Date/Time : 12 Jan 2022 09:00
Venue : via Zoom
Speaker : Cheng Mao, Georgia Tech

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https://nus-sg.zoom.us/j/85910065038?pwd=ay9nT0hzR2ROeUs4U3d5dTBoMGNBdz09

Meeting ID: 859 1006 5038
Password: 753065

Abstract: Finding latent structures in networks is an important task in many fields of science and engineering.  For a variety of problems, the task can be formulated as inferring a latent permutation of vertices of a network from noisy data. Problems in this class are often computationally infeasible in the worst case due to the combinatorial nature of permutations, so statistical methods are essential for inference in large-scale networks. This talk will provide an overview of two problems: ranking items from comparisons and matching correlated networks. For each problem, I will introduce an average-case model and the associated task of learning a latent permutation. Then I will discuss recent development of efficient algorithms that come with theoretical guarantees.

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Date/Time : 16 Dec 2021 09:00
Venue : via Zoom
Speaker : Guillaume Remy, Columbia University

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https://nus-sg.zoom.us/j/82279401256?pwd=ZTg0M3dueXVNaUUrMzlIcTlsUUlLQT09

Meeting ID: 822 7940 1256
Passcode: 044547

Abstract: Liouville theory is a fundamental example of a conformal field theory (CFT) first introduced in physics by A. Polyakov to describe a canonical random 2d surface. In recent years it has been rigorously studied using probabilistic techniques. In this talk we will take a look at the integrable structure of Liouville CFT on a domain with boundary by proving exact formulas for its correlation functions. We will also discuss the connection with the conformal blocks of CFT which are fundamental functions determined by conformal invariance that underlie the exact solvability of CFT. Based on joint works with Morris Ang, Promit Ghosal, Xin Sun, Yi Sun and Tunan Zhu.

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Date/Time : 15 Dec 2021 09:00
Venue : via Zoom
Speaker : Souvik Dhara, MIT

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https://nus-sg.zoom.us/j/85163689192?pwd=cXdBOE9oa2NCU2tPZUFlMWZTV2s4Zz09

Meeting ID: 851 6368 9192
Passcode: 322049

Abstract: In this talk, I will discuss some recent challenges arising in the study of large and complex networks. Over the last decades, improved data collection methods have significantly increased the availability of empirical data on networks, and the study of networks has become relevant across multiple disciplines such as biology, computer science, physics, and statistics. This has stimulated enormous activity in the mathematics research community to understand (1) local and global structure of networks, (2) dynamic processes on them, and (3) algorithms to discover hidden patterns in networks. In this talk, I will discuss my research on the above three topics in the context of percolation process, graph limits, and community detection on networks.

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Date/Time : 08 Dec 2021 09:00
Venue : via Zoom
Speaker : Konstantin Matetski, Columbia University

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https://nus-sg.zoom.us/j/89132660362?pwd=SHB5bkRwVU9UUDRKVUd0UzY0Vk02QT09

Meeting ID: 891 3266 0362
Passcode: 880312

The KPZ universality class includes random growing interfaces, which, after rescaling, are conjectured to converge to the KPZ fixed point. The latter is a Markov process, which has been characterized through the exact solution of TASEP, a particular model in the class. The KPZ equation plays a special role and is conjectured to be the only model connecting the Edwards-Wilkinson (Gaussian) and the KPZ fixed points. In the talk, I will introduce the KPZ fixed point and review recent work on the KPZ universality done by myself and my collaborators.

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Date/Time : 01 Dec 2021 16:00
Venue : via Zoom
Speaker : Pierre-Francois Rodriguez, Imperial College, London

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https://nus-sg.zoom.us/j/85694125031?pwd=eGJuMWk5SXRCS2hWc1JITXpRWmdRUT09

Meeting ID: 856 9412 5031
Passcode: 918464

Abstract: I will report on recent progress regarding the near-critical behavior of certain statistical physics models in dimension 3. Our results deal with the critical scaling exponents associated to the second-order phase transition for two percolation problems involving the Gaussian free field in 3D. In one case, they determine a unique “fixed point” corresponding to the transition, which is proved to obey one of several scaling relations. Such laws are classically conjectured to hold by physicists on the grounds of a corresponding scaling ansatz.

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Date/Time : 24 Nov 2021 09:00
Venue : via Zoom
Speaker : Yair Shenfeld, MIT

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https://nus-sg.zoom.us/j/87967891890?pwd=R1k4L2FLUGZKVURjd0ZiU0h5L013dz09

Meeting ID: 879 6789 1890
Passcode: 176920

Abstract: What does a ball and a half space have in common? The former is the unique shape which minimizes surface area among all shapes of equal Euclidean volume, while the latter solves the analogous optimization problem for Gaussian volume. These shapes are examples of extremal structures and they play a prominent role in geometric and
probabilistic phenomena: from the shape of water droplets to concentration of measure.

Once we go deeper into the world of extremal structures, we find that they seem hopelessly complex, while permeating mathematics, ranging from probability to combinations to algebraic geometry. In fact, the
characterization of some of these structures is only conjectural, while for others, not even conjectures exist. I will talk about how we resolve several of these conjectures using stochastic, analytic, and geometric tools.

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Date/Time : 17 Jan 2020 14:00
Venue : S16 #05-98
Speaker : Xinyi Li , Peiking University

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Date/Time : 16 Jan 2020 14:00
Venue : S16 #05-98
Speaker : Xinyi Li , Peiking University

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Date/Time : 15 Jan 2020 14:00
Venue : S16 #05-98
Speaker : Xinyyi Li , Peiking University

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