Date/Time : 27 Dec 2019 14:00
Venue : S17 #04-06 SR1
Speaker : Xiaoming Wang, Southern University of Science and Technology

We show that the Principle of Exchange of Stability holds for convection in a layer of fluids overlaying a porous media with proper interface boundary conditions and suitable assumption on the parameters. The physically relevant small Darcy number regime as well as the dependence of the convection on various parameters will be discussed. A theory on the dependence of the depth ratio of the onset of deep convection will be put forth together with supporting numerical evidence. A decoupled uniquely solvable, unconditionally stable numerical scheme for solving the system will be presented as well.

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Date/Time : 26 Dec 2019 16:00
Venue : S17 #05-11 SR5
Speaker : Hu Jingwei, Purdue University

Date/Time:26 Dec 2019 16:00 Venue: S17 #05-11 SR5 Speaker: Hu Jingwei, Purdue University A second-order asymptotic-preserving and positivity-preserving exponential Runge-Kutta method for a class of stiff kinetic equations We introduce a second-order time discretization method for stiff kinetic equations. The method is asymptotic-preserving (AP) — can capture the Euler limit without numerically resolving the small Knudsen number; and positivity-preserving — can preserve the non- negativity of the solution which is a probability density function for arbitrary Knudsen numbers. The method is based on a new formulation of the exponential Runge-Kutta method and can be applied to a large class of stiff kinetic equations including the BGK/ES-BGK equation (relaxation type), the Fokker-Planck equation (diffusion type), and even the full Boltzmann equation (nonlinear integral type). Furthermore, we show that when coupled with suitable spatial discretizations the fully discrete scheme satisfies an entropy-decay property. Various numerical results are provided to demonstrate the theoretical properties of the method. This is joint work with Ruiwen Shu (University of Maryland). Add to calendar: 

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Date/Time : 21 Dec 2019 15:00
Venue : S17 #04-06 SR1
Speaker : Oleg Evnin , Chulalongkorn University

Date/Time:21 Dec 2018 15:00 Venue: S17 #04-06 SR1 Speaker: Oleg Evnin, Chulalongkorn University Large structured matrices and quantum chaos in resonant systems Resonant systems emerge as weakly nonlinear approximations to problems of mathematical physics with highly resonant linearized perturbations, including Bose-Einstein condensates in harmonic traps and dynamics in AdS spacetimes. The classical dynamics within this class of systems can be very rich, ranging from fully integrable to chaotic as one changes the values of the mode coupling coefficients. Despite the complexity of the corresponding classical dynamics, the quantum version turns out to be remarkably simple: the Hamiltonian is block-diagonal in the Fock basis, with all blocks of varying finite sizes. One thus deals with the systematics of eigenvalues of highly structured finite matrices, including limits when these matrices become very large. I’ll report on a recent study of both numerical patterns emerging for the integrable cases, and the spectral statistics, which efficiently distinguishes the special integrable cases from generic (chaotic) points in the parameter space, and discuss a range of potential applications.

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Date/Time : 10 Dec 2019 14:00
Venue : S17 #04-04 SR3
Speaker : Cheng-Chiang Tsai, Stanford University

Date/Time:10 Dec 2019 14:00 Venue: S17 #04-04 SR3 Speaker: Cheng-Chiang Tsai, Stanford University Local Langlands and character sheaves Let G be a connected reductive group and G^{\vee} be its dual group. For example, G=SO_{2n+1} and G^{\vee}=Sp_{2n} the symplectic group on a 2n-dimensional space. The Langlands correspondence can be interpreted as attaching monodromies to representations. Over a local or global field, to certain representation one can attach a Galois representation (or some variant of it), in other words monodromic datum over the field. While local/global Langlands is largely mysterious, over a finite field there is the Deligne-Lusztig theory and theory of character sheaves; to each irreducible representation of G(F_q) or character sheaf on G one can attache a monodromy as a semisimple element in G^{\vee}. This finite field picture is completely established by Lusztig. In this talk, we survey three seemingly unrelated connections between the local picture (in depth-zero case) and the finite field picture, raising new questions and proposing new conjectures. There will be no theorem in this talk. Add to calendar: 

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Date/Time : 09 Dec 2019 15:30
Venue : S17 #05-12 SR4
Speaker : Zhao Lifeng, University of Science and Technology of China

Date/Time:09 Dec 2019 15:30 Venue: S17 #05-12 SR4 Speaker: Zhao Lifeng, University of Science and Technology of China Asymptotic behaviours for energy-subcritical damped Klein-Gordon equations In this talk, we will investigate the long-time behaviour of damped Klein-Gordon equation in the energy subcritical case. In fact, we will establish the soliton resolution for this equation which means that the global bounded solution evolves into the super-position of moving solitons. Moreover, we will give some further information about the resolution. The talk is based on joint works with Ze Li, Raphael Cote, Yvan Martel and Xu Yuan. Add to calendar: 

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Date/Time : 02 Dec 2019 17:00
Venue : S17 #06-11
Speaker : Rupert Hoelzl, University of the Bundeswehr, Munich

