this talk I will talk about the Fredholm mapping property and L^2 cohomology of such metrics. This is ongoing work joint with Rafe Mazzeo.
| 5 - General Relativity Seminar
11:00 am-12:00 pm 12/05/2023  General Relativity Seminar Speaker: Andras Vasy (Stanford) Title: The Feynman propagator and self-adjointness Abstract: In this talk I will discuss the Feynman and anti-Feynman inverses for wave operators on certain Lorentzian manifolds; these are two inverses which from a microlocal analysis perspective are more natural than the standard causal (advanced/retarded) ones. For instance, for the spectral family of the wave operator, these are the natural inverses when the spectral parameter is non-real. Indeed, I will explain that these connect to the self-adjointness of the wave operator, and the positivity properties that follow. - CMSA Q&A Seminar
12:30 pm-1:30 pm 12/05/2023 20 Garden Street, Cambridge, MA 02138 USA CMSA Q and A Seminar Speakers: Mike Douglas (Harvard CMSA) and Anurag Anshu (Harvard Computer Science) Topics: Mike Douglas: What are scaling laws in deep learning? Anurag Anshu: What’s the difference between classical information theory and quantum information theory (or classical computation vs quantum computation)?
| 6 - Topological Quantum Matter Seminar
10:30 am-11:30 am 12/06/2023 Topological Quantum Matter Seminar Speaker: Yunqin Zheng, Stony Brook University Title: Gapless SPT States from Kennedy Tasaki Transformation - New Technologies in Mathematics Seminar
2:00 pm-3:00 pm 12/06/2023 CMSA, 20 Garden Street, Cambridge, MA 02138 USA  New Technologies in Mathematics Seminar Speakers: Katherine Collins and Albert Jiang, Department of Computer Science and Technology, University of Cambridge Title: Evaluating Language Models for Mathematics through Interactions Abstract: There is much excitement about the opportunity to harness the power of large language models (LLMs) when building problem-solving assistants. However, the standard methodology of evaluating LLMs based on static pairs of inputs and outputs is insufficient to be able to make an informed decision about which LLMs, and under what assistive settings they can be sensibly utilised. Static assessment fails to take into account the essential interactive element in their deployment, and therefore limits how we understand language model capabilities. In this talk, we present our recent work introducing CheckMate, an adaptable prototype platform for humans to interact with and evaluate LLMs. We discuss our study with CheckMate to evaluate three language models (InstructGPT, ChatGPT, and GPT-4) as assistants in proving undergraduate-level mathematics, with a mixed cohort of participants from undergraduate students to professors of mathematics. We release the resulting interaction and rating dataset, MathConverse. By analysing MathConverse, we derive a taxonomy of human behaviours and uncover that despite a generally positive correlation, there are notable instances of divergence between correctness and perceived helpfulness in LLM generations, amongst other findings. Further, we identify useful scenarios and existing issues of GPT-4 in mathematical reasoning through a series of case studies contributed by expert mathematicians. We conclude with actionable takeaways for ML practitioners and mathematicians: models which communicate uncertainty, respond well to user corrections, and are more interpretable and concise may constitute better assistants; interactive evaluation is a promising way to navigate the capability of these models; humans should be aware of language models’ algebraic fallibility and discern where they are appropriate to use.
| 7 - Active Matter Seminar
1:00 pm-2:00 pm 12/07/2023 CMSA, 20 Garden Street, Cambridge, MA 02138 USA  Speaker: Michael Shelley (Flatiron) Title: Active structures and flows in living cells Abstract: Flows in the fluidic interior of living cells can serve biological function or act as signatures of how intracellular forces are exerted. I’ll discuss examples of each. One is understanding the emergence of cell-spanning vortical flows in large developing egg cells, while the other arises in studying the nature of force transduction in single cell embryos moving towards their first cell division. Both involve the cytoskeleton, that set of polymers, cross-linkers, and molecular motors that underlie much of the active mechanics within cells, and has led to the development of new coarse-grained active matter models and novel instabilities.
| 8 - Quantum Matter
10:00 am-11:30 am 12/08/2023 CMSA, 20 Garden Street, Cambridge, MA 02138 USA - Member Seminar
12:00 pm-1:00 pm 12/08/2023 CMSA, 20 Garden Street, Cambridge, MA 02138 USA Member Seminar Speaker: Juven Wang
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