Date/Time : 18 Jun 2025 14:00
Venue : S17 #04-04 (SR3)
Speaker : Khanh Le, Rice University

For a hyperbolic surface X with non-empty boundary, the ortho-length spectrum of X is the multi-set of lengths of (ortho)-geodesic arcs meeting the boundary of X perpendicularly at both endpoints. The spectrum was introduced by Basmajian for hyperbolic n-manifolds in the context of studying co-dimensional one embedded geodesic submanifolds. The ortho-length spectrum has been studied extensively in relation to geometric identities, hyperbolic geometry of surfaces and inverse geometry. In this work, we initiate a new investigation into the arithmetic properties of the ortho-length spectrum. In particular, we consider hyperbolic surfaces whose cosh-of-length of ortho-geodesics are all integers, ortho-integral surfaces. We prove that there are only finitely many ortho-integral surfaces for a fixed topological type. We also constructed infinitely many pairwise non-commensurable ortho-integral surfaces. In the talk, I will motivate the consideration of such surfaces and discuss some ideas and tools going into the proof. If time permits, I will also discuss some further questions that we would like to investigate. This is joint work with Minh Doan.

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Date/Time : 18 Jun 2025 16:00
Venue : S17 #06-11 (SR6)
Speaker : Jaydeep Singh, Princeton University

In this talk we will discuss self-similar solutions to the Einstein-scalar field system, first studied by Christodoulou (’94). These are a family of C^{1,\alpha} solutions modeling spacetime singularities without an event horizon. In BV spaces their instability is well understood via a geometric blue-shift effect, and leads to the formation of black holes. We will share progress on extending these results to Hölder spaces, and discuss some of the analytical and conceptual obstacles to doing so.

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Date/Time : 06 Jun 2025 14:00
Venue : S17 #04-05 (SR2)
Speaker : Xie Xingyu, National University of Singapore

Large language models excel at pattern completion yet struggle with multi-step mathematics, logical deduction, and tool-assisted problem solving. Recent work shows that reinforcement learning can provide the “slow-thinking” mechanisms needed for such tasks. This talk formulates reasoning as a sequential decision process and explains how policy-gradient objectives are adapted to text generation. The main case study, DeepSeek-R1, is examined in detail, covering its Group Relative Policy Optimisation objective, reward design, and the resulting gains on contest-level mathematics. The talk also surveys subsequent refinements that build on R1’s principles, illustrating how practical adjustments to reward formulation and output control further enhance reasoning performance. Together these methods illustrate how RL is currently advancing the reasoning abilities of state-of-the-art language models.

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Date/Time : 26 May 2025 14:00
Venue : S17 #04-05 (SR2)
Speaker : Gus Lehrer, University of Sydney

I shall show how to use algebraic geometric methods to convert invariants of OSp into invariants of GL. This will be used to obtain precise versions of the first and second fundamental theorems for OSp.

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Date/Time : 13 May 2025 15:00
Venue : S17 #06-11 (SR6)
Speaker : Shahab Asoodeh, McMaster University

The problem of sampling under local differential privacy has recently gained attention due to its potential applications in generative models. However, a thorough understanding of the privacy-utility trade-off in this context is still lacking. In this talk, I’ll discuss the minimax optimality of locally private sampling with f-divergence as the utility measure. I’ll demonstrate that this setup corresponds to the limiting case of distribution estimation under “user-level” local differential privacy, where each user has access to a large amount of data. As the main result of the talk, I’ll present families of optimal sampling mechanisms for both discrete and continuous domains. Remarkably, these samplers are universally optimal across all f-divergences, distinguishing sampling from typical learning problems. If time permits, I’ll also discuss how non-private data can be integrated into private sampling problems. I’ll conclude the talk by highlighting several open questions in the area of private sampling.

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Date/Time : 09 May 2025 14:00
Venue : S17 #04-04 (SR3)
Speaker : Emmanuel Bengio ,

In this talk I will share some recent progress on training GFlowNets and applying them to scientific problems, as well as speculate on the bigger picture; using GFNs to be good Bayesians. I will start the talk with a quick tutorial/refresher on GFlowNets to set the stage, and hope to finish with an open discussion of next steps and open problems. Interruptions, debates, and clarifications will be welcome throughout.

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Date/Time : 08 May 2025 11:00
Venue : S17 #04-04 (SR3)
Speaker : Tianqi Wang, Yale University

We construct an example of discrete, faithful and simple-stable representation of a closed hyperbolic surface groups into $SO^+(4,1)$ that is not convex-cocompact but deforms to a Fuchsian one continuously. Therefore the simple-stable characters forma domain of discontinuity for the mapping class group action on the character variety, who has a connected component strictly containing the convex-cocompact characters. We further talk about some general notions of ending currents in the study of discrete faithful representations into $SO^+(4,1)$.

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Date/Time : 30 Apr 2025 15:00
Venue : S17 #04-05 (SR2)
Speaker : Liu Jinpeng, Tsinghua University

Nonlinear dynamics play a prominent role in scientific computation and artificial intelligence. Whereas previous quantum algorithms for general nonlinear equations have been severely limited due to the linearity of quantum mechanics, we gave the first efficient quantum algorithm for nonlinear differential equations with sufficiently strong dissipation. This is an exponential improvement over the best previous quantum algorithms, whose complexity is exponential in the evolution time. Furthermore, we design the first quantum algorithm for training classical sparse neural networks with end-to-end settings. We benchmark instances of ResNet with sparse pruning applied to Cifar-100 dataset and DPM-Solver for U-ViT applied to ImageNet-100 dataset, and we find that a quantum enhancement is possible at the early stage of learning. Our work shows that fault-tolerant quantum computing can contribute to the training and inference processes of most state-of-the-art large language models and diffusion models.

References:
[1]Efficient quantum algorithm for dissipative nonlinear differential equations. Proceedings of the National Academy of Science 118, 35 (2021).
[2]Towards provably efficient quantum algorithms for large-scale machine learning models. Nature Communications 15, 434 (2024)
[3]Towards efficient quantum algorithms for diffusion probability models. arXiv:2502.14252

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Date/Time : 30 Apr 2025 16:00
Venue : S17 #04-05 (SR2)
Speaker : Silu Yin, Hangzhou Normal University

In this talk, we investigate the ill-posedness of the non-strictly hyperbolic compressible ideal MHD (IMHD) system in two dimensions，which exhibits multiple propagation speeds. For scalar quasilinear wave equation, Smith-Tataru showed its local well-posedness in $H^{11/4+}(R^2)\times H^{7/4+}(R^2)$. Here, we construct a counterexample to the local existence of low-regularity solutions to the IMHD system in the borderline space $H^{7/4}(R^2)$. Our proof is based on a coalition of a carefully designed algebraic approach and Christodoulou’s geometric approach. We give a complete description of solutions’ dynamics up to the earliest singular event, when a shock forms. This talk is based on a joint work with Xinliang An and Haoyang Chen.

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