Date/Time:02 Dec 2019 17:00 Venue: S17 #06-11 Speaker: Rupert Hoelzl, University of the Bundeswehr, Munich Randomness for computable measures and complexity We study the possible growth rates of the Kolmogorov complexity of initial segments of sequences that are random with respect to some computable measure on the Cantor Space, the so-called proper sequences. Our main results are as follows: (1) We show that the initial segment complexity of a proper sequence X is bounded from below by a computable function (that is, X is complex) if and only if X is random with respect to some computable, continuous measure. (2) We prove that a uniform version of the previous result fails to hold: there is a family of complex sequences that are random with respect to a single computable measure such that for every computable, continuous measure mu, some sequence in this family fails to be random with respect to mu. (3) We show that there are proper sequences with extremely slow-growing initial segment complexity, that is, there is a proper sequence the initial segment complexity of which is infinitely often below every computable function, and even a proper sequence the initial segment complexity of which is dominated by all computable functions. (4) We prove various facts about the Turing degrees of such sequences and show that they are useful in the study of certain classes of pathological measures on the Cantor Space, namely diminutive measures and trivial measures. Add to calendar: 

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Date/Time : 22 Nov 2019 14:00
Venue : S17 #04-04 SR3
Speaker : Brice Loustau, TU Darmstat

Date/Time:22 Nov 2019 14:00 Venue: S17 #04-04 SR3 Speaker: Brice Loustau , TU Darmstat Computing harmonic maps between Riemannian manifolds The theory of harmonic maps between Riemannian manifolds goes back to the foundational work of Eells-Sampson and Hartman. Using the heat flow method, i.e. the gradient flow for the energy functional, they showed existence and uniqueness of harmonic maps between compact Riemannian manifolds when the target has negative sectional curvature. In order to compute such harmonic maps effectively, we discretize the theory by introducing meshes of the domain manifold, which consist of a geodesic triangulation with vertex and edge weights. By studying the convexity properties of the energy functional, we show that the discrete heat flow method converges to unique discrete harmonic maps. Moreover, under suitable assumptions, the discrete theory converges back to the smooth theory when taking finer and finer meshes. In particular, the smooth harmonic map can be obtained as the limit of discrete harmonic maps, equivalently as the double limit of the discrete heat flow when iterating both the time and space discretization steps. Time permits, we will also discuss center of mass methods to compute harmonic maps. We feature a concrete illustration of these methods withHarmony, a computer software with a graphical user interface that we developed in C++, whose main functionality is to numerically compute and display equivariant harmonic maps between hyperbolic disks. Add to calendar: 

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Date/Time : 21 Nov 2019 10:00
Venue : S17 #04-06 SR1
Speaker : Yao Cheng, Institute of Mathematics, Academia Sinica

Date/Time:21 Nov 2019 10:00 Venue: S17 #04-06 SR1 Speaker: Yao Cheng, Institute of Mathematics, Academia Sinica On Applications of Spherical Functions on Spherical Varieties and Integral Representations of L-functions This is the last talk of a series of four talks on the discussion of the papers [Sak08], [Sak13] and [Sak12]. The present talk consists of two parts. In the first part of this talk I will first briefly review some results in the previous talks and then discuss [Sak13, Part 3] on applications of the explicit formulae for spherical functions on spherical varieties. In the second part of this talk I will give an overview of the paper [Sak12] with emphasis on section 3 and section 4 which I hope it can be served as an introduction to that paper. References [Sak08] Yiannis Sakellaridis. On the unramified spectrum of spherical varieties over p-adic fields. Compositio Mathematica, 144(4):978–1016, 2008. [Sak12] Yiannis Sakellaridis. Spherical varieties and integral representations of L-functions . Algebra number theory, 6(4):611–667, 2012. [Sak13] Yiannis Sakellaridis. Spherical functions on spherical varieties. American Journal of Mathematics, 135(5):1291–1381, 2013. Add to calendar: 

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Date/Time : 21 Nov 2019 10:00
Venue : S17 #04-06 SR1
Speaker : Yao Cheng, Institute of Mathematics, Academia Sinica

This is the last talk of a series of four talks on the discussion of the papers [Sak08], [Sak13] and [Sak12]. The present talk consists of two parts. In the first part of this talk I will first briefly review some results in the previous talks and then discuss [Sak13, Part 3] on applications of the explicit formulae for spherical functions on spherical varieties. In the second part of this talk I will give an overview of the paper [Sak12] with emphasis on section 3 and section 4 which I hope it can be served as an introduction to that paper. References [Sak08] Yiannis Sakellaridis. On the unramified spectrum of spherical varieties over p-adic fields. Compositio Mathematica, 144(4):978–1016, 2008. [Sak12] Yiannis Sakellaridis. Spherical varieties and integral representations of L-functions . Algebra number theory, 6(4):611–667, 2012. [Sak13] Yiannis Sakellaridis. Spherical functions on spherical varieties. American Journal of Mathematics, 135(5):1291–1381, 2013.  

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