Date/Time : 10 Feb 2023 14:00
Venue : S17 #04-06 (SR1)
Speaker : Håkan Hedenmalm, KTH Royal Institute of Technology

Fourier series is a classical method to expand periodic functions on the line, with roots in the theory of heat conduction. If we want to expand non-periodic functions on the line, we are told to use the Fourier transform instead and accept that the result is a distribution. In 2011, Hedenmalm and Montes-Rodriguez suggested an alternative expansion. It now turns out that this expansion exists uniquely and that it connects with the Fourier interpolation of Radchenko and Viazovska (2019). We will explain how the hyperbolic Fourier series is very natural and corresponds to a “low temperature” expansion where automorphic forms and theta functions are examples from a high temperature regime where nonuniqueness holds.

This reports on joint work (with Viazovska, Radchenko, Bakan, Montes-Rodriguez).

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Date/Time : 09 Feb 2023 16:00
Venue : via Zoom
Speaker : Jing Yifan, University of Oxford

The celebrated Brunn-Minkowski inequality states that for compact subsets A and B of R^d, m(A+B)^{1/d} \geq m(A)^{1/d} + m(B)^{1/d}, where m() is the Lebesgue measure. It is a cornerstone in convex geometry and plays an important role in other areas of mathematics, particularly combinatorics. In this talk, I will present a generalization of the Brunn-Minkowski inequality in non-abelian groups. More refined phenomena for compact and discrete groups will also be discussed. If time permits I will mention some applications of these results.

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Date/Time : 08 Feb 2023 17:00
Venue : via Zoom
Speaker : Will Johnson, Fudan University

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https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09

Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3

Is every NIP integral domain a henselian local ring? In this talk, I will give evidence for this conjecture, sketching why it holds in the positive characteristic case and the finite dp-rank case. I will also discuss how this “generalized henselianity conjecture” is related to the standard conjectures on NIP fields and valued fields. For example, the henselianity conjecture for NIP valued fields implies the generalized henselianity conjecture for Noetherian NIP integral domains. Lastly I will discuss how this conjecture fits into the general problem of classifying NIP fields and NIP commutative rings. For example, it implies that NIP fields with definable field topologies must be ample/large in the sense of Pop, and NIP commutative rings must be finite products of henselian local rings.

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Date/Time : 08 Feb 2023 15:30
Venue : S17 #04-04 (SR3)
Speaker : Fabrizio Bianchi, University of Lille

We show that every Hölder observable satisfies the Central Limit Theorem (CLT) with respect to the measure of maximal entropy of every complex Hénon map. The proof is based on a general criterion to ensure the validity of the CLT, valid for abstract measurable dynamical systems. This is a joint work with Tien-Cuong Dinh.

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Date/Time : 07 Feb 2023 10:00
Venue : S17 #04-06 (SR1)
Speaker : Zhang Zhe, Georgia Institute of Technology

The modern big data infrastructure has drastically transformed the computation landscape of operations research. Novel decision-making strategies are imperative for handling the sheer volume and the exceptional dimension of the data we are generating. To store and process such data, advanced computing networks, from cloud computing to edge computing, is ubiquitous. Nevertheless, the fundamental objective of operations research remains unchanged: to provide robust and optimal decision-making tools to ensure safe and consistent outcomes. Risk-averse optimization is an essential framework to achieve this goal. However, while distributed optimization without risk consideration has been thoroughly studied, our understanding of distributed risk-averse optimization is limited. In this talk, we will discuss our recent progress that helps to shed light on the subject. Specifically, for a distributed network with a computationally powerful central server, we introduce novel distributed optimization methods to solve risk-averse optimization with the same communication complexity as that of risk-neutral optimization. Extensions to the decentralized network setting and the fully stochastic setting will also be discussed.

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Date/Time : 02 Feb 2023 17:00
Venue : S17 #04-06 (SR1)
Speaker : Jan Sbierski, University of Edinburgh

The strong cosmic censorship conjecture roughly states that Einstein’s theory of general relativity is generically a deterministic theory. Using the language of PDEs this can be paraphrased as stating that generically global uniqueness holds for the initial value problem for the Einstein equations. I will start out this talk by giving a non-technical introduction to this conjecture restricted to the interior of rotating black holes. Moreover, I will discuss the analytic as well as the geometric aspects of the conjecture and outline its current state.

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Date/Time : 01 Feb 2023 09:00
Venue : via Zoom
Speaker : Yair Shenfeld, MIT

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https://nus-sg.zoom.us/j/82637054452?pwd=ZkpEVllwN3g1YUNYRHIwMXF3TmUzdz09

Meeting ID: 826 3705 4452
Passcode: 332211

It is classical that the ball is the unique shape which minimizes surface area for a given fixed volume. But what if we want to minimize surface area where in addition to fixing the volume we also fix the average width of the shape? This question turns out to be a very special case of long-standing conjectures at the heart of convex geometry. In the first part of the talk I will explain these conjectures and the significant progress that we made towards their resolutions. In the second part of the talk I will explain how these geometric problems can provide information on problems in combinatorics, which led us to the discovery of some surprising results in the theory of partially ordered sets.

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Date/Time : 01 Feb 2023 17:00
Venue : S17 #05-11 (SR5)
Speaker : Yu Liang, Nanjing University

I shall present some recent results in set theory which are based on proof methods and results from recursion theory.

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Date/Time : 30 Jan 2023 10:00
Venue : S17 #04-05 (SR2)
Speaker : Eric Chen, Princeton University

In the recent framework proposed by Ben-Zvi–Sakellaridis–Venkatesh, automorphic periods ought to, very roughly speaking, come in Langlands dual pairs. I will give a short introduction of this prediction and motivate the need to consider certain singular automorphic periods. In particular, I will present an example in joint work with Akshay Venkatesh, where we establish duality using a generalization of L-functions.

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