Date/Time : 12 Oct 2022 17:00
Venue : S17 #04-05 (SR2)
Speaker : Frank Stephan, National University of Singapore

The talk will present selected results from the joint work of Andre Nies and Frank Stephan on complexity of measures aThe talk will present selected results from the joint work of Andre Nies and Frank Stephan on complexity of measures as it is found on https://arxiv.org/abs/1902.07871s it is found on https://arxiv.org/abs/1902.07871

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Date/Time : 12 Oct 2022 10:00
Venue : via Zoom
Speaker : Mehtaab Sawhney, MIT

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https://nus-sg.zoom.us/j/85443285113?pwd=eVE5bFk4d01pN2FQbjFzZmtKbnVzQT09

Meeting ID: 854 4328 5113
Passcode: 23571113

Abstract: An n-vertex graph is called C-Ramsey if it has no clique or independent set of size C\log_2 n (i.e., if it has near-optimal Ramsey behavior). In this paper, we study edge-statistics in Ramsey graphs, in particular obtaining very precise control of the distribution of the number of edges in a random vertex subset of a C-Ramsey graph. This brings together two ongoing lines of research: the study of “random-like” properties of Ramsey graphs and the study of small-ball probability for low-degree polynomials of independent random variables.

The proof proceeds via an “additive structure” dichotomy on the degree sequence, and involves a wide range of different tools from Fourier analysis, random matrix theory, the theory of Boolean functions, probabilistic combinatorics, and low-rank approximation. One of the consequences of our result is the resolution of an old conjecture of Erdős and McKay, for which he offered one of his notorious monetary prizes.

Joint w. Matthew Kwan, Ashwin Sah, and Lisa Sauermann.

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Date/Time : 11 Oct 2022 16:00
Venue : S17 #05-11 (SR5)
Speaker : Mahan Maharaj, Tata Institute of Fundamental Research

Abstract: We develop a new orbit equivalence framework for mating Fuchsian groups with polynomial maps, adding to the Sullivan dictionary between Kleinian groups and rational dynamics. A surprising fallout is that topological orbit equivalence rigidity fails for Fuchsian groups. This is joint work with Sabyasachi Mukherjee.

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Date/Time : 07 Oct 2022 14:00
Venue : S17 #05-12 (SR4)
Speaker : Chung-Ru Lee, National University of Singapore

Abstract: One of the main application of the Relative Langlands Program is providing a description of distinguished representation, which itself has profuse interpretations. In this talk series I will introduce a method to study such problem through the comparison of relative trace formulae, where the theory of endoscopy plays a significant role. In particular, the study of representations on unitary groups that are distinguished by an orthogonal subgroup remains mysterious due to the presence of a type N-spherical root, which requires extra caution when dealt with.

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Date/Time : 06 Oct 2022 10:00
Venue : via Zoom
Speaker : Ruqi Zhang, Purdue University

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https://nus-sg.zoom.us/j/9775606531?pwd=cVZ6eTRYS3ZzVUlFNXRuSlhMVjJSUT09

Meeting ID: 977 560 6531
Passcode: 123321

Abstract:  Probabilistic modeling provides a principled framework for learning from data, with the key advantage of offering rigorous solutions for uncertainty quantification. In the era of big and complex data, there is an urgent need for new inference methods in probabilistic modeling to extract information from data effectively and efficiently.

This talk will show how to do theoretically guaranteed scalable and reliable inference for modern machine learning. First, I will introduce a general and theoretically grounded framework to enable fast and asymptotically correct inference, with applications to Metropolis-Hastings and Gibbs sampling. Then, I will highlight the key challenges of probabilistic inference in deep learning, and present a novel approach for fast posterior inference of neural network weights. This method has achieved state-of-the-art results and has been regarded as one of the benchmarks in deep probabilistic modeling.

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Date/Time : 05 Oct 2022 15:00
Venue : S17 #05-12 (SR4)
Speaker : Abdul Basit, Johns Hopkins University

Abstract:  A celebrated conjecture of Tuza says that in any (finite) graph, the minimum size of a cover of triangles by edges is at most twice the maximum size of a set of edge-disjoint triangles. We will discuss some recent results regarding a generalization of this conjecture to hypergraphs which was proposed by Aharoni and Zerbib.

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Date/Time : 05 Oct 2022 17:00
Venue : S17 #04-05 (SR2)
Speaker : Yang Yue, National University of Singapore

Abstract: Yang Yue will talk about his past and concurrent research in Reverse Mathematics and also provide the background of other researchers on the same topic. Please see the abstract on

https://www.comp.nus.edu.sg/~fstephan/logicseminar20221005abs.pdf

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Date/Time : 04 Oct 2022 17:00
Venue : S17 #04-06 (SR1)
Speaker : Sun Rongfeng, National University of Singapore

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https://nus-sg.zoom.us/j/85460997100?pwd=S2FVVXUzSGU0U0tSN3Z4MURVSGhVUT09

Meeting ID: 854 6099 7100
Passcode: 504631

Abstract: The stochastic heat equation (SHE) and the Kardar-Parisi-Zhang (KPZ) equation are singular stochastic partial differential equations, for which robust solution theories have been developed in dimension 1. But in the critical dimension 2 for SHE and KPZ, no robust solution theory exists. I will review joint work with Caravenna and Zygouras on the scaling limit of the 2-dimensional directed polymer model, a space-time discretisation of the SHE, which implies that the 2-dimensional SHE and KPZ undergo a phase transition. Below the critical point, both SHE and KPZ have Gaussian fluctuations. At the critical point, we recently showed that the directed polymer model has a unique limit, which can be interpreted as the solution of the critical 2-dimensional SHE.

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Date/Time : 30 Sep 2022 14:00
Venue : S17 #05-12 (SR4)
Speaker : Chung-Ru Lee, National University of Singapore

Abstract: One of the main application of the Relative Langlands Program is providing a description of distinguished representation, which itself has profuse interpretations. In this talk series I will introduce a method to study such problem through the comparison of relative trace formulae, where the theory of endoscopy plays a significant role. In particular, the study of representations on unitary groups that are distinguished by an orthogonal subgroup remains mysterious due to the presence of a type N-spherical root, which requires extra caution when dealt with.

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