1. Prof. David Pointcheval, ENS Paris

Title: Privacy-Preserving Data Analytics

Abstract: Big data and data lakes are gold mines for data scientists with tons of applications to finance, medicine, economics, etc. But most of these data are quite sensitive and cannot be widely distributed or even just used without strong protection. One is thus facing the huge dilemma of having to make the choice between highly valuable analytics and privacy guarantees. Cryptography has developed several primitives to address these issues. During this talk, we will present some of the recent cryptographic techniques, which include Fully Homomorphic Encryption, Functional Encryption, and Secure Multi-Party Computation, to perform computations on data, without revealing them. Applications then cover externalized computations, federated learning, blind inference, private analytics, etc.

Lecture Notes: here

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2. Prof. Nguyen Huu Du, VNU University of Science

Title: Asymptotic Behavior Of Solutions Of Stochastic Differential Equations And Applications

Abstract: This talk deals with some new results concerning to the dynamic behavior of solutions for stochastic differential equations perurbed simultaneously by colour noise and white noise.

dx = a(ξ(t); x)dt + b(ξ(t); x)dW; x(0) 2 Rd;

where (ξ(t)) is a Markov process valued in a finite set S; W is a Brownian motion and a; b are functions defined on S × Rd +.
This equation can be used to describe the evolution of eco-systems, epidemic models as well as the development of a financial markets under the random environment. The Markov noise ξ(t) can be considered as a factor which switches environment conditions meanwhile W are unpredictable perturbations.
We are interested in describing !-limit sets, attractors of the system; giving sufficient and almost necessary conditions to the permanence or extinction of solutions by constructing a threshold. The ergodicity of systems has been studied in case it is permanent.
Some applications of these results to consider the evolutions of eco-systems or disease spread are concerned with.

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3. Prof. John R. Birge, The University of Chicago Booth School of Business

Title: The use and value of operations research in pandemic modeling and control

Abstract: The COVID-19 pandemic has led to developments in many fields. This talk will focus on the effects of the use of tools for optimal decision making from operations research. In particular, the talk will describe advances made in disease modeling, control through non-pharmaceutical interventions, vaccine distribution policy, and overall cost-benefit analysis.

Reference: here

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4. Prof. Oscar Garcia-Prada, Institute of Mathematical Sciences ( Madrid)

Title: Non-abelian Hodge theory and higher Teichmüller spaces

Abstract: Non-abelian Hodge theory relates representations of the fundamental group of a compact Riemann surface X into a Lie group G with holomorphic objects on X known as Higgs bundles. These objects, introduced by Hitchin around 35 years ago, play an important role in Ngô's proof of the fundamental lemma. Starting with the case in which G is the circle, and the 19th century Abel-Jacobi's theory, we will move to the case of G=SL(2,R) and the relation to Teichmüller theory. We will then explain how, using Higgs bundles, one can construct generalizations of the classical Teichmüller space for certain higher rank Lie groups.

Lecture Notes: here

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5. Prof. Phan Van Tuoc, University of Tennessee – Knoxville

Title: Recent results on regularity theory for linear parabolic equations with singular and degenerate coefficients

Abstract: We discuss recent results and developments on regularity estimates for linear parabolic equations singular and degenerate coefficients. The considered equations include the extensional equations arising in the study of fractional Laplace equations or fractional heat equations, and a class of degenerate viscous Hamilton-Jacobi equations. The boundary conditions are either homogeneous Dirichlet or conormal one. Generic weighted Sobolev spaces are found in which existence, uniqueness, and regularity estimates of solutions are proved. The main feature in our study is that the coefficients may not be in the A_2 class of Muckenhoupt weights as commonly studied in the literature. The talk is based on several recent papers that are the joint work with Hongjie Dong (Brown University) and with Hung Vinh Tran (University of Wisconsin Madison).

Lecture Notes: here

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