Date/Time : 29 Oct 2020 09:00
Venue : via Zoom
Speaker : Charlotte Chan, MIT

Join Zoom Meeting https://nus-sg.zoom.us/j/91964791213?pwd=ZFlvbVdySWNlL2NpNzJXSnlSOUtxQT09 Meeting ID: 919 6479 1213 Password: 006362 Abstract:  Deligne–Lusztig varieties are subvarieties of flag varieties whose cohomology encodes the representations of reductive groups over finite fields. These give rise to so-called “depth-zero” supercuspidal representations of p-adic groups. In this talk, we discuss geometric constructions of positive depth supercuspidal representations and the implications of such realizations towards the Langlands program. This is partially based on joint work with Alexander Ivanov and joint work with Masao Oi.

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Date/Time : 28 Oct 2020 17:00
Venue : via Zoom
Speaker : Liao Yuke, National University of Singapore

Join Zoom Meeting https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? Abstract:  TTE-computable is one of the major definitions of computable real functions. We focus on a generalisation of TTE  and check the basic cases of computability of Julia sets. We prove quadratic polynomials with Siegel disc incomputable in TTE is still incomputable in generalisation.

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Date/Time : 28 Oct 2020 16:00
Venue : via Zoom
Speaker : Lukas Einkemmer, University of Innsbruck

Join Zoom Meeting https://nus-sg.zoom.us/j/84355509004?pwd=ZEpxWEFMVjd2d0hDamliVUMvY1ozdz09 Meeting ID: 843 5550 9004 Password: 357874 Abstract: Computational fluid dynamics has become an extremely successful framework to understand a range of natural phenomena. Despite these successes, it is increasingly realized that many phenomena in both space and laboratory plasmas require a kinetic description. However, kinetic models come with a range of computational challenges that have to be addressed before these simulations can be routinely employed. The most challenging aspect is certainly the up to six-dimensional phase space. A promising approach to break the so-called curse of dimensionality are low-rank techniques. Contrary to many other complexity reduction methods, such as sparse grids or particle methods, low-rank techniques are able to resolve the small structures that are inherent in such problems. In this talk, we will discuss some of the algorithmic, analytic, and computational advances that have been made in the last few years and explain how this will enable the large scale simulation of kinetic equations using dynamical low-rank approximation.

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Date/Time : 27 Oct 2020 17:00
Venue : via Zoom
Speaker : Andreas Höring, Université de Nice - Sophia Antipolis, France

Join Zoom Meeting https://nus-sg.zoom.us/j/87501413614?pwd=MXBqd1ZxVS9jRlBUcmVLOTdIMklTQT09 Meeting ID: 875 0141 3614 Password: 804632 Abstract: While the canonical bundle is the central object of the minimal model program and has been studied by many authors, the positivity of the cotangent bundle is much more elusive. In this talk I will show how foliation theory leads to renewed interest in the cotangent bundle and give some recent results for varieties with trivial canonical class and elliptic surfaces.

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Date/Time : 23 Oct 2020 09:00
Venue : via Zoom
Speaker : Georgios Moschidis, University of California, Berkeley

Join Zoom Meeting Meeting ID: 833 7724 5924 Password: 105581 In the presence of a negative cosmological constant, the Einstein equations admit solutions which are asymptotically anti-de Sitter. These solutions, which play a key role in the putative AdS/CFT correspondence in high energy physics, possess a timelike conformal boundary at infinity, which can act as a mirror for gravitational perturbations. The resulting confinement of the gravitational evolution is believed to lead to the emergence of weakly turbulent phenomena: According to the AdS instability conjecture, under reflecting conditions at conformal infinity, arbitrarily small perturbations of anti-de Sitter spacetime are expected to collapse into black holes after sufficiently long time.  During the last decade, a large number of numerical and heuristic works have been dedicated to understanding the dynamics of the Einstein equations in a neighborhood of anti-de Sitter spacetime. In this talk, I will discuss the complex picture revealed by these works. I will then proceed to present a rigorous proof of the AdS instability conjecture in the setting of the spherically symmetric Einstein–scalar field system.

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Date/Time : 22 Oct 2020 10:00
Venue : via Zoom
Speaker : Jonathan Wang, MIT

Join Zoom Meeting https://nus-sg.zoom.us/j/92431908138?pwd=NGs4eWRENWRERWlJRUZIUDdyVFVOUT09 Meeting ID: 924 3190 8138 Password: 865981 Abstract:  Part of the aim of the relative Langlands program is to produce new integral representations of automorphic L-functions in order to study their analytic properties. The program is still very much in progress, but generalized Ichino-Ikeda formulas of Sakellaridis-Venkatesh relate the global problem to certain problems in local harmonic analysis on spherical varieties. I will explain how we can use techniques from geometric Langlands to compute “new” integrals which give special values of unramified local L-functions over a local function field. Our results also give new integral representations of L-functions (in a right half plane) over global function fields when the integral “unfolds”. This is joint work with Yiannis Sakellaridis.

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Date/Time : 21 Oct 2020 14:00
Venue : via Zoom
Speaker : Jia Jia, National University of Singapore

Join Zoom Meeting https://nus-sg.zoom.us/j/83889134319?pwd=SVA4YURXYlZtSUVQSUFzWFB3Mlg2Zz09 Meeting ID: 838 8913 4319 Password: 067273 Abstract:  In this talk, we will give a structure theorem of endomorphisms of normal projective surfaces via the equivariant minimal model program. Combining with some local dynamics and known results, we will give an application of the main theorem to Zariski dense orbit property in dimension two. This is joint work with Doctor Junyi Xie and Professor De-Qi Zhang.

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Date/Time : 21 Oct 2020 16:00
Venue : via Zoom
Speaker : Milan Korda, LAAS-CNRS

Join Zoom Meeting https://nus-sg.zoom.us/j/82236914659?pwd=ZzgyeDU5SjJ1bFRNd1lHVURlV2wzQT09 Meeting ID: 822 3691 4659 Password: 083341 Abstract: This talk will give an overview of the applications of the moment-sum-of-squares hierarchy in the fields of dynamical systems and control. We will explain how a number of problems such as optimal control, region of attraction or invariant set computation can be cast as linear programming problems in the space of Borel measures and how these linear programs can be approximated using the moment-sum-of-squares hierarchy of semidefinite programming problems with guaranteed convergence. The talk will finish by describing how sparsity of the underlying dynamics can be exploited, leading to a decoupled computation, thereby allowing for a significant reduction in computation time without sacrificing convergence guarantees.  

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Date/Time : 21 Oct 2020 17:00
Venue : via Zoom
Speaker : Rupert Hoelzl, Universitaet der Bundeswehr Muenchen

Join Zoom Meeting https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? Abstract:  We introduce Monte Carlo computability as a probabilistic concept of computability on infinite objects and prove that Monte Carlo computable functions are closed under composition. We then mutually separate the following classes of functions from each other: the class of multi-valued functions that are non-deterministically computable, that of Las Vegas computable functions, and that of Monte Carlo computable functions. We give natural examples of computational problems witnessing these separations. As a specific problem which is Monte Carlo computable but neither Las Vegas computable nor non-deterministically computable, we study the problem of sorting infinite sequences that was recently introduced by Neumann and Pauly. Their results allow us to draw conclusions about the relation between algebraic models and Monte Carlo computability.

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