Date/Time : 14 Sep 2022 14:00
Venue : S17 #04-04 (SR3)
Speaker : Ta Duy-Hoang, ENS Lyon

Abstract: There is a large and important collection of Ramsey-type combinatorial problems, closely related to central problems in complexity theory, that can be formulated in terms of the asymptotic growth of the size of the maximum independent sets in powers of a fixed small (directed or undirected) hypergraph, also called the Shannon capacity. An important instance of this is the corner problem studied in the context of multiparty communication complexity in the Number On the Forehead (NOF) model (and other important instances are the cap set problem in additive combinatorics and the USP capacity problem in the complexity theory of matrix multiplication).

We introduce a general method for lower bounding the Shannon capacity of hypergraphs via combinatorial degenerations, a combinatorial kind of “approximation” of subgraphs that originates from the study of matrix multiplication in algebraic complexity theory (and which plays an important role there) but which we use in a novel way. This allows us to obtain the best-known lower bounds for multiple combinatorial problems, including the corner problem and its application in communication complexity.

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Date/Time : 14 Sep 2022 17:00
Venue : S17 #04-05 (SR2)
Speaker : Ammar Fathin Sabili, National University of Singapore

Abstract: We introduce and study a new computation model called an Alternating Automatic Register Machine (AARM). An AARM possesses a basic features of a conventional register machine and an alternating Turing machine, but can carry out computations using bounded automatic relations in a single step. One particular finding is that an AARM can recognize some NP-complete problems, including CNF-SAT (using a particular encoding), in logstar n + O(1) steps. Furthermore, we also show that padding the input with a polynomial-size string will recognize polynomial hierarchy in also logstar n + O(1) steps. These results illustrate the power of alternation when combined with computations involving automatic relations.

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Date/Time : 14 Sep 2022 16:00
Venue : S17 #06-11 (SR6)
Speaker : Zhang Huangwei, National University of Singapore

Abstract: High-fidelity numerical simulations with detailed chemistry have played significant roles not only in revealing fundamental physicochemical processes in combustion transient, but also designing next-generation propulsion systems. In this talk, an overview of development history and the state of the art of numerical combustion will be first provided. Then the hybrid Eulerian-Lagrangian method with two-way coupling is used in our studies for modelling detonation wave dynamics in two-phase gas-droplet mixture and the numerical implementations based on the open-source CFD package OpenFOAM will be introduced. We have studied hydrogen detonation transmission in fine water sprays based on the one-dimensional and two-dimensional problems. It is found that the existence of the dispersed droplets leads to varied detonation propagation modes depending on the droplet mass loading. Meanwhile, two-phase interfacial instability occurs due to the Kelvin–Helmholtz instability, arising from the pronounced velocity difference across the spray cloud boundary. Moreover, detonative combustion based on liquid n-heptane fuel is also studied. The results show that the fuel droplet heating and evaporation considerably affect detonation propagation speed, composite structure of shock and reaction front, as well as unsteady phenomena.

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Date/Time : 13 Sep 2022 16:00
Venue : via Zoom
Speaker : Piyush Srivastava, Tata Institute of Fundamental Research

Join Zoom Meeting
https://nus-sg.zoom.us/j/83199111482?pwd=L09Yd054dDNTbDBpRkNtc0tmQnk5Zz09

Meeting ID: 831 9911 1482
Passcode: 569991

Abstract: This series of lectures will survey various applications to algorithms of a collection of techniques that are broadly referred to as “geometry of polynomials”. Specific examples include:

1) Real stable polynomials and constructions of Ramanujan expanders
2) Lee-Yang theory and deterministic “approximate counting” algorithms”
3) Lorentzian or “strongly log concave” polynomials and applications to sampling

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Date/Time : 09 Sep 2022 10:00
Venue : S17 #05-11 (SR5)
Speaker : Anirban Basak, International Centre for Theoretical Sciences

Abstract:  The classical theory of large deviations deals with precise estimates on the probabilities of rare events (e.g. normalized sum of independent and identically distributed random variables exceed its expectation by a constant factor greater than one) involving linear functions of independent random variables. Beyond the linear setting, possibly the simplest non-trivial interesting question is the large deviations of the triangle counts in Erd\H{o}s-R\’enyi graphs. In the past fifteen years there has been a lot of work in this direction. In this talk we will discuss some of them, focusing mainly on the large deviations of (i) regular subgraph counts and (ii) the spectral radius for sparse Erd\H{o}s-R\’enyi graphs.

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Date/Time : 09 Sep 2022 16:00
Venue : S17 #04-06 (SR1)
Speaker : Chen Haoyang, National University of Singapore

Abstract:  We construct counterexamples to the local existence of low-regularity solutions to elastic wave equations and to the ideal compressible magnetohydrodynamics (MHD) system in three and two spatial dimensions (3D and 2D). For 3D, inspired by the recent works of Christodoulou, we generalize Lindblad’s classic results on the scalar wave equation by showing that the Cauchy problems for 3D elastic waves and for 3D MHD system are ill-posed in $H^3$ and $H^2$, respectively. Both elastic waves and MHD are physical systems with multiple wave-speeds. We further prove that the ill-posedness is caused by instantaneous shock formation, which is characterized by the vanishing of the inverse foliation density. In particular, when the magnetic field is absent in MHD, we also provide a desired low-regularity ill-posedness result for the 3D compressible Euler equations, and it is sharp with respect to the regularity of the fluid velocity. Our proofs for elastic waves and for MHD are based on a coalition of a carefully designed algebraic approach and a geometric approach. In 2D, we prove the $H^11/4$ and $H^7/4$ ill-posedness for the elastic wave equations and ideal MHD system (also for Euler equations). Compared with the 3D case, the construction of ill-posed profile in 2D is more delicate. This talk is based on joint works with Xinliang An and Silu Yin.

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Date/Time : 09 Sep 2022 14:00
Venue : S17 #05-12 (SR4)
Speaker : Emile Takahiro Okada, National University of Singapore

Abstract: In my talk last year I introduced new methods for computing the wavefront set of depth 0 representations using local wavefront sets. In this series of talks I will begin by briefly recalling the main results from that talk before I go on to outline new results and open questions that have come from these ideas. These will fall into roughly 3 categories: the structure theory of nilpotent orbits, new results on the wavefront set, and finally applications to Arthurs packets.

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Date/Time : 08 Sep 2022 15:00
Venue : S17 #04-06 (SR1)
Speaker : Thibaut Vasseur, University of Lille

Abstract:  A periodic Riesz gas is any microscopic thermodynamic limit of Gibbs particle systems on the torus interacting via the Riesz potential of parameter s. We focus on the non-integrable case d − 1 < s < d, where the point process can be described by canonical DLR equations. Our main result ensures, for any dimension and inverse temperature, the existence of a periodic Riesz gas which is not number-rigid. Recall that a point process is said number rigid if the number of points in a bounded Borel set is a function of the point configuration outside the set. As a consequence, we show that this particular Riesz gas satisfies a grand-canonical DLR equation and allows a renormalization of the energy of a point inside an infinite configuration. Based on a joint work with D. Dereudre.

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Date/Time : 07 Sep 2022 17:00
Venue : S17 #04-05 (SR2)
Speaker : Liao Luke,

Abstract:  We construct a computable coloring function such that any Pi^0_3 set with apartness can not be a witness of Hindman theorem for this coloring. And we can modify the coloring function and drop the condition “with apartness”.

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