Date/Time : 17 Aug 2023 13:00
Venue : S17 #04-04 (SR3)
Speaker : Wang Fei, Shanghai Jiaotong University.

This paper concerns the existence of global weak solutions {\it \`a la Leray} for compressible Navier–Stokes–Fourier system with periodic boundary conditions and the truncated virial pressure law which is assumed to be thermodynamically unstable. More precisely, the main novelty is that the pressure law is not assumed to be monotone with respect to the density. This provides the first global weak solutions result for the compressible Navier-Stokes-Fourier system with such kind of pressure law which is strongly used as a generalization of the perfect gas law. The paper is based on a new construction of approximate solutions through an iterative scheme and fixed point procedure which could be very helpful to design efficient numerical schemes. Note that our method involves the recent paper by the authors published in Nonlinearity (2021) for the compactness of the density when the temperature is given.

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Date/Time : 16 Aug 2023 15:00
Venue : S17 #04-04 (SR3)
Speaker : Chengbo Wang, Zhejiang University

In this talk, I will present a sharp local well-posedness result for spherically symmetric solutions to quasilinear wave equations with rough initial data, when the spatial dimension is three or higher. Our approach is based on Morawetz type local energy estimates with fractional regularity for linear wave equations with variable C^1 coefficients, which rely on multiplier method, weighted Littlewood-Paley theory, duality and interpolation. Together with weighted linear and nonlinear estimates (including weighted trace estimates, Hardy’s inequality, fractional chain rule and fractional Leibniz rule) which are adapted for the problem, the well-posed result is proved by iteration. In addition, our argument yields almost global existence for n=3 and global existence for dimension 4 and higher, when the initial data are small, spherically symmetric with almost critical Sobolev regularity.

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Date/Time : 16 Aug 2023 16:10
Venue : S17 #04-04 (SR3)
Speaker : Naqing Xie, Fudan University

We discuss a uniqueness result of the electro-vacuum Einstein-Maxwell equations near the null infinity. This talk is based on a recent joint work with Xiaokai He (Hunan First Normal, Changsha) and Xiaoning Wu (AMSS, CAS, Beijing).

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Date/Time : 16 Aug 2023 14:00
Venue : S17 #04-05 (SR2)
Speaker : Yifan Jing, University of Oxford

Let G be a connected compact group equipped with the normalised Haar measure μ. Our first result shows that given α, β > 0, there is a constant c = c(α, β) > 0 such that for any compact sets A, B ⊆ G with αμ(B)≥μ(A)≥μ(B) and μ(A)+μ(B)≤1−β, there exist b_1, …, b_c∈ B such that μ(A · {b_1,…,b_c}) ≥ μ(A) + μ(B). A special case of this, that is, when G is the d-dimensional torus confirms a recent conjecture of Bollobas, Leader and Tiba.

We also prove a quantitatively stronger version of such a result in the discrete setting of d -dimensional Euclidean space. Thus, given d ∈ N, we show that there exists c = c(d) > 0 such that for any finite, non-empty set A ⊆ R^d which is not contained in a translate of a hyperplane, one can find a_1,…,a_c∈ A satisfying
|A + {a_1, . . . , a_c}| ≥ (d + 1)|A| − O_d(1). The main term here is optimal and recovers the bounds given by Freiman’s lemma up to the O_d(1) error term.

(Joint with Akshat Mudgal)

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Date/Time : 08 Aug 2023 15:00
Venue : S17 #05-12 (SR4)
Speaker : Barbara Wohlmuth, Technical University of Munich

In this talk, we discuss several aspects of time‐fractional differential operators. The non‐local nature of the operator is challenging from a theoretical and algorithmic point of view but allows us to account for memory effects in the mathematical model. We consider a wide class of time‐fractional PDE models, including gradient flow, viscoelasticity, random field generators, and polymeric fluids. Of special interest is the equivalence of the time fractional gradient flow model with an integer order system in a higher dimension. Exploiting this equivalence allows us to construct efficient algorithms for time fractional PDEs. Replacing the kernel by a finite sum of exponentials transforms the non‐local PDE into an integer‐order system for the modes. To balance the discretization error in time and space with the kernel approximation error, the number of modes has to grow logarithmically. However, we observe numerically that the number of modes is very moderate if the finite sum of exponentials is based on a rational approximation of the kernel function. In this talk, we present theoretical existence results, algorithmic aspects and show several applications in which fractional operators play an important role. Numerical examples illustrate the large flexibility of the proposed techniques.

Joint work with Marvin Fritz (RICAM, Austria), Brendan Keith (Brown University, USA), Ustim Khristenko (Safran, France) and Endre Süli (University of Oxford, UK).

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Date/Time : 03 Aug 2023 14:30
Venue : S17 #04-05 (SR2)
Speaker : Dinesh Thakur, University of Rochester

Without assuming any background, we will explain how some basic techniques and results from computer science help us in understanding the nature of some naturally occurring numbers.

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Date/Time : 03 Aug 2023 16:00
Venue : S17 #04-05 (SR2)
Speaker : Wong Tian An, University of Michigan, Deerfield

Following Langlands’ original Beyond Endoscopy proposal, Arthur has outlined two refinements of the stable trace formula: the r-trace formula and the primitive trace formula. Spectrally, the first should detect specific functorial transfers from smaller groups, while the second should consist of certain primitive automorphic forms. In this talk, I will give a friendly introduction to these ideas. Then I will present a framework for establishing each of them separately, and report on some progress along these lines.

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Date/Time : 03 Aug 2023 16:00
Venue : S17 #04-06 (SR1)
Speaker : Aijun An, York University

Generating revenue has been a significant issue for the news industry over the past decade. Due to the wide availability of numerous online news media, readers have many choices in selecting the news source. In a collaborative project with The Globe and Mail, we address the problem of user acquisition and engagement and investigate how data mining techniques can be used to solve the problem. In this talk, I will present two pieces of work in this project. One is a time-aware user subscription prediction model and the other is an adaptive paywall model. The goal of the time-aware user subscription prediction model is to identify potential subscribers and predict their prediction time so that effective targeted marketing can be used. We propose to learn a probabilistic model from user click streams that can predict the probability that a user subscribes the newspaper and estimate their subscription time. In the second piece of work, we address the problem of previous fixed paywall models that offer a non-subscribed reader a fixed number of free articles in a period of time. Such models treat all readers equally and do not consider the potential of a reader in becoming a subscriber. We propose an adaptive paywall model that considers the user’s browsing history in making paywall decisions. It provides potential subscribers with more free articles to engage them. I will present the models, the experimental results and the impact of our work.

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Date/Time : 03 Aug 2023 14:00
Venue : S17 #04-06 (SR1)
Speaker : Lu Jian, South China Normal University

Minkowski type problems arise from modern convex geometry. In the smooth case, they are usually equivalent to solving a class of Monge-Ampere type equations defined on the unit hypersphere. These equations could be degenerate or singular in different conditions. We will talk about some new results on the existence, uniqueness, and regularity of solutions to several Minkowski type problems.

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