Date/Time : 04 Dec 2024 15:00
Venue : S17 #04-06 (SR1)
Speaker : Thomas Karam, University of Oxford

This talk shall be essentially composed of four parts, each consisting of a short introduction to a research area followed by some contributions. We shall begin by discussing a central conjecture in Ramsey theory unifying several generalisations of the van der Waerden theorem. Thereafter, our focus shall move to the extension of basic properties of the rank of matrices to the different notions of rank of tensors, followed by the extension of basic properties of polynomials over finite fields to restrictions of these polynomials with Boolean variables. Finally, we shall study the Brunn-Minkowski inequality in more arbitrary ambient spaces than R^n, in particular in the torus (R/Z)^n for subsets satisfying various levels of constraints.

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Date/Time : 27 Nov 2024 15:00
Venue : S17 #04-06 (SR1)
Speaker : Ruiyi Yang, Princeton University

Gaussian processes (GPs) are important random function models with desirable analytic properties that have found wide applications in inverse problems, spatial statistics, and machine learning. In this talk, we shall investigate a generalization of the popular Matérn GP to the manifold setting. In the first part, we formalize its definition and introduce a graph-based approximation that is computable given only a point cloud of samples from the manifold. The resulting graph Matérn GP enjoys a sparsity structure that facilitates computation and is widely applicable in many aspects of Bayesian methodologies. In the second part, we discuss in detail its application in a manifold optimization problem where gradients are intractable to obtain. Exploiting tools from Bayesian optimization, we propose an efficient algorithm with provable guarantees, whose effectiveness is further demonstrated by numerical examples.

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Date/Time : 28 Oct 2024 10:00
Venue : via Zoom
Speaker : Qijun Tan, Google DeepMind

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https://nus-sg.zoom.us/j/82351206827?pwd=L6NM7PEa9BfIlfHqeare8XkoY0IKnr.1

Meeting ID: 823 5120 6827
Passcode: 077539

In this talk, we will explain how Large Language Models (LLM) obtain their capability in solving difficult math problems. In particular, We will go over key techniques that unearth the reasoning potential of LLMs. We will also illustrate key challenges in LLM reasoning.

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Date/Time : 17 Oct 2024 16:00
Venue : S17 #05-12 (SR4)
Speaker : Wang Yutong, National University of Singapore

The growing of verifiable formal languages, particularly interactive proof assistants like Lean 4, is shaping the future of mathematics and transforming how large language models (LLMs) can assist in automated reasoning. However, navigating the vast and complex Mathlib and composing reliable formal statements remains a challenge, with arcane syntax and scattered lemmas.

In this talk, I will present our recent developments: the LeanSearch platform V2 and the Herald translator, which features Lean-aware LLMs to streamline proof writing and auto-formalization of statements. We will explore specialized model training and data augmentation techniques that enhance LLM-accelerated formalization. I will demonstrate how these tools can assist both mathematicians and Lean developers.

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Date/Time : 14 Aug 2024 16:00
Venue : S17 #06-11 (SR6)
Speaker : Felix Schremmer, The University of Hong Kong

This talk presents a novel, interdisciplinary study that leverages a Machine Learning (ML) assisted framework to explore the geometry of affine Deligne-Lusztig varieties (ADLV). The primary objective is to investigate the nonemptiness pattern, dimension and enumeration of irreducible components of ADLV. Our proposed framework demonstrates a recursive pipeline of data generation, model training, pattern analysis, and human examination, presenting an intricate interplay between ML and pure mathematical research. Notably, our data-generation process is nuanced, emphasizing the selection of meaningful subsets and appropriate feature sets. We demonstrate that this framework has a potential to accelerate pure mathematical research, leading to the discovery of new conjectures and promising research directions that could otherwise take significant time to uncover. We rediscover the virtual dimension formula and provide a mathematical proof of a newly identified problem concerning a certain lower bound of dimension. This is joint work with Bin Dong, Xuhua He, Pengfei Jin and Qingchao Yu, and the corresponding paper can be found on arXiv and the Peking Mathematical Journal.

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Date/Time : 12 Aug 2024 15:00
Venue : S17 #04-06 (SR1)
Speaker : Daniel Bartl, University of Vienna

A major challenge in modern optimization problems is their instability, where small data perturbations can have disproportionately significant effects. We address this challenge in two settings. First, we focus on a distributionally robust approach, a popular method to counteract instability generically using optimal transport. Specifically, we demonstrate how this approach can systematically quantify the (in-)stability of a given optimization problem. In the second part, we focus on statistical robustness, dealing with data subject to outliers, such as those caused by adversarial corruption. We design robust estimators for optimization problems and risk measures.

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Date/Time : 08 Jul 2024 16:00
Venue : S17 #04-06 (SR1)
Speaker : Panel Discussion: Various speakers,

The leap from higher education to industry is a pivotal stage for many graduate students. Emphasising the necessity of an interdisciplinary approach and the application of the robust analytical skills honed during graduate studies, this panel discussion offers a comprehensive exploration of the journey that awaits MSc and PhD graduates who are looking to bridge the gap between academic accomplishment and professional fulfilment in the industry. Panellists will provide candid reflections on their personal pathways, highlighting the obstacles they encountered and the successes they achieved within various industrial domains. Attendees of the session will be encouraged to engage with live inquiries and raise pertinent topics for discussion. Discussions will revolve around the symbiotic relationship between advanced academic preparation and industry expectations, strategic planning for entering the corporate sector, the diverse opportunities ranging from employment in small to large-scale organisations to the launch of deep tech ventures, as well as the innovative trends and fruitful careers found in today’s industrial research and development.

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Date/Time : 19 Apr 2024 10:00
Venue : S17 #04-06 (SR1)
Speaker : Riccardo Brasca, Université Paris Cité

Workshop on Formal Proofs and Lean

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Date/Time : 17 Apr 2024 10:00
Venue : S17 #04-06 (SR1)
Speaker : Riccardo Brasca, Université Paris Cité

Workshop on Formal Proofs and Lean

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